TSTP Solution File: ALG133+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ALG133+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 16:36:43 EDT 2023
% Result : Unsatisfiable 25.83s 4.30s
% Output : Proof 136.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ALG133+1 : TPTP v8.1.2. Released v2.7.0.
% 0.07/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 02:55:58 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.62 ________ _____
% 0.21/0.62 ___ __ \_________(_)________________________________
% 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62
% 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.62 (2023-06-19)
% 0.21/0.62
% 0.21/0.62 (c) Philipp Rümmer, 2009-2023
% 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62 Amanda Stjerna.
% 0.21/0.62 Free software under BSD-3-Clause.
% 0.21/0.62
% 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62
% 0.21/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.69/1.43 Prover 4: Preprocessing ...
% 4.69/1.44 Prover 1: Preprocessing ...
% 4.69/1.48 Prover 3: Preprocessing ...
% 4.69/1.48 Prover 2: Preprocessing ...
% 4.69/1.48 Prover 6: Preprocessing ...
% 4.69/1.48 Prover 5: Preprocessing ...
% 4.69/1.48 Prover 0: Preprocessing ...
% 8.10/1.91 Prover 3: Constructing countermodel ...
% 8.10/1.92 Prover 2: Constructing countermodel ...
% 8.10/1.94 Prover 0: Constructing countermodel ...
% 8.10/1.95 Prover 6: Constructing countermodel ...
% 8.10/1.95 Prover 1: Constructing countermodel ...
% 8.88/1.97 Prover 4: Constructing countermodel ...
% 10.62/2.23 Prover 5: Constructing countermodel ...
% 25.83/4.29 Prover 3: proved (3654ms)
% 25.83/4.30
% 25.83/4.30 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.83/4.30
% 25.83/4.30 Prover 2: stopped
% 25.83/4.30 Prover 5: stopped
% 25.83/4.30 Prover 6: stopped
% 25.83/4.31 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 25.83/4.31 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 25.83/4.31 Prover 0: stopped
% 25.83/4.31 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 25.83/4.31 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 25.83/4.31 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 27.77/4.56 Prover 7: Preprocessing ...
% 28.47/4.57 Prover 11: Preprocessing ...
% 28.47/4.57 Prover 10: Preprocessing ...
% 28.47/4.58 Prover 8: Preprocessing ...
% 28.47/4.58 Prover 13: Preprocessing ...
% 29.08/4.69 Prover 8: Constructing countermodel ...
% 30.08/4.79 Prover 10: Constructing countermodel ...
% 30.08/4.79 Prover 13: Constructing countermodel ...
% 30.08/4.80 Prover 11: Constructing countermodel ...
% 30.08/4.81 Prover 7: Constructing countermodel ...
% 67.66/9.65 Prover 13: stopped
% 67.66/9.68 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 68.26/9.78 Prover 16: Preprocessing ...
% 69.45/9.96 Prover 16: Constructing countermodel ...
% 112.58/15.52 Prover 16: stopped
% 112.66/15.54 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 112.66/15.60 Prover 19: Preprocessing ...
% 113.88/15.73 Prover 19: Constructing countermodel ...
% 115.76/15.98 Prover 1: stopped
% 126.83/17.47 Prover 10: Found proof (size 60597)
% 126.83/17.47 Prover 10: proved (13167ms)
% 126.83/17.47 Prover 11: stopped
% 126.83/17.47 Prover 8: stopped
% 126.83/17.47 Prover 7: stopped
% 126.83/17.47 Prover 4: stopped
% 126.83/17.47 Prover 19: stopped
% 126.83/17.47
% 126.83/17.47 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 126.83/17.47
% 128.21/17.80 % SZS output start Proof for theBenchmark
% 128.59/17.88 Assumptions after simplification:
% 128.59/17.88 ---------------------------------
% 128.59/17.88
% 128.59/17.88 (ax1)
% 128.59/17.93 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 128.59/17.93 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 128.59/17.93 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 128.59/17.93 $i] : ? [v14: $i] : ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 &
% 128.59/17.93 op(e3, e1) = v13 & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 &
% 128.59/17.93 op(e2, e1) = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 &
% 128.59/17.93 op(e1, e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 128.59/17.93 op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 128.59/17.93 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 128.59/17.93 $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15 = e2 | v15 = e1 | v15 =
% 128.59/17.93 e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14 = e0) & (v13 = e3 | v13 = e2 |
% 128.59/17.93 v13 = e1 | v13 = e0) & (v12 = e3 | v12 = e2 | v12 = e1 | v12 = e0) & (v11
% 128.59/17.93 = e3 | v11 = e2 | v11 = e1 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 |
% 128.59/17.93 v10 = e0) & (v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 |
% 128.86/17.93 v8 = e1 | v8 = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 |
% 128.86/17.93 v6 = e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) &
% 128.86/17.93 (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 = e1 | v3
% 128.86/17.93 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3 | v1 = e2 | v1
% 128.86/17.93 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0))
% 128.86/17.93
% 128.86/17.93 (ax10)
% 128.86/17.93 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 128.86/17.93 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(e0, e2) = v2 &
% 128.86/17.93 $i(v2)) | ( ~ (v1 = e3) & op(e0, e0) = v1 & $i(v1))))
% 128.86/17.93
% 128.86/17.93 (ax11)
% 128.86/17.94 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 128.86/17.94 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(e0, e1) = v2 &
% 128.86/17.94 $i(v2)) | ( ~ (v1 = e3) & op(e0, e0) = v1 & $i(v1))))
% 128.86/17.94
% 128.86/17.94 (ax12)
% 128.86/17.94 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 128.86/17.94 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(e1, e3) = v2 &
% 128.86/17.94 $i(v2)) | ( ~ (v1 = e0) & op(e1, e1) = v1 & $i(v1))))
% 128.86/17.94
% 128.86/17.94 (ax13)
% 128.86/17.94 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 128.86/17.94 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(e1, e2) = v2 &
% 128.86/17.94 $i(v2)) | ( ~ (v1 = e0) & op(e1, e1) = v1 & $i(v1))))
% 128.86/17.94
% 128.86/17.94 (ax14)
% 128.86/17.94 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 128.86/17.94 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(e1, e3) = v2 &
% 128.86/17.94 $i(v2)) | ( ~ (v1 = e2) & op(e1, e1) = v1 & $i(v1))))
% 128.86/17.94
% 128.86/17.94 (ax15)
% 128.86/17.95 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 128.86/17.95 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(e1, e0) = v2 &
% 128.86/17.95 $i(v2)) | ( ~ (v1 = e2) & op(e1, e1) = v1 & $i(v1))))
% 128.86/17.95
% 128.86/17.95 (ax16)
% 128.86/17.95 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 128.86/17.95 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(e1, e2) = v2 &
% 128.86/17.95 $i(v2)) | ( ~ (v1 = e3) & op(e1, e1) = v1 & $i(v1))))
% 128.86/17.95
% 128.86/17.95 (ax17)
% 128.86/17.95 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 128.86/17.95 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(e1, e0) = v2 &
% 128.86/17.95 $i(v2)) | ( ~ (v1 = e3) & op(e1, e1) = v1 & $i(v1))))
% 128.86/17.95
% 128.86/17.95 (ax18)
% 128.86/17.95 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 128.86/17.95 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(e2, e3) = v2 &
% 128.86/17.95 $i(v2)) | ( ~ (v1 = e0) & op(e2, e2) = v1 & $i(v1))))
% 128.86/17.95
% 128.86/17.95 (ax19)
% 128.86/17.96 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 128.86/17.96 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(e2, e1) = v2 &
% 128.86/17.96 $i(v2)) | ( ~ (v1 = e0) & op(e2, e2) = v1 & $i(v1))))
% 128.86/17.96
% 128.86/17.96 (ax2)
% 128.99/17.99 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 128.99/17.99 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 128.99/17.99 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 128.99/17.99 $i] : ? [v14: $i] : ? [v15: $i] : (((v15 = e3 & op(e3, e3) = e3) | (v14 =
% 128.99/17.99 e3 & op(e3, e2) = e3) | (v11 = e3 & op(e3, e1) = e3) | (v6 = e3 & op(e3,
% 128.99/17.99 e0) = e3)) & ((v15 = e3 & op(e3, e3) = e3) | (v13 = e3 & op(e2, e3) =
% 128.99/17.99 e3) | (v9 = e3 & op(e1, e3) = e3) | (v3 = e3 & op(e0, e3) = e3)) & ((v15
% 128.99/17.99 = e2 & op(e3, e3) = e2) | (v14 = e2 & op(e3, e2) = e2) | (v11 = e2 &
% 128.99/17.99 op(e3, e1) = e2) | (v6 = e2 & op(e3, e0) = e2)) & ((v15 = e2 & op(e3,
% 128.99/17.99 e3) = e2) | (v13 = e2 & op(e2, e3) = e2) | (v9 = e2 & op(e1, e3) = e2)
% 128.99/17.99 | (v3 = e2 & op(e0, e3) = e2)) & ((v15 = e1 & op(e3, e3) = e1) | (v14 = e1
% 128.99/17.99 & op(e3, e2) = e1) | (v11 = e1 & op(e3, e1) = e1) | (v6 = e1 & op(e3,
% 128.99/17.99 e0) = e1)) & ((v15 = e1 & op(e3, e3) = e1) | (v13 = e1 & op(e2, e3) =
% 128.99/17.99 e1) | (v9 = e1 & op(e1, e3) = e1) | (v3 = e1 & op(e0, e3) = e1)) & ((v15
% 128.99/17.99 = e0 & op(e3, e3) = e0) | (v14 = e0 & op(e3, e2) = e0) | (v11 = e0 &
% 128.99/17.99 op(e3, e1) = e0) | (v6 = e0 & op(e3, e0) = e0)) & ((v15 = e0 & op(e3,
% 128.99/17.99 e3) = e0) | (v13 = e0 & op(e2, e3) = e0) | (v9 = e0 & op(e1, e3) = e0)
% 128.99/17.99 | (v3 = e0 & op(e0, e3) = e0)) & ((v14 = e3 & op(e3, e2) = e3) | (v12 = e3
% 128.99/17.99 & op(e2, e2) = e3) | (v8 = e3 & op(e1, e2) = e3) | (v2 = e3 & op(e0, e2)
% 128.99/17.99 = e3)) & ((v14 = e2 & op(e3, e2) = e2) | (v12 = e2 & op(e2, e2) = e2) |
% 128.99/17.99 (v8 = e2 & op(e1, e2) = e2) | (v2 = e2 & op(e0, e2) = e2)) & ((v14 = e1 &
% 128.99/17.99 op(e3, e2) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v8 = e1 & op(e1, e2)
% 128.99/17.99 = e1) | (v2 = e1 & op(e0, e2) = e1)) & ((v14 = e0 & op(e3, e2) = e0) |
% 128.99/17.99 (v12 = e0 & op(e2, e2) = e0) | (v8 = e0 & op(e1, e2) = e0) | (v2 = e0 &
% 128.99/17.99 op(e0, e2) = e0)) & ((v13 = e3 & op(e2, e3) = e3) | (v12 = e3 & op(e2,
% 128.99/17.99 e2) = e3) | (v10 = e3 & op(e2, e1) = e3) | (v5 = e3 & op(e2, e0) =
% 128.99/17.99 e3)) & ((v13 = e2 & op(e2, e3) = e2) | (v12 = e2 & op(e2, e2) = e2) |
% 128.99/17.99 (v10 = e2 & op(e2, e1) = e2) | (v5 = e2 & op(e2, e0) = e2)) & ((v13 = e1 &
% 128.99/17.99 op(e2, e3) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v10 = e1 & op(e2, e1)
% 128.99/17.99 = e1) | (v5 = e1 & op(e2, e0) = e1)) & ((v13 = e0 & op(e2, e3) = e0) |
% 128.99/17.99 (v12 = e0 & op(e2, e2) = e0) | (v10 = e0 & op(e2, e1) = e0) | (v5 = e0 &
% 128.99/17.99 op(e2, e0) = e0)) & ((v11 = e3 & op(e3, e1) = e3) | (v10 = e3 & op(e2,
% 128.99/17.99 e1) = e3) | (v7 = e3 & op(e1, e1) = e3) | (v1 = e3 & op(e0, e1) = e3))
% 128.99/17.99 & ((v11 = e2 & op(e3, e1) = e2) | (v10 = e2 & op(e2, e1) = e2) | (v7 = e2 &
% 128.99/17.99 op(e1, e1) = e2) | (v1 = e2 & op(e0, e1) = e2)) & ((v11 = e1 & op(e3,
% 128.99/17.99 e1) = e1) | (v10 = e1 & op(e2, e1) = e1) | (v7 = e1 & op(e1, e1) = e1)
% 128.99/17.99 | (v1 = e1 & op(e0, e1) = e1)) & ((v11 = e0 & op(e3, e1) = e0) | (v10 = e0
% 128.99/17.99 & op(e2, e1) = e0) | (v7 = e0 & op(e1, e1) = e0) | (v1 = e0 & op(e0, e1)
% 128.99/17.99 = e0)) & ((v9 = e3 & op(e1, e3) = e3) | (v8 = e3 & op(e1, e2) = e3) |
% 128.99/17.99 (v7 = e3 & op(e1, e1) = e3) | (v4 = e3 & op(e1, e0) = e3)) & ((v9 = e2 &
% 128.99/17.99 op(e1, e3) = e2) | (v8 = e2 & op(e1, e2) = e2) | (v7 = e2 & op(e1, e1) =
% 128.99/17.99 e2) | (v4 = e2 & op(e1, e0) = e2)) & ((v9 = e1 & op(e1, e3) = e1) | (v8
% 128.99/17.99 = e1 & op(e1, e2) = e1) | (v7 = e1 & op(e1, e1) = e1) | (v4 = e1 &
% 128.99/17.99 op(e1, e0) = e1)) & ((v9 = e0 & op(e1, e3) = e0) | (v8 = e0 & op(e1, e2)
% 128.99/17.99 = e0) | (v7 = e0 & op(e1, e1) = e0) | (v4 = e0 & op(e1, e0) = e0)) &
% 128.99/17.99 ((v6 = e3 & op(e3, e0) = e3) | (v5 = e3 & op(e2, e0) = e3) | (v4 = e3 &
% 128.99/17.99 op(e1, e0) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v6 = e2 & op(e3, e0)
% 128.99/17.99 = e2) | (v5 = e2 & op(e2, e0) = e2) | (v4 = e2 & op(e1, e0) = e2) | (v0
% 128.99/17.99 = e2 & op(e0, e0) = e2)) & ((v6 = e1 & op(e3, e0) = e1) | (v5 = e1 &
% 128.99/17.99 op(e2, e0) = e1) | (v4 = e1 & op(e1, e0) = e1) | (v0 = e1 & op(e0, e0) =
% 128.99/17.99 e1)) & ((v3 = e3 & op(e0, e3) = e3) | (v2 = e3 & op(e0, e2) = e3) | (v1
% 128.99/17.99 = e3 & op(e0, e1) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v3 = e2 &
% 128.99/17.99 op(e0, e3) = e2) | (v2 = e2 & op(e0, e2) = e2) | (v1 = e2 & op(e0, e1) =
% 128.99/17.99 e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v3 = e1 & op(e0, e3) = e1) | (v2
% 128.99/17.99 = e1 & op(e0, e2) = e1) | (v1 = e1 & op(e0, e1) = e1) | (v0 = e1 &
% 128.99/17.99 op(e0, e0) = e1)) & ((v0 = e0 & op(e0, e0) = e0) | (((v6 = e0 & op(e3,
% 128.99/17.99 e0) = e0) | (v5 = e0 & op(e2, e0) = e0) | (v4 = e0 & op(e1, e0) =
% 128.99/17.99 e0)) & ((v3 = e0 & op(e0, e3) = e0) | (v2 = e0 & op(e0, e2) = e0) |
% 128.99/17.99 (v1 = e0 & op(e0, e1) = e0)))))
% 128.99/17.99
% 128.99/17.99 (ax20)
% 128.99/17.99 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 128.99/17.99 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(e2, e3) = v2 &
% 128.99/17.99 $i(v2)) | ( ~ (v1 = e1) & op(e2, e2) = v1 & $i(v1))))
% 128.99/17.99
% 128.99/17.99 (ax21)
% 128.99/17.99 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 128.99/17.99 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(e2, e0) = v2 &
% 128.99/17.99 $i(v2)) | ( ~ (v1 = e1) & op(e2, e2) = v1 & $i(v1))))
% 128.99/17.99
% 128.99/17.99 (ax22)
% 128.99/17.99 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 128.99/17.99 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(e2, e1) = v2 &
% 128.99/17.99 $i(v2)) | ( ~ (v1 = e3) & op(e2, e2) = v1 & $i(v1))))
% 128.99/17.99
% 128.99/17.99 (ax23)
% 128.99/18.00 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 128.99/18.00 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(e2, e0) = v2 &
% 128.99/18.00 $i(v2)) | ( ~ (v1 = e3) & op(e2, e2) = v1 & $i(v1))))
% 128.99/18.00
% 128.99/18.00 (ax24)
% 128.99/18.00 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 128.99/18.00 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(e3, e2) = v2 &
% 128.99/18.00 $i(v2)) | ( ~ (v1 = e0) & op(e3, e3) = v1 & $i(v1))))
% 128.99/18.00
% 128.99/18.00 (ax25)
% 128.99/18.00 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 128.99/18.00 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(e3, e1) = v2 &
% 128.99/18.00 $i(v2)) | ( ~ (v1 = e0) & op(e3, e3) = v1 & $i(v1))))
% 128.99/18.00
% 128.99/18.00 (ax26)
% 128.99/18.00 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 128.99/18.00 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(e3, e2) = v2 &
% 128.99/18.00 $i(v2)) | ( ~ (v1 = e1) & op(e3, e3) = v1 & $i(v1))))
% 128.99/18.00
% 128.99/18.00 (ax27)
% 128.99/18.00 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 128.99/18.00 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(e3, e0) = v2 &
% 128.99/18.00 $i(v2)) | ( ~ (v1 = e1) & op(e3, e3) = v1 & $i(v1))))
% 128.99/18.00
% 128.99/18.00 (ax28)
% 128.99/18.00 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 128.99/18.00 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(e3, e1) = v2 &
% 128.99/18.00 $i(v2)) | ( ~ (v1 = e2) & op(e3, e3) = v1 & $i(v1))))
% 128.99/18.00
% 128.99/18.00 (ax29)
% 128.99/18.00 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 128.99/18.00 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(e3, e0) = v2 &
% 128.99/18.00 $i(v2)) | ( ~ (v1 = e2) & op(e3, e3) = v1 & $i(v1))))
% 128.99/18.00
% 128.99/18.00 (ax3)
% 128.99/18.01 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 128.99/18.01 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 128.99/18.01 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 128.99/18.01 $i] : ? [v14: $i] : ? [v15: $i] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~
% 128.99/18.01 (v15 = v12) & ~ (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v14 =
% 128.99/18.01 v13) & ~ (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = v2) &
% 128.99/18.01 ~ (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = v1) & ~ (v12 =
% 128.99/18.01 v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 = v9) & ~
% 128.99/18.01 (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v3) & ~ (v10 = v9) & ~ (v10 = v8) &
% 128.99/18.01 ~ (v10 = v6) & ~ (v10 = v2) & ~ (v9 = v8) & ~ (v9 = v5) & ~ (v9 = v1) &
% 128.99/18.01 ~ (v8 = v4) & ~ (v8 = v0) & ~ (v7 = v6) & ~ (v7 = v5) & ~ (v7 = v4) &
% 128.99/18.01 ~ (v7 = v3) & ~ (v6 = v5) & ~ (v6 = v4) & ~ (v6 = v2) & ~ (v5 = v4) & ~
% 128.99/18.01 (v5 = v1) & ~ (v4 = v0) & ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~
% 128.99/18.01 (v2 = v1) & ~ (v2 = v0) & ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) =
% 128.99/18.01 v11 & op(e3, e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) =
% 128.99/18.01 v10 & op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) = v9
% 128.99/18.01 & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0, e2) = v8 &
% 128.99/18.01 op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 128.99/18.01 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 128.99/18.01 $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 128.99/18.01
% 128.99/18.01 (ax4)
% 128.99/18.01 ~ (e3 = e2) & ~ (e3 = e1) & ~ (e3 = e0) & ~ (e2 = e1) & ~ (e2 = e0) & ~
% 128.99/18.01 (e1 = e0) & $i(e3) & $i(e2) & $i(e1) & $i(e0)
% 128.99/18.01
% 128.99/18.01 (ax5)
% 129.33/18.03 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 129.33/18.03 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 129.33/18.03 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 129.33/18.03 $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18:
% 129.33/18.03 $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23:
% 129.33/18.03 $i] : ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? [v28:
% 129.33/18.03 $i] : ? [v29: $i] : ? [v30: $i] : ? [v31: $i] : (((v31 = v30 & op(v30,
% 129.33/18.03 e3) = v30 & op(e3, e3) = v30 & $i(v30)) | (v29 = v28 & op(v28, e2) =
% 129.33/18.03 v28 & op(e2, e3) = v28 & $i(v28)) | (v27 = v26 & op(v26, e1) = v26 &
% 129.33/18.03 op(e1, e3) = v26 & $i(v26)) | (v25 = v24 & op(v24, e0) = v24 & op(e0,
% 129.33/18.03 e3) = v24 & $i(v24))) & ((v30 = e2 & v22 = e3 & ~ (v28 = e3) & ~
% 129.33/18.03 (v20 = e2) & ~ (v12 = e1) & ~ (v4 = e0) & op(e3, e3) = e2 & op(e3, e2)
% 129.33/18.03 = e3 & op(e2, e3) = v28 & op(e2, e2) = v20 & op(e2, e1) = v12 & op(e2,
% 129.33/18.03 e0) = v4 & $i(v28) & $i(v20) & $i(v12) & $i(v4)) | (v30 = e1 & v14 =
% 129.33/18.03 e3 & ~ (v26 = e3) & ~ (v18 = e2) & ~ (v10 = e1) & ~ (v2 = e0) &
% 129.33/18.03 op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = v26 & op(e1, e2) = v18
% 129.33/18.03 & op(e1, e1) = v10 & op(e1, e0) = v2 & $i(v26) & $i(v18) & $i(v10) &
% 129.33/18.03 $i(v2)) | (v30 = e0 & v6 = e3 & ~ (v24 = e3) & ~ (v16 = e2) & ~ (v8 =
% 129.33/18.03 e1) & ~ (v0 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) =
% 129.33/18.03 v24 & op(e0, e2) = v16 & op(e0, e1) = v8 & op(e0, e0) = v0 & $i(v24) &
% 129.33/18.03 $i(v16) & $i(v8) & $i(v0)) | (v28 = e2 & v20 = e3 & ~ (v30 = e3) & ~
% 129.33/18.03 (v22 = e2) & ~ (v14 = e1) & ~ (v6 = e0) & op(e3, e3) = v30 & op(e3,
% 129.33/18.03 e2) = v22 & op(e3, e1) = v14 & op(e3, e0) = v6 & op(e2, e3) = e2 &
% 129.33/18.03 op(e2, e2) = e3 & $i(v30) & $i(v22) & $i(v14) & $i(v6)) | (v26 = e1 &
% 129.33/18.03 v10 = e3 & ~ (v30 = e3) & ~ (v22 = e2) & ~ (v14 = e1) & ~ (v6 = e0)
% 129.33/18.03 & op(e3, e3) = v30 & op(e3, e2) = v22 & op(e3, e1) = v14 & op(e3, e0) =
% 129.33/18.03 v6 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(v30) & $i(v22) & $i(v14) &
% 129.33/18.03 $i(v6)) | (v20 = e1 & v12 = e2 & ~ (v26 = e3) & ~ (v18 = e2) & ~ (v10
% 129.33/18.03 = e1) & ~ (v2 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3)
% 129.33/18.03 = v26 & op(e1, e2) = v18 & op(e1, e1) = v10 & op(e1, e0) = v2 & $i(v26)
% 129.33/18.03 & $i(v18) & $i(v10) & $i(v2)) | (v20 = e0 & v4 = e2 & ~ (v24 = e3) & ~
% 129.33/18.03 (v16 = e2) & ~ (v8 = e1) & ~ (v0 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 129.33/18.03 = e2 & op(e0, e3) = v24 & op(e0, e2) = v16 & op(e0, e1) = v8 & op(e0,
% 129.33/18.03 e0) = v0 & $i(v24) & $i(v16) & $i(v8) & $i(v0)) | (v18 = e1 & v10 = e2
% 129.33/18.03 & ~ (v28 = e3) & ~ (v20 = e2) & ~ (v12 = e1) & ~ (v4 = e0) & op(e2,
% 129.33/18.03 e3) = v28 & op(e2, e2) = v20 & op(e2, e1) = v12 & op(e2, e0) = v4 &
% 129.33/18.03 op(e1, e2) = e1 & op(e1, e1) = e2 & $i(v28) & $i(v20) & $i(v12) &
% 129.33/18.03 $i(v4)) | (op(e0, e0) = v0 & $i(v0) & ((v24 = e0 & v0 = e3 & ~ (v30 =
% 129.33/18.03 e3) & ~ (v22 = e2) & ~ (v14 = e1) & ~ (v6 = e0) & op(e3, e3) =
% 129.33/18.03 v30 & op(e3, e2) = v22 & op(e3, e1) = v14 & op(e3, e0) = v6 & op(e0,
% 129.33/18.03 e3) = e0 & $i(v30) & $i(v22) & $i(v14) & $i(v6)) | (v16 = e0 & v0
% 129.33/18.03 = e2 & ~ (v28 = e3) & ~ (v20 = e2) & ~ (v12 = e1) & ~ (v4 = e0)
% 129.33/18.03 & op(e2, e3) = v28 & op(e2, e2) = v20 & op(e2, e1) = v12 & op(e2,
% 129.33/18.03 e0) = v4 & op(e0, e2) = e0 & $i(v28) & $i(v20) & $i(v12) & $i(v4))
% 129.33/18.03 | (v10 = e0 & v2 = e1 & ~ (v24 = e3) & ~ (v16 = e2) & ~ (v8 = e1) &
% 129.33/18.03 ~ (v0 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = v24
% 129.33/18.03 & op(e0, e2) = v16 & op(e0, e1) = v8 & $i(v24) & $i(v16) & $i(v8)) |
% 129.33/18.03 (v8 = e0 & v0 = e1 & ~ (v26 = e3) & ~ (v18 = e2) & ~ (v10 = e1) &
% 129.33/18.03 ~ (v2 = e0) & op(e1, e3) = v26 & op(e1, e2) = v18 & op(e1, e1) = v10
% 129.33/18.03 & op(e1, e0) = v2 & op(e0, e1) = e0 & $i(v26) & $i(v18) & $i(v10) &
% 129.33/18.03 $i(v2))))) & ((v23 = v22 & op(v22, e3) = v22 & op(e3, e2) = v22 &
% 129.33/18.03 $i(v22)) | (v21 = v20 & op(v20, e2) = v20 & op(e2, e2) = v20 & $i(v20))
% 129.33/18.03 | (v19 = v18 & op(v18, e1) = v18 & op(e1, e2) = v18 & $i(v18)) | (v17 =
% 129.33/18.03 v16 & op(v16, e0) = v16 & op(e0, e2) = v16 & $i(v16))) & ((v15 = v14 &
% 129.33/18.03 op(v14, e3) = v14 & op(e3, e1) = v14 & $i(v14)) | (v13 = v12 & op(v12,
% 129.33/18.03 e2) = v12 & op(e2, e1) = v12 & $i(v12)) | (v11 = v10 & op(v10, e1) =
% 129.33/18.03 v10 & op(e1, e1) = v10 & $i(v10)) | (v9 = v8 & op(v8, e0) = v8 & op(e0,
% 129.33/18.03 e1) = v8 & $i(v8))) & ((v7 = v6 & op(v6, e3) = v6 & op(e3, e0) = v6 &
% 129.33/18.03 $i(v6)) | (v5 = v4 & op(v4, e2) = v4 & op(e2, e0) = v4 & $i(v4)) | (v3 =
% 129.33/18.03 v2 & op(v2, e1) = v2 & op(e1, e0) = v2 & $i(v2)) | (v1 = v0 & op(v0, e0)
% 129.33/18.03 = v0 & op(e0, e0) = v0 & $i(v0))))
% 129.33/18.03
% 129.33/18.03 (ax6)
% 129.33/18.04 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 129.33/18.04 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(e0, e3) = v2 &
% 129.33/18.04 $i(v2)) | ( ~ (v1 = e1) & op(e0, e0) = v1 & $i(v1))))
% 129.33/18.04
% 129.33/18.04 (ax7)
% 129.33/18.04 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 129.33/18.04 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(e0, e2) = v2 &
% 129.33/18.04 $i(v2)) | ( ~ (v1 = e1) & op(e0, e0) = v1 & $i(v1))))
% 129.33/18.04
% 129.33/18.04 (ax8)
% 129.33/18.04 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 129.33/18.04 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(e0, e3) = v2 &
% 129.33/18.04 $i(v2)) | ( ~ (v1 = e2) & op(e0, e0) = v1 & $i(v1))))
% 129.33/18.04
% 129.33/18.04 (ax9)
% 129.33/18.04 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 129.33/18.04 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(e0, e1) = v2 &
% 129.33/18.04 $i(v2)) | ( ~ (v1 = e2) & op(e0, e0) = v1 & $i(v1))))
% 129.33/18.04
% 129.33/18.04 (function-axioms)
% 129.33/18.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (op(v3,
% 129.33/18.04 v2) = v1) | ~ (op(v3, v2) = v0))
% 129.33/18.04
% 129.33/18.04 Those formulas are unsatisfiable:
% 129.33/18.04 ---------------------------------
% 129.33/18.04
% 129.33/18.04 Begin of proof
% 129.33/18.04 |
% 129.33/18.04 | ALPHA: (ax1) implies:
% 129.33/18.05 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 129.33/18.05 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 129.33/18.05 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 129.33/18.05 | ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & op(e3, e1) = v13
% 129.33/18.05 | & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 & op(e2, e1)
% 129.33/18.05 | = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 & op(e1,
% 129.33/18.05 | e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 129.33/18.05 | op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) &
% 129.33/18.05 | $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 129.33/18.05 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15
% 129.33/18.05 | = e2 | v15 = e1 | v15 = e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14
% 129.33/18.05 | = e0) & (v13 = e3 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 = e3 |
% 129.33/18.05 | v12 = e2 | v12 = e1 | v12 = e0) & (v11 = e3 | v11 = e2 | v11 = e1 |
% 129.33/18.05 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 | v10 = e0) & (v9 = e3
% 129.33/18.05 | | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 | v8 = e1 | v8
% 129.33/18.05 | = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 | v6 =
% 129.33/18.05 | e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) &
% 129.33/18.05 | (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 =
% 129.33/18.05 | e1 | v3 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3
% 129.33/18.05 | | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0
% 129.33/18.05 | = e0))
% 129.33/18.05 |
% 129.33/18.05 | ALPHA: (ax2) implies:
% 129.52/18.07 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 129.52/18.07 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 129.52/18.07 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 129.52/18.07 | ? [v15: $i] : (((v15 = e3 & op(e3, e3) = e3) | (v14 = e3 & op(e3, e2)
% 129.52/18.07 | = e3) | (v11 = e3 & op(e3, e1) = e3) | (v6 = e3 & op(e3, e0) =
% 129.52/18.07 | e3)) & ((v15 = e3 & op(e3, e3) = e3) | (v13 = e3 & op(e2, e3) =
% 129.52/18.07 | e3) | (v9 = e3 & op(e1, e3) = e3) | (v3 = e3 & op(e0, e3) = e3))
% 129.52/18.07 | & ((v15 = e2 & op(e3, e3) = e2) | (v14 = e2 & op(e3, e2) = e2) | (v11
% 129.52/18.07 | = e2 & op(e3, e1) = e2) | (v6 = e2 & op(e3, e0) = e2)) & ((v15 =
% 129.52/18.07 | e2 & op(e3, e3) = e2) | (v13 = e2 & op(e2, e3) = e2) | (v9 = e2 &
% 129.52/18.07 | op(e1, e3) = e2) | (v3 = e2 & op(e0, e3) = e2)) & ((v15 = e1 &
% 129.52/18.07 | op(e3, e3) = e1) | (v14 = e1 & op(e3, e2) = e1) | (v11 = e1 &
% 129.52/18.07 | op(e3, e1) = e1) | (v6 = e1 & op(e3, e0) = e1)) & ((v15 = e1 &
% 129.52/18.07 | op(e3, e3) = e1) | (v13 = e1 & op(e2, e3) = e1) | (v9 = e1 &
% 129.52/18.07 | op(e1, e3) = e1) | (v3 = e1 & op(e0, e3) = e1)) & ((v15 = e0 &
% 129.52/18.07 | op(e3, e3) = e0) | (v14 = e0 & op(e3, e2) = e0) | (v11 = e0 &
% 129.52/18.07 | op(e3, e1) = e0) | (v6 = e0 & op(e3, e0) = e0)) & ((v15 = e0 &
% 129.52/18.07 | op(e3, e3) = e0) | (v13 = e0 & op(e2, e3) = e0) | (v9 = e0 &
% 129.52/18.07 | op(e1, e3) = e0) | (v3 = e0 & op(e0, e3) = e0)) & ((v14 = e3 &
% 129.52/18.07 | op(e3, e2) = e3) | (v12 = e3 & op(e2, e2) = e3) | (v8 = e3 &
% 129.52/18.07 | op(e1, e2) = e3) | (v2 = e3 & op(e0, e2) = e3)) & ((v14 = e2 &
% 129.52/18.07 | op(e3, e2) = e2) | (v12 = e2 & op(e2, e2) = e2) | (v8 = e2 &
% 129.52/18.07 | op(e1, e2) = e2) | (v2 = e2 & op(e0, e2) = e2)) & ((v14 = e1 &
% 129.52/18.07 | op(e3, e2) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v8 = e1 &
% 129.52/18.07 | op(e1, e2) = e1) | (v2 = e1 & op(e0, e2) = e1)) & ((v14 = e0 &
% 129.52/18.07 | op(e3, e2) = e0) | (v12 = e0 & op(e2, e2) = e0) | (v8 = e0 &
% 129.52/18.07 | op(e1, e2) = e0) | (v2 = e0 & op(e0, e2) = e0)) & ((v13 = e3 &
% 129.52/18.07 | op(e2, e3) = e3) | (v12 = e3 & op(e2, e2) = e3) | (v10 = e3 &
% 129.52/18.07 | op(e2, e1) = e3) | (v5 = e3 & op(e2, e0) = e3)) & ((v13 = e2 &
% 129.52/18.07 | op(e2, e3) = e2) | (v12 = e2 & op(e2, e2) = e2) | (v10 = e2 &
% 129.52/18.07 | op(e2, e1) = e2) | (v5 = e2 & op(e2, e0) = e2)) & ((v13 = e1 &
% 129.52/18.07 | op(e2, e3) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v10 = e1 &
% 129.52/18.07 | op(e2, e1) = e1) | (v5 = e1 & op(e2, e0) = e1)) & ((v13 = e0 &
% 129.52/18.07 | op(e2, e3) = e0) | (v12 = e0 & op(e2, e2) = e0) | (v10 = e0 &
% 129.52/18.07 | op(e2, e1) = e0) | (v5 = e0 & op(e2, e0) = e0)) & ((v11 = e3 &
% 129.52/18.07 | op(e3, e1) = e3) | (v10 = e3 & op(e2, e1) = e3) | (v7 = e3 &
% 129.52/18.07 | op(e1, e1) = e3) | (v1 = e3 & op(e0, e1) = e3)) & ((v11 = e2 &
% 129.52/18.07 | op(e3, e1) = e2) | (v10 = e2 & op(e2, e1) = e2) | (v7 = e2 &
% 129.52/18.07 | op(e1, e1) = e2) | (v1 = e2 & op(e0, e1) = e2)) & ((v11 = e1 &
% 129.52/18.07 | op(e3, e1) = e1) | (v10 = e1 & op(e2, e1) = e1) | (v7 = e1 &
% 129.52/18.07 | op(e1, e1) = e1) | (v1 = e1 & op(e0, e1) = e1)) & ((v11 = e0 &
% 129.52/18.07 | op(e3, e1) = e0) | (v10 = e0 & op(e2, e1) = e0) | (v7 = e0 &
% 129.52/18.07 | op(e1, e1) = e0) | (v1 = e0 & op(e0, e1) = e0)) & ((v9 = e3 &
% 129.52/18.07 | op(e1, e3) = e3) | (v8 = e3 & op(e1, e2) = e3) | (v7 = e3 &
% 129.52/18.07 | op(e1, e1) = e3) | (v4 = e3 & op(e1, e0) = e3)) & ((v9 = e2 &
% 129.52/18.07 | op(e1, e3) = e2) | (v8 = e2 & op(e1, e2) = e2) | (v7 = e2 &
% 129.52/18.07 | op(e1, e1) = e2) | (v4 = e2 & op(e1, e0) = e2)) & ((v9 = e1 &
% 129.52/18.07 | op(e1, e3) = e1) | (v8 = e1 & op(e1, e2) = e1) | (v7 = e1 &
% 129.52/18.07 | op(e1, e1) = e1) | (v4 = e1 & op(e1, e0) = e1)) & ((v9 = e0 &
% 129.52/18.07 | op(e1, e3) = e0) | (v8 = e0 & op(e1, e2) = e0) | (v7 = e0 &
% 129.52/18.07 | op(e1, e1) = e0) | (v4 = e0 & op(e1, e0) = e0)) & ((v6 = e3 &
% 129.52/18.07 | op(e3, e0) = e3) | (v5 = e3 & op(e2, e0) = e3) | (v4 = e3 &
% 129.52/18.07 | op(e1, e0) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v6 = e2 &
% 129.52/18.07 | op(e3, e0) = e2) | (v5 = e2 & op(e2, e0) = e2) | (v4 = e2 &
% 129.52/18.07 | op(e1, e0) = e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v6 = e1 &
% 129.52/18.07 | op(e3, e0) = e1) | (v5 = e1 & op(e2, e0) = e1) | (v4 = e1 &
% 129.52/18.07 | op(e1, e0) = e1) | (v0 = e1 & op(e0, e0) = e1)) & ((v3 = e3 &
% 129.52/18.07 | op(e0, e3) = e3) | (v2 = e3 & op(e0, e2) = e3) | (v1 = e3 &
% 129.52/18.07 | op(e0, e1) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v3 = e2 &
% 129.52/18.07 | op(e0, e3) = e2) | (v2 = e2 & op(e0, e2) = e2) | (v1 = e2 &
% 129.52/18.07 | op(e0, e1) = e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v3 = e1 &
% 129.52/18.07 | op(e0, e3) = e1) | (v2 = e1 & op(e0, e2) = e1) | (v1 = e1 &
% 129.52/18.07 | op(e0, e1) = e1) | (v0 = e1 & op(e0, e0) = e1)) & ((v0 = e0 &
% 129.52/18.07 | op(e0, e0) = e0) | (((v6 = e0 & op(e3, e0) = e0) | (v5 = e0 &
% 129.52/18.07 | op(e2, e0) = e0) | (v4 = e0 & op(e1, e0) = e0)) & ((v3 = e0 &
% 129.52/18.07 | op(e0, e3) = e0) | (v2 = e0 & op(e0, e2) = e0) | (v1 = e0 &
% 129.52/18.07 | op(e0, e1) = e0)))))
% 129.52/18.07 |
% 129.52/18.07 | ALPHA: (ax3) implies:
% 129.52/18.08 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 129.52/18.08 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 129.52/18.08 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 129.52/18.08 | ? [v15: $i] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~ (v15 = v12) & ~
% 129.52/18.08 | (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v14 = v13) & ~
% 129.52/18.08 | (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = v2) & ~
% 129.52/18.08 | (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = v1) & ~ (v12
% 129.52/18.08 | = v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 =
% 129.52/18.08 | v9) & ~ (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v3) & ~ (v10 = v9)
% 129.52/18.08 | & ~ (v10 = v8) & ~ (v10 = v6) & ~ (v10 = v2) & ~ (v9 = v8) & ~
% 129.52/18.08 | (v9 = v5) & ~ (v9 = v1) & ~ (v8 = v4) & ~ (v8 = v0) & ~ (v7 = v6)
% 129.52/18.08 | & ~ (v7 = v5) & ~ (v7 = v4) & ~ (v7 = v3) & ~ (v6 = v5) & ~ (v6
% 129.52/18.08 | = v4) & ~ (v6 = v2) & ~ (v5 = v4) & ~ (v5 = v1) & ~ (v4 = v0) &
% 129.52/18.08 | ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) & ~ (v2 =
% 129.52/18.08 | v0) & ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) = v11 & op(e3,
% 129.52/18.08 | e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) = v10 &
% 129.52/18.08 | op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) =
% 129.52/18.08 | v9 & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0,
% 129.52/18.08 | e2) = v8 & op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) &
% 129.52/18.08 | $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) &
% 129.52/18.08 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 129.52/18.08 |
% 129.52/18.08 | ALPHA: (ax4) implies:
% 129.52/18.08 | (4) ~ (e1 = e0)
% 129.52/18.08 | (5) ~ (e2 = e0)
% 129.52/18.08 | (6) ~ (e2 = e1)
% 129.52/18.08 | (7) ~ (e3 = e0)
% 129.52/18.08 | (8) ~ (e3 = e1)
% 129.52/18.08 | (9) ~ (e3 = e2)
% 129.52/18.08 |
% 129.52/18.08 | ALPHA: (ax5) implies:
% 129.52/18.09 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 129.52/18.09 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 129.52/18.09 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14:
% 129.52/18.09 | $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ?
% 129.52/18.09 | [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i]
% 129.52/18.09 | : ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? [v28:
% 129.52/18.09 | $i] : ? [v29: $i] : ? [v30: $i] : ? [v31: $i] : (((v31 = v30 &
% 129.52/18.09 | op(v30, e3) = v30 & op(e3, e3) = v30 & $i(v30)) | (v29 = v28 &
% 129.52/18.09 | op(v28, e2) = v28 & op(e2, e3) = v28 & $i(v28)) | (v27 = v26 &
% 129.52/18.09 | op(v26, e1) = v26 & op(e1, e3) = v26 & $i(v26)) | (v25 = v24 &
% 129.52/18.09 | op(v24, e0) = v24 & op(e0, e3) = v24 & $i(v24))) & ((v30 = e2 &
% 129.52/18.09 | v22 = e3 & ~ (v28 = e3) & ~ (v20 = e2) & ~ (v12 = e1) & ~
% 129.52/18.09 | (v4 = e0) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = v28
% 129.52/18.09 | & op(e2, e2) = v20 & op(e2, e1) = v12 & op(e2, e0) = v4 &
% 129.52/18.09 | $i(v28) & $i(v20) & $i(v12) & $i(v4)) | (v30 = e1 & v14 = e3 &
% 129.52/18.09 | ~ (v26 = e3) & ~ (v18 = e2) & ~ (v10 = e1) & ~ (v2 = e0) &
% 129.52/18.09 | op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = v26 & op(e1,
% 129.52/18.09 | e2) = v18 & op(e1, e1) = v10 & op(e1, e0) = v2 & $i(v26) &
% 129.52/18.09 | $i(v18) & $i(v10) & $i(v2)) | (v30 = e0 & v6 = e3 & ~ (v24 =
% 129.52/18.09 | e3) & ~ (v16 = e2) & ~ (v8 = e1) & ~ (v0 = e0) & op(e3, e3)
% 129.52/18.09 | = e0 & op(e3, e0) = e3 & op(e0, e3) = v24 & op(e0, e2) = v16 &
% 129.52/18.09 | op(e0, e1) = v8 & op(e0, e0) = v0 & $i(v24) & $i(v16) & $i(v8) &
% 129.52/18.09 | $i(v0)) | (v28 = e2 & v20 = e3 & ~ (v30 = e3) & ~ (v22 = e2) &
% 129.52/18.09 | ~ (v14 = e1) & ~ (v6 = e0) & op(e3, e3) = v30 & op(e3, e2) =
% 129.52/18.09 | v22 & op(e3, e1) = v14 & op(e3, e0) = v6 & op(e2, e3) = e2 &
% 129.52/18.09 | op(e2, e2) = e3 & $i(v30) & $i(v22) & $i(v14) & $i(v6)) | (v26 =
% 129.52/18.09 | e1 & v10 = e3 & ~ (v30 = e3) & ~ (v22 = e2) & ~ (v14 = e1) &
% 129.52/18.09 | ~ (v6 = e0) & op(e3, e3) = v30 & op(e3, e2) = v22 & op(e3, e1) =
% 129.52/18.09 | v14 & op(e3, e0) = v6 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 129.52/18.09 | $i(v30) & $i(v22) & $i(v14) & $i(v6)) | (v20 = e1 & v12 = e2 &
% 129.52/18.09 | ~ (v26 = e3) & ~ (v18 = e2) & ~ (v10 = e1) & ~ (v2 = e0) &
% 129.52/18.09 | op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = v26 & op(e1,
% 129.52/18.09 | e2) = v18 & op(e1, e1) = v10 & op(e1, e0) = v2 & $i(v26) &
% 129.52/18.09 | $i(v18) & $i(v10) & $i(v2)) | (v20 = e0 & v4 = e2 & ~ (v24 =
% 129.52/18.09 | e3) & ~ (v16 = e2) & ~ (v8 = e1) & ~ (v0 = e0) & op(e2, e2)
% 129.52/18.09 | = e0 & op(e2, e0) = e2 & op(e0, e3) = v24 & op(e0, e2) = v16 &
% 129.52/18.09 | op(e0, e1) = v8 & op(e0, e0) = v0 & $i(v24) & $i(v16) & $i(v8) &
% 129.52/18.09 | $i(v0)) | (v18 = e1 & v10 = e2 & ~ (v28 = e3) & ~ (v20 = e2) &
% 129.52/18.09 | ~ (v12 = e1) & ~ (v4 = e0) & op(e2, e3) = v28 & op(e2, e2) =
% 129.52/18.09 | v20 & op(e2, e1) = v12 & op(e2, e0) = v4 & op(e1, e2) = e1 &
% 129.52/18.09 | op(e1, e1) = e2 & $i(v28) & $i(v20) & $i(v12) & $i(v4)) |
% 129.52/18.09 | (op(e0, e0) = v0 & $i(v0) & ((v24 = e0 & v0 = e3 & ~ (v30 = e3) &
% 129.52/18.09 | ~ (v22 = e2) & ~ (v14 = e1) & ~ (v6 = e0) & op(e3, e3) =
% 129.52/18.09 | v30 & op(e3, e2) = v22 & op(e3, e1) = v14 & op(e3, e0) = v6
% 129.52/18.09 | & op(e0, e3) = e0 & $i(v30) & $i(v22) & $i(v14) & $i(v6)) |
% 129.52/18.09 | (v16 = e0 & v0 = e2 & ~ (v28 = e3) & ~ (v20 = e2) & ~ (v12
% 129.52/18.09 | = e1) & ~ (v4 = e0) & op(e2, e3) = v28 & op(e2, e2) = v20
% 129.52/18.09 | & op(e2, e1) = v12 & op(e2, e0) = v4 & op(e0, e2) = e0 &
% 129.52/18.09 | $i(v28) & $i(v20) & $i(v12) & $i(v4)) | (v10 = e0 & v2 = e1
% 129.52/18.09 | & ~ (v24 = e3) & ~ (v16 = e2) & ~ (v8 = e1) & ~ (v0 =
% 129.52/18.09 | e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = v24
% 129.52/18.09 | & op(e0, e2) = v16 & op(e0, e1) = v8 & $i(v24) & $i(v16) &
% 129.52/18.09 | $i(v8)) | (v8 = e0 & v0 = e1 & ~ (v26 = e3) & ~ (v18 = e2)
% 129.52/18.09 | & ~ (v10 = e1) & ~ (v2 = e0) & op(e1, e3) = v26 & op(e1,
% 129.52/18.09 | e2) = v18 & op(e1, e1) = v10 & op(e1, e0) = v2 & op(e0,
% 129.52/18.09 | e1) = e0 & $i(v26) & $i(v18) & $i(v10) & $i(v2))))) &
% 129.52/18.09 | ((v23 = v22 & op(v22, e3) = v22 & op(e3, e2) = v22 & $i(v22)) | (v21
% 129.52/18.09 | = v20 & op(v20, e2) = v20 & op(e2, e2) = v20 & $i(v20)) | (v19 =
% 129.52/18.09 | v18 & op(v18, e1) = v18 & op(e1, e2) = v18 & $i(v18)) | (v17 =
% 129.52/18.09 | v16 & op(v16, e0) = v16 & op(e0, e2) = v16 & $i(v16))) & ((v15 =
% 129.52/18.09 | v14 & op(v14, e3) = v14 & op(e3, e1) = v14 & $i(v14)) | (v13 =
% 129.52/18.09 | v12 & op(v12, e2) = v12 & op(e2, e1) = v12 & $i(v12)) | (v11 =
% 129.52/18.09 | v10 & op(v10, e1) = v10 & op(e1, e1) = v10 & $i(v10)) | (v9 = v8
% 129.52/18.09 | & op(v8, e0) = v8 & op(e0, e1) = v8 & $i(v8))) & ((v7 = v6 &
% 129.52/18.09 | op(v6, e3) = v6 & op(e3, e0) = v6 & $i(v6)) | (v5 = v4 & op(v4,
% 129.52/18.09 | e2) = v4 & op(e2, e0) = v4 & $i(v4)) | (v3 = v2 & op(v2, e1) =
% 129.52/18.09 | v2 & op(e1, e0) = v2 & $i(v2)) | (v1 = v0 & op(v0, e0) = v0 &
% 129.52/18.09 | op(e0, e0) = v0 & $i(v0))))
% 129.52/18.09 |
% 129.52/18.09 | ALPHA: (ax6) implies:
% 129.52/18.09 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 129.52/18.09 | ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(e0, e3) = v2 & $i(v2)) | ( ~ (v1
% 129.52/18.09 | = e1) & op(e0, e0) = v1 & $i(v1))))
% 129.52/18.09 |
% 129.52/18.09 | ALPHA: (ax7) implies:
% 129.52/18.09 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 129.52/18.09 | ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(e0, e2) = v2 & $i(v2)) | ( ~ (v1
% 129.52/18.09 | = e1) & op(e0, e0) = v1 & $i(v1))))
% 129.52/18.09 |
% 129.52/18.09 | ALPHA: (ax8) implies:
% 129.52/18.10 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 129.52/18.10 | ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(e0, e3) = v2 & $i(v2)) | ( ~ (v1
% 129.52/18.10 | = e2) & op(e0, e0) = v1 & $i(v1))))
% 129.52/18.10 |
% 129.52/18.10 | ALPHA: (ax9) implies:
% 129.52/18.10 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 129.52/18.10 | ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(e0, e1) = v2 & $i(v2)) | ( ~ (v1
% 129.52/18.10 | = e2) & op(e0, e0) = v1 & $i(v1))))
% 129.52/18.10 |
% 129.52/18.10 | ALPHA: (ax10) implies:
% 129.52/18.10 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 129.52/18.10 | ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(e0, e2) = v2 & $i(v2)) | ( ~ (v1
% 129.52/18.10 | = e3) & op(e0, e0) = v1 & $i(v1))))
% 129.52/18.10 |
% 129.52/18.10 | ALPHA: (ax11) implies:
% 129.52/18.10 | (16) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 129.52/18.10 | ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(e0, e1) = v2 & $i(v2)) | ( ~ (v1
% 129.52/18.10 | = e3) & op(e0, e0) = v1 & $i(v1))))
% 129.52/18.10 |
% 129.52/18.10 | ALPHA: (ax12) implies:
% 129.52/18.10 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 129.52/18.10 | ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(e1, e3) = v2 & $i(v2)) | ( ~ (v1
% 129.52/18.10 | = e0) & op(e1, e1) = v1 & $i(v1))))
% 129.52/18.10 |
% 129.52/18.10 | ALPHA: (ax13) implies:
% 129.52/18.10 | (18) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 129.52/18.10 | ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(e1, e2) = v2 & $i(v2)) | ( ~ (v1
% 129.52/18.10 | = e0) & op(e1, e1) = v1 & $i(v1))))
% 129.52/18.10 |
% 129.52/18.10 | ALPHA: (ax14) implies:
% 129.52/18.10 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 129.52/18.10 | ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(e1, e3) = v2 & $i(v2)) | ( ~ (v1
% 129.52/18.10 | = e2) & op(e1, e1) = v1 & $i(v1))))
% 129.52/18.10 |
% 129.52/18.10 | ALPHA: (ax15) implies:
% 129.52/18.10 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 129.52/18.10 | ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(e1, e0) = v2 & $i(v2)) | ( ~ (v1
% 129.52/18.10 | = e2) & op(e1, e1) = v1 & $i(v1))))
% 129.52/18.10 |
% 129.52/18.10 | ALPHA: (ax16) implies:
% 129.52/18.10 | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 129.52/18.10 | ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(e1, e2) = v2 & $i(v2)) | ( ~ (v1
% 129.52/18.10 | = e3) & op(e1, e1) = v1 & $i(v1))))
% 129.52/18.10 |
% 129.52/18.10 | ALPHA: (ax17) implies:
% 129.52/18.10 | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 129.52/18.10 | ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(e1, e0) = v2 & $i(v2)) | ( ~ (v1
% 129.52/18.10 | = e3) & op(e1, e1) = v1 & $i(v1))))
% 129.52/18.10 |
% 129.52/18.10 | ALPHA: (ax18) implies:
% 129.52/18.10 | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 129.52/18.10 | ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(e2, e3) = v2 & $i(v2)) | ( ~ (v1
% 129.52/18.10 | = e0) & op(e2, e2) = v1 & $i(v1))))
% 129.52/18.10 |
% 129.52/18.10 | ALPHA: (ax19) implies:
% 129.52/18.10 | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 129.52/18.10 | ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(e2, e1) = v2 & $i(v2)) | ( ~ (v1
% 129.52/18.10 | = e0) & op(e2, e2) = v1 & $i(v1))))
% 129.52/18.10 |
% 129.52/18.10 | ALPHA: (ax20) implies:
% 129.52/18.10 | (25) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 129.52/18.10 | ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(e2, e3) = v2 & $i(v2)) | ( ~ (v1
% 129.52/18.11 | = e1) & op(e2, e2) = v1 & $i(v1))))
% 129.52/18.11 |
% 129.52/18.11 | ALPHA: (ax21) implies:
% 129.52/18.11 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 129.52/18.11 | ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(e2, e0) = v2 & $i(v2)) | ( ~ (v1
% 129.52/18.11 | = e1) & op(e2, e2) = v1 & $i(v1))))
% 129.52/18.11 |
% 129.52/18.11 | ALPHA: (ax22) implies:
% 129.52/18.11 | (27) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 129.52/18.11 | ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(e2, e1) = v2 & $i(v2)) | ( ~ (v1
% 129.52/18.11 | = e3) & op(e2, e2) = v1 & $i(v1))))
% 129.52/18.11 |
% 129.52/18.11 | ALPHA: (ax23) implies:
% 129.52/18.11 | (28) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 129.52/18.11 | ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(e2, e0) = v2 & $i(v2)) | ( ~ (v1
% 129.52/18.11 | = e3) & op(e2, e2) = v1 & $i(v1))))
% 129.52/18.11 |
% 129.52/18.11 | ALPHA: (ax24) implies:
% 129.52/18.11 | (29) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 129.52/18.11 | ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(e3, e2) = v2 & $i(v2)) | ( ~ (v1
% 129.52/18.11 | = e0) & op(e3, e3) = v1 & $i(v1))))
% 129.52/18.11 |
% 129.52/18.11 | ALPHA: (ax25) implies:
% 129.52/18.11 | (30) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 129.52/18.11 | ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(e3, e1) = v2 & $i(v2)) | ( ~ (v1
% 129.52/18.11 | = e0) & op(e3, e3) = v1 & $i(v1))))
% 129.52/18.11 |
% 129.52/18.11 | ALPHA: (ax26) implies:
% 129.52/18.11 | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 129.52/18.11 | ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(e3, e2) = v2 & $i(v2)) | ( ~ (v1
% 129.52/18.11 | = e1) & op(e3, e3) = v1 & $i(v1))))
% 129.52/18.11 |
% 129.52/18.11 | ALPHA: (ax27) implies:
% 129.52/18.11 | (32) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 129.52/18.11 | ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(e3, e0) = v2 & $i(v2)) | ( ~ (v1
% 129.52/18.11 | = e1) & op(e3, e3) = v1 & $i(v1))))
% 129.52/18.11 |
% 129.52/18.11 | ALPHA: (ax28) implies:
% 129.52/18.11 | (33) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 129.52/18.11 | ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(e3, e1) = v2 & $i(v2)) | ( ~ (v1
% 129.52/18.11 | = e2) & op(e3, e3) = v1 & $i(v1))))
% 129.52/18.11 |
% 129.52/18.11 | ALPHA: (ax29) implies:
% 129.52/18.11 | (34) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 129.52/18.11 | ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(e3, e0) = v2 & $i(v2)) | ( ~ (v1
% 129.52/18.11 | = e2) & op(e3, e3) = v1 & $i(v1))))
% 129.52/18.11 |
% 129.52/18.11 | DELTA: instantiating (20) with fresh symbols all_4_0, all_4_1, all_4_2 gives:
% 129.52/18.11 | (35) op(e0, e0) = all_4_2 & $i(all_4_2) & ( ~ (all_4_2 = e1) | ( ~ (all_4_0
% 129.52/18.11 | = e3) & op(e1, e0) = all_4_0 & $i(all_4_0)) | ( ~ (all_4_1 = e2)
% 129.52/18.11 | & op(e1, e1) = all_4_1 & $i(all_4_1)))
% 129.52/18.11 |
% 129.52/18.11 | ALPHA: (35) implies:
% 129.52/18.11 | (36) op(e0, e0) = all_4_2
% 129.52/18.11 | (37) ~ (all_4_2 = e1) | ( ~ (all_4_0 = e3) & op(e1, e0) = all_4_0 &
% 129.52/18.11 | $i(all_4_0)) | ( ~ (all_4_1 = e2) & op(e1, e1) = all_4_1 &
% 129.52/18.11 | $i(all_4_1))
% 129.52/18.11 |
% 129.52/18.11 | DELTA: instantiating (27) with fresh symbols all_6_0, all_6_1, all_6_2 gives:
% 129.52/18.11 | (38) op(e1, e1) = all_6_2 & $i(all_6_2) & ( ~ (all_6_2 = e2) | ( ~ (all_6_0
% 129.52/18.11 | = e0) & op(e2, e1) = all_6_0 & $i(all_6_0)) | ( ~ (all_6_1 = e3)
% 129.52/18.11 | & op(e2, e2) = all_6_1 & $i(all_6_1)))
% 129.52/18.11 |
% 129.52/18.11 | ALPHA: (38) implies:
% 129.52/18.11 | (39) op(e1, e1) = all_6_2
% 129.52/18.11 | (40) ~ (all_6_2 = e2) | ( ~ (all_6_0 = e0) & op(e2, e1) = all_6_0 &
% 129.52/18.11 | $i(all_6_0)) | ( ~ (all_6_1 = e3) & op(e2, e2) = all_6_1 &
% 129.52/18.11 | $i(all_6_1))
% 129.52/18.11 |
% 129.52/18.11 | DELTA: instantiating (21) with fresh symbols all_8_0, all_8_1, all_8_2 gives:
% 129.52/18.12 | (41) op(e2, e2) = all_8_2 & $i(all_8_2) & ( ~ (all_8_2 = e1) | ( ~ (all_8_0
% 129.52/18.12 | = e0) & op(e1, e2) = all_8_0 & $i(all_8_0)) | ( ~ (all_8_1 = e3)
% 129.52/18.12 | & op(e1, e1) = all_8_1 & $i(all_8_1)))
% 129.52/18.12 |
% 129.52/18.12 | ALPHA: (41) implies:
% 129.52/18.12 | (42) op(e2, e2) = all_8_2
% 129.52/18.12 | (43) ~ (all_8_2 = e1) | ( ~ (all_8_0 = e0) & op(e1, e2) = all_8_0 &
% 129.52/18.12 | $i(all_8_0)) | ( ~ (all_8_1 = e3) & op(e1, e1) = all_8_1 &
% 129.52/18.12 | $i(all_8_1))
% 129.52/18.12 |
% 129.52/18.12 | DELTA: instantiating (11) with fresh symbols all_10_0, all_10_1, all_10_2
% 129.52/18.12 | gives:
% 129.52/18.12 | (44) op(e3, e3) = all_10_2 & $i(all_10_2) & ( ~ (all_10_2 = e0) | ( ~
% 129.52/18.12 | (all_10_0 = e2) & op(e0, e3) = all_10_0 & $i(all_10_0)) | ( ~
% 129.52/18.12 | (all_10_1 = e1) & op(e0, e0) = all_10_1 & $i(all_10_1)))
% 129.52/18.12 |
% 129.52/18.12 | ALPHA: (44) implies:
% 129.52/18.12 | (45) op(e3, e3) = all_10_2
% 129.52/18.12 | (46) ~ (all_10_2 = e0) | ( ~ (all_10_0 = e2) & op(e0, e3) = all_10_0 &
% 129.52/18.12 | $i(all_10_0)) | ( ~ (all_10_1 = e1) & op(e0, e0) = all_10_1 &
% 129.52/18.12 | $i(all_10_1))
% 129.52/18.12 |
% 129.52/18.12 | DELTA: instantiating (22) with fresh symbols all_12_0, all_12_1, all_12_2
% 129.52/18.12 | gives:
% 129.52/18.12 | (47) op(e0, e0) = all_12_2 & $i(all_12_2) & ( ~ (all_12_2 = e1) | ( ~
% 129.52/18.12 | (all_12_0 = e2) & op(e1, e0) = all_12_0 & $i(all_12_0)) | ( ~
% 129.52/18.12 | (all_12_1 = e3) & op(e1, e1) = all_12_1 & $i(all_12_1)))
% 129.52/18.12 |
% 129.52/18.12 | ALPHA: (47) implies:
% 129.52/18.12 | (48) op(e0, e0) = all_12_2
% 129.52/18.12 | (49) ~ (all_12_2 = e1) | ( ~ (all_12_0 = e2) & op(e1, e0) = all_12_0 &
% 129.52/18.12 | $i(all_12_0)) | ( ~ (all_12_1 = e3) & op(e1, e1) = all_12_1 &
% 129.52/18.12 | $i(all_12_1))
% 129.52/18.12 |
% 129.52/18.12 | DELTA: instantiating (29) with fresh symbols all_14_0, all_14_1, all_14_2
% 129.52/18.12 | gives:
% 129.52/18.12 | (50) op(e2, e2) = all_14_2 & $i(all_14_2) & ( ~ (all_14_2 = e3) | ( ~
% 129.52/18.12 | (all_14_0 = e1) & op(e3, e2) = all_14_0 & $i(all_14_0)) | ( ~
% 129.52/18.12 | (all_14_1 = e0) & op(e3, e3) = all_14_1 & $i(all_14_1)))
% 129.52/18.12 |
% 129.52/18.12 | ALPHA: (50) implies:
% 129.52/18.12 | (51) op(e2, e2) = all_14_2
% 129.52/18.12 | (52) ~ (all_14_2 = e3) | ( ~ (all_14_0 = e1) & op(e3, e2) = all_14_0 &
% 129.52/18.12 | $i(all_14_0)) | ( ~ (all_14_1 = e0) & op(e3, e3) = all_14_1 &
% 129.52/18.12 | $i(all_14_1))
% 129.52/18.12 |
% 129.52/18.12 | DELTA: instantiating (23) with fresh symbols all_16_0, all_16_1, all_16_2
% 129.52/18.12 | gives:
% 129.52/18.12 | (53) op(e3, e3) = all_16_2 & $i(all_16_2) & ( ~ (all_16_2 = e2) | ( ~
% 129.52/18.12 | (all_16_0 = e1) & op(e2, e3) = all_16_0 & $i(all_16_0)) | ( ~
% 129.52/18.12 | (all_16_1 = e0) & op(e2, e2) = all_16_1 & $i(all_16_1)))
% 129.52/18.12 |
% 129.52/18.12 | ALPHA: (53) implies:
% 129.52/18.12 | (54) op(e3, e3) = all_16_2
% 129.52/18.12 | (55) ~ (all_16_2 = e2) | ( ~ (all_16_0 = e1) & op(e2, e3) = all_16_0 &
% 129.52/18.12 | $i(all_16_0)) | ( ~ (all_16_1 = e0) & op(e2, e2) = all_16_1 &
% 129.52/18.12 | $i(all_16_1))
% 129.52/18.12 |
% 129.52/18.12 | DELTA: instantiating (24) with fresh symbols all_18_0, all_18_1, all_18_2
% 129.52/18.12 | gives:
% 129.52/18.12 | (56) op(e1, e1) = all_18_2 & $i(all_18_2) & ( ~ (all_18_2 = e2) | ( ~
% 129.52/18.12 | (all_18_0 = e3) & op(e2, e1) = all_18_0 & $i(all_18_0)) | ( ~
% 129.52/18.12 | (all_18_1 = e0) & op(e2, e2) = all_18_1 & $i(all_18_1)))
% 129.52/18.12 |
% 129.52/18.12 | ALPHA: (56) implies:
% 129.52/18.12 | (57) op(e1, e1) = all_18_2
% 129.52/18.12 | (58) ~ (all_18_2 = e2) | ( ~ (all_18_0 = e3) & op(e2, e1) = all_18_0 &
% 129.52/18.12 | $i(all_18_0)) | ( ~ (all_18_1 = e0) & op(e2, e2) = all_18_1 &
% 129.52/18.12 | $i(all_18_1))
% 129.52/18.12 |
% 129.52/18.12 | DELTA: instantiating (26) with fresh symbols all_20_0, all_20_1, all_20_2
% 129.52/18.12 | gives:
% 129.52/18.12 | (59) op(e0, e0) = all_20_2 & $i(all_20_2) & ( ~ (all_20_2 = e2) | ( ~
% 129.52/18.12 | (all_20_0 = e3) & op(e2, e0) = all_20_0 & $i(all_20_0)) | ( ~
% 129.52/18.12 | (all_20_1 = e1) & op(e2, e2) = all_20_1 & $i(all_20_1)))
% 129.52/18.12 |
% 129.52/18.12 | ALPHA: (59) implies:
% 129.52/18.12 | (60) op(e0, e0) = all_20_2
% 129.52/18.12 | (61) ~ (all_20_2 = e2) | ( ~ (all_20_0 = e3) & op(e2, e0) = all_20_0 &
% 129.52/18.12 | $i(all_20_0)) | ( ~ (all_20_1 = e1) & op(e2, e2) = all_20_1 &
% 129.52/18.12 | $i(all_20_1))
% 129.52/18.12 |
% 129.52/18.12 | DELTA: instantiating (31) with fresh symbols all_22_0, all_22_1, all_22_2
% 129.52/18.12 | gives:
% 129.52/18.12 | (62) op(e2, e2) = all_22_2 & $i(all_22_2) & ( ~ (all_22_2 = e3) | ( ~
% 129.52/18.12 | (all_22_0 = e0) & op(e3, e2) = all_22_0 & $i(all_22_0)) | ( ~
% 129.52/18.12 | (all_22_1 = e1) & op(e3, e3) = all_22_1 & $i(all_22_1)))
% 129.52/18.12 |
% 129.52/18.12 | ALPHA: (62) implies:
% 129.52/18.12 | (63) op(e2, e2) = all_22_2
% 129.52/18.12 | (64) ~ (all_22_2 = e3) | ( ~ (all_22_0 = e0) & op(e3, e2) = all_22_0 &
% 129.52/18.12 | $i(all_22_0)) | ( ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 &
% 129.52/18.12 | $i(all_22_1))
% 129.52/18.12 |
% 129.52/18.12 | DELTA: instantiating (13) with fresh symbols all_24_0, all_24_1, all_24_2
% 129.52/18.12 | gives:
% 129.52/18.12 | (65) op(e3, e3) = all_24_2 & $i(all_24_2) & ( ~ (all_24_2 = e0) | ( ~
% 129.52/18.12 | (all_24_0 = e1) & op(e0, e3) = all_24_0 & $i(all_24_0)) | ( ~
% 129.52/18.12 | (all_24_1 = e2) & op(e0, e0) = all_24_1 & $i(all_24_1)))
% 129.52/18.12 |
% 129.52/18.12 | ALPHA: (65) implies:
% 129.52/18.13 | (66) op(e3, e3) = all_24_2
% 129.52/18.13 | (67) ~ (all_24_2 = e0) | ( ~ (all_24_0 = e1) & op(e0, e3) = all_24_0 &
% 129.52/18.13 | $i(all_24_0)) | ( ~ (all_24_1 = e2) & op(e0, e0) = all_24_1 &
% 129.52/18.13 | $i(all_24_1))
% 129.52/18.13 |
% 129.52/18.13 | DELTA: instantiating (28) with fresh symbols all_26_0, all_26_1, all_26_2
% 129.52/18.13 | gives:
% 129.52/18.13 | (68) op(e0, e0) = all_26_2 & $i(all_26_2) & ( ~ (all_26_2 = e2) | ( ~
% 129.52/18.13 | (all_26_0 = e1) & op(e2, e0) = all_26_0 & $i(all_26_0)) | ( ~
% 129.52/18.13 | (all_26_1 = e3) & op(e2, e2) = all_26_1 & $i(all_26_1)))
% 129.52/18.13 |
% 129.52/18.13 | ALPHA: (68) implies:
% 129.52/18.13 | (69) op(e0, e0) = all_26_2
% 129.52/18.13 | (70) ~ (all_26_2 = e2) | ( ~ (all_26_0 = e1) & op(e2, e0) = all_26_0 &
% 129.52/18.13 | $i(all_26_0)) | ( ~ (all_26_1 = e3) & op(e2, e2) = all_26_1 &
% 129.52/18.13 | $i(all_26_1))
% 129.52/18.13 |
% 129.52/18.13 | DELTA: instantiating (30) with fresh symbols all_28_0, all_28_1, all_28_2
% 129.52/18.13 | gives:
% 129.52/18.13 | (71) op(e1, e1) = all_28_2 & $i(all_28_2) & ( ~ (all_28_2 = e3) | ( ~
% 129.52/18.13 | (all_28_0 = e2) & op(e3, e1) = all_28_0 & $i(all_28_0)) | ( ~
% 129.52/18.13 | (all_28_1 = e0) & op(e3, e3) = all_28_1 & $i(all_28_1)))
% 129.52/18.13 |
% 129.52/18.13 | ALPHA: (71) implies:
% 129.52/18.13 | (72) op(e1, e1) = all_28_2
% 129.52/18.13 | (73) ~ (all_28_2 = e3) | ( ~ (all_28_0 = e2) & op(e3, e1) = all_28_0 &
% 129.52/18.13 | $i(all_28_0)) | ( ~ (all_28_1 = e0) & op(e3, e3) = all_28_1 &
% 129.52/18.13 | $i(all_28_1))
% 129.52/18.13 |
% 129.52/18.13 | DELTA: instantiating (12) with fresh symbols all_30_0, all_30_1, all_30_2
% 129.52/18.13 | gives:
% 129.52/18.13 | (74) op(e2, e2) = all_30_2 & $i(all_30_2) & ( ~ (all_30_2 = e0) | ( ~
% 129.52/18.13 | (all_30_0 = e3) & op(e0, e2) = all_30_0 & $i(all_30_0)) | ( ~
% 129.52/18.13 | (all_30_1 = e1) & op(e0, e0) = all_30_1 & $i(all_30_1)))
% 129.52/18.13 |
% 129.52/18.13 | ALPHA: (74) implies:
% 129.52/18.13 | (75) op(e2, e2) = all_30_2
% 129.52/18.13 | (76) ~ (all_30_2 = e0) | ( ~ (all_30_0 = e3) & op(e0, e2) = all_30_0 &
% 129.52/18.13 | $i(all_30_0)) | ( ~ (all_30_1 = e1) & op(e0, e0) = all_30_1 &
% 129.52/18.13 | $i(all_30_1))
% 129.52/18.13 |
% 129.52/18.13 | DELTA: instantiating (19) with fresh symbols all_32_0, all_32_1, all_32_2
% 129.52/18.13 | gives:
% 129.52/18.13 | (77) op(e3, e3) = all_32_2 & $i(all_32_2) & ( ~ (all_32_2 = e1) | ( ~
% 129.52/18.13 | (all_32_0 = e0) & op(e1, e3) = all_32_0 & $i(all_32_0)) | ( ~
% 129.52/18.13 | (all_32_1 = e2) & op(e1, e1) = all_32_1 & $i(all_32_1)))
% 129.52/18.13 |
% 129.52/18.13 | ALPHA: (77) implies:
% 129.52/18.13 | (78) op(e3, e3) = all_32_2
% 129.52/18.13 | (79) ~ (all_32_2 = e1) | ( ~ (all_32_0 = e0) & op(e1, e3) = all_32_0 &
% 129.52/18.13 | $i(all_32_0)) | ( ~ (all_32_1 = e2) & op(e1, e1) = all_32_1 &
% 129.52/18.13 | $i(all_32_1))
% 129.52/18.13 |
% 129.52/18.13 | DELTA: instantiating (32) with fresh symbols all_34_0, all_34_1, all_34_2
% 129.52/18.13 | gives:
% 129.52/18.13 | (80) op(e0, e0) = all_34_2 & $i(all_34_2) & ( ~ (all_34_2 = e3) | ( ~
% 129.52/18.13 | (all_34_0 = e2) & op(e3, e0) = all_34_0 & $i(all_34_0)) | ( ~
% 129.52/18.13 | (all_34_1 = e1) & op(e3, e3) = all_34_1 & $i(all_34_1)))
% 129.52/18.13 |
% 129.52/18.13 | ALPHA: (80) implies:
% 129.52/18.13 | (81) op(e0, e0) = all_34_2
% 129.52/18.13 | (82) ~ (all_34_2 = e3) | ( ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 &
% 129.52/18.13 | $i(all_34_0)) | ( ~ (all_34_1 = e1) & op(e3, e3) = all_34_1 &
% 129.52/18.13 | $i(all_34_1))
% 129.52/18.13 |
% 129.52/18.13 | DELTA: instantiating (33) with fresh symbols all_36_0, all_36_1, all_36_2
% 129.52/18.13 | gives:
% 129.52/18.13 | (83) op(e1, e1) = all_36_2 & $i(all_36_2) & ( ~ (all_36_2 = e3) | ( ~
% 129.52/18.13 | (all_36_0 = e0) & op(e3, e1) = all_36_0 & $i(all_36_0)) | ( ~
% 129.52/18.13 | (all_36_1 = e2) & op(e3, e3) = all_36_1 & $i(all_36_1)))
% 129.52/18.13 |
% 129.52/18.13 | ALPHA: (83) implies:
% 129.52/18.13 | (84) op(e1, e1) = all_36_2
% 129.52/18.13 | (85) ~ (all_36_2 = e3) | ( ~ (all_36_0 = e0) & op(e3, e1) = all_36_0 &
% 129.52/18.13 | $i(all_36_0)) | ( ~ (all_36_1 = e2) & op(e3, e3) = all_36_1 &
% 129.52/18.13 | $i(all_36_1))
% 129.52/18.13 |
% 129.52/18.13 | DELTA: instantiating (25) with fresh symbols all_38_0, all_38_1, all_38_2
% 129.52/18.13 | gives:
% 129.52/18.13 | (86) op(e3, e3) = all_38_2 & $i(all_38_2) & ( ~ (all_38_2 = e2) | ( ~
% 129.52/18.13 | (all_38_0 = e0) & op(e2, e3) = all_38_0 & $i(all_38_0)) | ( ~
% 129.52/18.13 | (all_38_1 = e1) & op(e2, e2) = all_38_1 & $i(all_38_1)))
% 129.52/18.13 |
% 129.52/18.13 | ALPHA: (86) implies:
% 129.52/18.13 | (87) op(e3, e3) = all_38_2
% 129.52/18.13 | (88) ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(e2, e3) = all_38_0 &
% 129.52/18.13 | $i(all_38_0)) | ( ~ (all_38_1 = e1) & op(e2, e2) = all_38_1 &
% 129.52/18.13 | $i(all_38_1))
% 129.52/18.13 |
% 129.52/18.13 | DELTA: instantiating (14) with fresh symbols all_40_0, all_40_1, all_40_2
% 129.52/18.13 | gives:
% 129.52/18.13 | (89) op(e1, e1) = all_40_2 & $i(all_40_2) & ( ~ (all_40_2 = e0) | ( ~
% 129.52/18.13 | (all_40_0 = e3) & op(e0, e1) = all_40_0 & $i(all_40_0)) | ( ~
% 129.52/18.13 | (all_40_1 = e2) & op(e0, e0) = all_40_1 & $i(all_40_1)))
% 129.52/18.13 |
% 129.52/18.13 | ALPHA: (89) implies:
% 129.52/18.13 | (90) op(e1, e1) = all_40_2
% 129.52/18.13 | (91) ~ (all_40_2 = e0) | ( ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 &
% 129.52/18.13 | $i(all_40_0)) | ( ~ (all_40_1 = e2) & op(e0, e0) = all_40_1 &
% 129.52/18.13 | $i(all_40_1))
% 129.52/18.13 |
% 129.52/18.13 | DELTA: instantiating (15) with fresh symbols all_42_0, all_42_1, all_42_2
% 129.52/18.13 | gives:
% 129.52/18.14 | (92) op(e2, e2) = all_42_2 & $i(all_42_2) & ( ~ (all_42_2 = e0) | ( ~
% 129.52/18.14 | (all_42_0 = e1) & op(e0, e2) = all_42_0 & $i(all_42_0)) | ( ~
% 129.52/18.14 | (all_42_1 = e3) & op(e0, e0) = all_42_1 & $i(all_42_1)))
% 129.52/18.14 |
% 129.52/18.14 | ALPHA: (92) implies:
% 129.52/18.14 | (93) op(e2, e2) = all_42_2
% 129.84/18.14 | (94) ~ (all_42_2 = e0) | ( ~ (all_42_0 = e1) & op(e0, e2) = all_42_0 &
% 129.84/18.14 | $i(all_42_0)) | ( ~ (all_42_1 = e3) & op(e0, e0) = all_42_1 &
% 129.84/18.14 | $i(all_42_1))
% 129.84/18.14 |
% 129.84/18.14 | DELTA: instantiating (34) with fresh symbols all_44_0, all_44_1, all_44_2
% 129.84/18.14 | gives:
% 129.84/18.14 | (95) op(e0, e0) = all_44_2 & $i(all_44_2) & ( ~ (all_44_2 = e3) | ( ~
% 129.84/18.14 | (all_44_0 = e1) & op(e3, e0) = all_44_0 & $i(all_44_0)) | ( ~
% 129.84/18.14 | (all_44_1 = e2) & op(e3, e3) = all_44_1 & $i(all_44_1)))
% 129.84/18.14 |
% 129.84/18.14 | ALPHA: (95) implies:
% 129.84/18.14 | (96) op(e0, e0) = all_44_2
% 129.84/18.14 | (97) ~ (all_44_2 = e3) | ( ~ (all_44_0 = e1) & op(e3, e0) = all_44_0 &
% 129.84/18.14 | $i(all_44_0)) | ( ~ (all_44_1 = e2) & op(e3, e3) = all_44_1 &
% 129.84/18.14 | $i(all_44_1))
% 129.84/18.14 |
% 129.84/18.14 | DELTA: instantiating (16) with fresh symbols all_46_0, all_46_1, all_46_2
% 129.84/18.14 | gives:
% 129.84/18.14 | (98) op(e1, e1) = all_46_2 & $i(all_46_2) & ( ~ (all_46_2 = e0) | ( ~
% 129.84/18.14 | (all_46_0 = e2) & op(e0, e1) = all_46_0 & $i(all_46_0)) | ( ~
% 129.84/18.14 | (all_46_1 = e3) & op(e0, e0) = all_46_1 & $i(all_46_1)))
% 129.84/18.14 |
% 129.84/18.14 | ALPHA: (98) implies:
% 129.84/18.14 | (99) op(e1, e1) = all_46_2
% 129.84/18.14 | (100) ~ (all_46_2 = e0) | ( ~ (all_46_0 = e2) & op(e0, e1) = all_46_0 &
% 129.84/18.14 | $i(all_46_0)) | ( ~ (all_46_1 = e3) & op(e0, e0) = all_46_1 &
% 129.84/18.14 | $i(all_46_1))
% 129.84/18.14 |
% 129.84/18.14 | DELTA: instantiating (18) with fresh symbols all_48_0, all_48_1, all_48_2
% 129.84/18.14 | gives:
% 129.84/18.14 | (101) op(e2, e2) = all_48_2 & $i(all_48_2) & ( ~ (all_48_2 = e1) | ( ~
% 129.84/18.14 | (all_48_0 = e3) & op(e1, e2) = all_48_0 & $i(all_48_0)) | ( ~
% 129.84/18.14 | (all_48_1 = e0) & op(e1, e1) = all_48_1 & $i(all_48_1)))
% 129.84/18.14 |
% 129.84/18.14 | ALPHA: (101) implies:
% 129.84/18.14 | (102) op(e2, e2) = all_48_2
% 129.84/18.14 | (103) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e3) & op(e1, e2) = all_48_0 &
% 129.84/18.14 | $i(all_48_0)) | ( ~ (all_48_1 = e0) & op(e1, e1) = all_48_1 &
% 129.84/18.14 | $i(all_48_1))
% 129.84/18.14 |
% 129.84/18.14 | DELTA: instantiating (17) with fresh symbols all_50_0, all_50_1, all_50_2
% 129.84/18.14 | gives:
% 129.84/18.14 | (104) op(e3, e3) = all_50_2 & $i(all_50_2) & ( ~ (all_50_2 = e1) | ( ~
% 129.84/18.14 | (all_50_0 = e2) & op(e1, e3) = all_50_0 & $i(all_50_0)) | ( ~
% 129.84/18.14 | (all_50_1 = e0) & op(e1, e1) = all_50_1 & $i(all_50_1)))
% 129.84/18.14 |
% 129.84/18.14 | ALPHA: (104) implies:
% 129.84/18.14 | (105) op(e3, e3) = all_50_2
% 129.84/18.14 | (106) ~ (all_50_2 = e1) | ( ~ (all_50_0 = e2) & op(e1, e3) = all_50_0 &
% 129.84/18.14 | $i(all_50_0)) | ( ~ (all_50_1 = e0) & op(e1, e1) = all_50_1 &
% 129.84/18.14 | $i(all_50_1))
% 129.84/18.14 |
% 129.84/18.14 | DELTA: instantiating (3) with fresh symbols all_52_0, all_52_1, all_52_2,
% 129.84/18.14 | all_52_3, all_52_4, all_52_5, all_52_6, all_52_7, all_52_8, all_52_9,
% 129.84/18.14 | all_52_10, all_52_11, all_52_12, all_52_13, all_52_14, all_52_15 gives:
% 129.84/18.14 | (107) ~ (all_52_0 = all_52_1) & ~ (all_52_0 = all_52_2) & ~ (all_52_0 =
% 129.84/18.14 | all_52_3) & ~ (all_52_0 = all_52_4) & ~ (all_52_0 = all_52_8) &
% 129.84/18.14 | ~ (all_52_0 = all_52_12) & ~ (all_52_1 = all_52_2) & ~ (all_52_1 =
% 129.84/18.14 | all_52_3) & ~ (all_52_1 = all_52_5) & ~ (all_52_1 = all_52_9) &
% 129.84/18.14 | ~ (all_52_1 = all_52_13) & ~ (all_52_2 = all_52_3) & ~ (all_52_2 =
% 129.84/18.14 | all_52_6) & ~ (all_52_2 = all_52_10) & ~ (all_52_2 = all_52_14) &
% 129.84/18.14 | ~ (all_52_3 = all_52_7) & ~ (all_52_3 = all_52_11) & ~ (all_52_3 =
% 129.84/18.14 | all_52_15) & ~ (all_52_4 = all_52_5) & ~ (all_52_4 = all_52_6) &
% 129.84/18.14 | ~ (all_52_4 = all_52_7) & ~ (all_52_4 = all_52_8) & ~ (all_52_4 =
% 129.84/18.14 | all_52_12) & ~ (all_52_5 = all_52_6) & ~ (all_52_5 = all_52_7) &
% 129.84/18.14 | ~ (all_52_5 = all_52_9) & ~ (all_52_5 = all_52_13) & ~ (all_52_6 =
% 129.84/18.14 | all_52_7) & ~ (all_52_6 = all_52_10) & ~ (all_52_6 = all_52_14) &
% 129.84/18.14 | ~ (all_52_7 = all_52_11) & ~ (all_52_7 = all_52_15) & ~ (all_52_8
% 129.84/18.14 | = all_52_9) & ~ (all_52_8 = all_52_10) & ~ (all_52_8 = all_52_11)
% 129.84/18.14 | & ~ (all_52_8 = all_52_12) & ~ (all_52_9 = all_52_10) & ~
% 129.84/18.14 | (all_52_9 = all_52_11) & ~ (all_52_9 = all_52_13) & ~ (all_52_10 =
% 129.84/18.14 | all_52_11) & ~ (all_52_10 = all_52_14) & ~ (all_52_11 =
% 129.84/18.14 | all_52_15) & ~ (all_52_12 = all_52_13) & ~ (all_52_12 =
% 129.84/18.14 | all_52_14) & ~ (all_52_12 = all_52_15) & ~ (all_52_13 =
% 129.84/18.14 | all_52_14) & ~ (all_52_13 = all_52_15) & ~ (all_52_14 =
% 129.84/18.14 | all_52_15) & op(e3, e3) = all_52_0 & op(e3, e2) = all_52_4 & op(e3,
% 129.84/18.14 | e1) = all_52_8 & op(e3, e0) = all_52_12 & op(e2, e3) = all_52_1 &
% 129.84/18.14 | op(e2, e2) = all_52_5 & op(e2, e1) = all_52_9 & op(e2, e0) =
% 129.84/18.14 | all_52_13 & op(e1, e3) = all_52_2 & op(e1, e2) = all_52_6 & op(e1,
% 129.84/18.14 | e1) = all_52_10 & op(e1, e0) = all_52_14 & op(e0, e3) = all_52_3 &
% 129.84/18.14 | op(e0, e2) = all_52_7 & op(e0, e1) = all_52_11 & op(e0, e0) =
% 129.84/18.14 | all_52_15 & $i(all_52_0) & $i(all_52_1) & $i(all_52_2) & $i(all_52_3)
% 129.84/18.14 | & $i(all_52_4) & $i(all_52_5) & $i(all_52_6) & $i(all_52_7) &
% 129.84/18.14 | $i(all_52_8) & $i(all_52_9) & $i(all_52_10) & $i(all_52_11) &
% 129.84/18.14 | $i(all_52_12) & $i(all_52_13) & $i(all_52_14) & $i(all_52_15)
% 129.84/18.14 |
% 129.84/18.14 | ALPHA: (107) implies:
% 129.84/18.14 | (108) ~ (all_52_14 = all_52_15)
% 129.84/18.14 | (109) ~ (all_52_13 = all_52_15)
% 129.84/18.14 | (110) ~ (all_52_13 = all_52_14)
% 129.84/18.14 | (111) ~ (all_52_12 = all_52_15)
% 129.84/18.14 | (112) ~ (all_52_12 = all_52_14)
% 129.84/18.14 | (113) ~ (all_52_12 = all_52_13)
% 129.84/18.15 | (114) ~ (all_52_11 = all_52_15)
% 129.84/18.15 | (115) ~ (all_52_10 = all_52_14)
% 129.84/18.15 | (116) ~ (all_52_10 = all_52_11)
% 129.84/18.15 | (117) ~ (all_52_9 = all_52_13)
% 129.84/18.15 | (118) ~ (all_52_9 = all_52_11)
% 129.84/18.15 | (119) ~ (all_52_9 = all_52_10)
% 129.84/18.15 | (120) ~ (all_52_8 = all_52_12)
% 129.84/18.15 | (121) ~ (all_52_8 = all_52_11)
% 129.84/18.15 | (122) ~ (all_52_8 = all_52_10)
% 129.84/18.15 | (123) ~ (all_52_8 = all_52_9)
% 129.84/18.15 | (124) ~ (all_52_7 = all_52_15)
% 129.84/18.15 | (125) ~ (all_52_7 = all_52_11)
% 129.84/18.15 | (126) ~ (all_52_6 = all_52_14)
% 129.84/18.15 | (127) ~ (all_52_6 = all_52_10)
% 129.84/18.15 | (128) ~ (all_52_6 = all_52_7)
% 129.84/18.15 | (129) ~ (all_52_5 = all_52_13)
% 129.84/18.15 | (130) ~ (all_52_5 = all_52_9)
% 129.84/18.15 | (131) ~ (all_52_5 = all_52_7)
% 129.84/18.15 | (132) ~ (all_52_5 = all_52_6)
% 129.84/18.15 | (133) ~ (all_52_4 = all_52_12)
% 129.84/18.15 | (134) ~ (all_52_4 = all_52_8)
% 129.84/18.15 | (135) ~ (all_52_4 = all_52_7)
% 129.84/18.15 | (136) ~ (all_52_4 = all_52_6)
% 129.84/18.15 | (137) ~ (all_52_4 = all_52_5)
% 129.84/18.15 | (138) ~ (all_52_3 = all_52_15)
% 129.84/18.15 | (139) ~ (all_52_3 = all_52_11)
% 129.84/18.15 | (140) ~ (all_52_3 = all_52_7)
% 129.84/18.15 | (141) ~ (all_52_2 = all_52_14)
% 129.84/18.15 | (142) ~ (all_52_2 = all_52_10)
% 129.84/18.15 | (143) ~ (all_52_2 = all_52_6)
% 129.84/18.15 | (144) ~ (all_52_2 = all_52_3)
% 129.84/18.15 | (145) ~ (all_52_1 = all_52_13)
% 129.84/18.15 | (146) ~ (all_52_1 = all_52_9)
% 129.84/18.15 | (147) ~ (all_52_1 = all_52_5)
% 129.84/18.15 | (148) ~ (all_52_1 = all_52_3)
% 129.84/18.15 | (149) ~ (all_52_1 = all_52_2)
% 129.84/18.15 | (150) ~ (all_52_0 = all_52_12)
% 129.84/18.15 | (151) ~ (all_52_0 = all_52_8)
% 129.84/18.15 | (152) ~ (all_52_0 = all_52_4)
% 129.84/18.15 | (153) ~ (all_52_0 = all_52_3)
% 129.84/18.15 | (154) ~ (all_52_0 = all_52_2)
% 129.84/18.15 | (155) ~ (all_52_0 = all_52_1)
% 129.84/18.15 | (156) op(e0, e0) = all_52_15
% 129.84/18.15 | (157) op(e0, e1) = all_52_11
% 129.84/18.15 | (158) op(e0, e2) = all_52_7
% 129.84/18.15 | (159) op(e0, e3) = all_52_3
% 129.84/18.15 | (160) op(e1, e0) = all_52_14
% 129.84/18.15 | (161) op(e1, e1) = all_52_10
% 129.84/18.15 | (162) op(e1, e2) = all_52_6
% 129.84/18.15 | (163) op(e1, e3) = all_52_2
% 129.84/18.15 | (164) op(e2, e0) = all_52_13
% 129.84/18.15 | (165) op(e2, e1) = all_52_9
% 129.84/18.15 | (166) op(e2, e2) = all_52_5
% 129.84/18.15 | (167) op(e2, e3) = all_52_1
% 129.84/18.15 | (168) op(e3, e0) = all_52_12
% 129.84/18.15 | (169) op(e3, e1) = all_52_8
% 129.84/18.15 | (170) op(e3, e2) = all_52_4
% 129.84/18.15 | (171) op(e3, e3) = all_52_0
% 129.84/18.15 |
% 129.84/18.15 | DELTA: instantiating (1) with fresh symbols all_54_0, all_54_1, all_54_2,
% 129.84/18.15 | all_54_3, all_54_4, all_54_5, all_54_6, all_54_7, all_54_8, all_54_9,
% 129.84/18.15 | all_54_10, all_54_11, all_54_12, all_54_13, all_54_14, all_54_15 gives:
% 129.84/18.15 | (172) op(e3, e3) = all_54_0 & op(e3, e2) = all_54_1 & op(e3, e1) = all_54_2
% 129.84/18.15 | & op(e3, e0) = all_54_3 & op(e2, e3) = all_54_4 & op(e2, e2) =
% 129.84/18.15 | all_54_5 & op(e2, e1) = all_54_6 & op(e2, e0) = all_54_7 & op(e1, e3)
% 129.84/18.15 | = all_54_8 & op(e1, e2) = all_54_9 & op(e1, e1) = all_54_10 & op(e1,
% 129.84/18.15 | e0) = all_54_11 & op(e0, e3) = all_54_12 & op(e0, e2) = all_54_13 &
% 129.84/18.15 | op(e0, e1) = all_54_14 & op(e0, e0) = all_54_15 & $i(all_54_0) &
% 129.84/18.15 | $i(all_54_1) & $i(all_54_2) & $i(all_54_3) & $i(all_54_4) &
% 129.84/18.15 | $i(all_54_5) & $i(all_54_6) & $i(all_54_7) & $i(all_54_8) &
% 129.84/18.15 | $i(all_54_9) & $i(all_54_10) & $i(all_54_11) & $i(all_54_12) &
% 129.84/18.15 | $i(all_54_13) & $i(all_54_14) & $i(all_54_15) & (all_54_0 = e3 |
% 129.84/18.15 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0) & (all_54_1 = e3 |
% 129.84/18.15 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0) & (all_54_2 = e3 |
% 129.84/18.15 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0) & (all_54_3 = e3 |
% 129.84/18.15 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0) & (all_54_4 = e3 |
% 129.84/18.15 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0) & (all_54_5 = e3 |
% 129.84/18.15 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0) & (all_54_6 = e3 |
% 129.84/18.15 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0) & (all_54_7 = e3 |
% 129.84/18.15 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0) & (all_54_8 = e3 |
% 129.84/18.15 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0) & (all_54_9 = e3 |
% 129.84/18.15 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0) & (all_54_10 = e3 |
% 129.84/18.15 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0) & (all_54_11 = e3
% 129.84/18.15 | | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0) & (all_54_12 =
% 129.84/18.15 | e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0) & (all_54_13
% 129.84/18.15 | = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0) &
% 129.84/18.15 | (all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0) &
% 129.84/18.15 | (all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0)
% 129.84/18.15 |
% 129.84/18.15 | ALPHA: (172) implies:
% 129.84/18.15 | (173) op(e0, e0) = all_54_15
% 129.84/18.15 | (174) op(e0, e1) = all_54_14
% 129.84/18.15 | (175) op(e0, e2) = all_54_13
% 129.84/18.15 | (176) op(e0, e3) = all_54_12
% 129.84/18.15 | (177) op(e1, e0) = all_54_11
% 129.84/18.15 | (178) op(e1, e1) = all_54_10
% 129.84/18.15 | (179) op(e1, e2) = all_54_9
% 129.84/18.15 | (180) op(e1, e3) = all_54_8
% 129.84/18.15 | (181) op(e2, e0) = all_54_7
% 129.84/18.16 | (182) op(e2, e1) = all_54_6
% 129.84/18.16 | (183) op(e2, e2) = all_54_5
% 129.84/18.16 | (184) op(e2, e3) = all_54_4
% 129.84/18.16 | (185) op(e3, e0) = all_54_3
% 129.84/18.16 | (186) op(e3, e1) = all_54_2
% 129.84/18.16 | (187) op(e3, e2) = all_54_1
% 129.84/18.16 | (188) op(e3, e3) = all_54_0
% 129.84/18.16 | (189) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 129.84/18.16 | (190) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 129.84/18.16 | (191) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 129.84/18.16 | (192) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 129.84/18.16 | (193) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 129.84/18.16 | (194) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 129.84/18.16 | (195) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 129.84/18.16 | (196) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 129.84/18.16 | (197) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 129.84/18.16 | (198) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 129.84/18.16 | (199) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 129.84/18.16 | (200) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 129.84/18.16 | (201) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 129.84/18.16 | (202) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 129.84/18.16 | (203) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 129.84/18.16 | (204) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 129.84/18.16 |
% 129.84/18.16 | DELTA: instantiating (10) with fresh symbols all_56_0, all_56_1, all_56_2,
% 129.84/18.16 | all_56_3, all_56_4, all_56_5, all_56_6, all_56_7, all_56_8, all_56_9,
% 129.84/18.16 | all_56_10, all_56_11, all_56_12, all_56_13, all_56_14, all_56_15,
% 129.84/18.16 | all_56_16, all_56_17, all_56_18, all_56_19, all_56_20, all_56_21,
% 129.84/18.16 | all_56_22, all_56_23, all_56_24, all_56_25, all_56_26, all_56_27,
% 129.84/18.16 | all_56_28, all_56_29, all_56_30, all_56_31 gives:
% 129.84/18.17 | (205) ((all_56_0 = all_56_1 & op(all_56_1, e3) = all_56_1 & op(e3, e3) =
% 129.84/18.17 | all_56_1 & $i(all_56_1)) | (all_56_2 = all_56_3 & op(all_56_3,
% 129.84/18.17 | e2) = all_56_3 & op(e2, e3) = all_56_3 & $i(all_56_3)) |
% 129.84/18.17 | (all_56_4 = all_56_5 & op(all_56_5, e1) = all_56_5 & op(e1, e3) =
% 129.84/18.17 | all_56_5 & $i(all_56_5)) | (all_56_6 = all_56_7 & op(all_56_7,
% 129.84/18.17 | e0) = all_56_7 & op(e0, e3) = all_56_7 & $i(all_56_7))) &
% 129.84/18.17 | ((all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11
% 129.84/18.17 | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3)
% 129.84/18.17 | = e2 & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 129.84/18.17 | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 129.84/18.17 | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 129.84/18.17 | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~
% 129.84/18.17 | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 129.84/18.17 | op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 &
% 129.84/18.17 | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 129.84/18.17 | all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 129.84/18.17 | $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 129.84/18.17 | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31
% 129.84/18.17 | = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) =
% 129.84/18.17 | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 129.84/18.17 | op(e0, e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 129.84/18.17 | $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3
% 129.84/18.17 | & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 129.84/18.17 | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) =
% 129.84/18.17 | all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 129.84/18.17 | op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 129.84/18.17 | $i(all_56_17) & $i(all_56_25)) | (all_56_5 = e1 & all_56_21 = e3
% 129.84/18.17 | & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 129.84/18.17 | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) =
% 129.84/18.17 | all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 129.84/18.17 | op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 129.84/18.17 | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2
% 129.84/18.17 | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 129.84/18.17 | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 129.84/18.17 | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 129.84/18.17 | all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13)
% 129.84/18.17 | & $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 & all_56_27 =
% 129.84/18.17 | e2 & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 129.84/18.17 | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 129.84/18.17 | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) =
% 129.84/18.17 | all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & $i(all_56_15)
% 129.84/18.17 | & $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 & all_56_21 =
% 129.84/18.17 | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 129.84/18.17 | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 129.84/18.17 | = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 129.84/18.17 | op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11)
% 129.84/18.17 | & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = all_56_31 &
% 129.84/18.17 | $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 129.84/18.17 | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 129.84/18.17 | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) =
% 129.84/18.17 | all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 129.84/18.17 | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17)
% 129.84/18.17 | & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~
% 129.84/18.17 | (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 129.84/18.17 | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 129.84/18.17 | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 129.84/18.17 | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 129.84/18.17 | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 & all_56_29
% 129.84/18.17 | = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~
% 129.84/18.17 | (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 129.84/18.17 | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 129.84/18.17 | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 129.84/18.17 | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 129.84/18.17 | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 129.84/18.17 | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 129.84/18.17 | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 129.84/18.17 | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 129.84/18.17 | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))))) &
% 129.84/18.17 | ((all_56_8 = all_56_9 & op(all_56_9, e3) = all_56_9 & op(e3, e2) =
% 129.84/18.17 | all_56_9 & $i(all_56_9)) | (all_56_10 = all_56_11 & op(all_56_11,
% 129.84/18.17 | e2) = all_56_11 & op(e2, e2) = all_56_11 & $i(all_56_11)) |
% 129.84/18.17 | (all_56_12 = all_56_13 & op(all_56_13, e1) = all_56_13 & op(e1, e2)
% 129.84/18.17 | = all_56_13 & $i(all_56_13)) | (all_56_14 = all_56_15 &
% 129.84/18.17 | op(all_56_15, e0) = all_56_15 & op(e0, e2) = all_56_15 &
% 129.84/18.17 | $i(all_56_15))) & ((all_56_16 = all_56_17 & op(all_56_17, e3) =
% 129.84/18.17 | all_56_17 & op(e3, e1) = all_56_17 & $i(all_56_17)) | (all_56_18
% 129.84/18.17 | = all_56_19 & op(all_56_19, e2) = all_56_19 & op(e2, e1) =
% 129.84/18.17 | all_56_19 & $i(all_56_19)) | (all_56_20 = all_56_21 &
% 129.84/18.17 | op(all_56_21, e1) = all_56_21 & op(e1, e1) = all_56_21 &
% 129.84/18.17 | $i(all_56_21)) | (all_56_22 = all_56_23 & op(all_56_23, e0) =
% 129.84/18.17 | all_56_23 & op(e0, e1) = all_56_23 & $i(all_56_23))) &
% 129.84/18.17 | ((all_56_24 = all_56_25 & op(all_56_25, e3) = all_56_25 & op(e3, e0)
% 129.84/18.17 | = all_56_25 & $i(all_56_25)) | (all_56_26 = all_56_27 &
% 129.84/18.17 | op(all_56_27, e2) = all_56_27 & op(e2, e0) = all_56_27 &
% 129.84/18.17 | $i(all_56_27)) | (all_56_28 = all_56_29 & op(all_56_29, e1) =
% 129.84/18.17 | all_56_29 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30
% 129.84/18.17 | = all_56_31 & op(all_56_31, e0) = all_56_31 & op(e0, e0) =
% 129.84/18.17 | all_56_31 & $i(all_56_31)))
% 129.84/18.17 |
% 129.84/18.17 | ALPHA: (205) implies:
% 129.98/18.17 | (206) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 129.98/18.17 | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2
% 129.98/18.17 | & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11
% 129.98/18.17 | & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 129.98/18.17 | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 129.98/18.17 | all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 129.98/18.17 | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 129.98/18.17 | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 129.98/18.17 | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 129.98/18.17 | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 &
% 129.98/18.17 | all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~
% 129.98/18.17 | (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3,
% 129.98/18.17 | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 129.98/18.17 | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 129.98/18.17 | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 &
% 129.98/18.17 | all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~
% 129.98/18.17 | (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 129.98/18.17 | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) =
% 129.98/18.17 | all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) &
% 129.98/18.17 | $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_5 = e1 &
% 129.98/18.17 | all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~
% 129.98/18.17 | (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 129.98/18.17 | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) =
% 129.98/18.17 | all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) &
% 129.98/18.17 | $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 &
% 129.98/18.17 | all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 129.98/18.17 | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2,
% 129.98/18.17 | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 129.98/18.17 | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 129.98/18.17 | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 &
% 129.98/18.17 | all_56_27 = e2 & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~
% 129.98/18.17 | (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 129.98/18.17 | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 129.98/18.17 | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 129.98/18.17 | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 &
% 129.98/18.17 | all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~
% 129.98/18.17 | (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 129.98/18.17 | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 129.98/18.17 | all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 129.98/18.17 | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 129.98/18.17 | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~
% 129.98/18.17 | (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 129.98/18.17 | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) =
% 129.98/18.17 | all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 129.98/18.17 | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 129.98/18.17 | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~
% 129.98/18.17 | (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 129.98/18.17 | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 129.98/18.17 | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 129.98/18.17 | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 129.98/18.17 | & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~
% 129.98/18.17 | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 129.98/18.17 | ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 129.98/18.17 | e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) =
% 129.98/18.17 | all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 129.98/18.17 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 129.98/18.17 | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 129.98/18.17 | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 129.98/18.17 | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 129.98/18.17 | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29))))
% 129.98/18.17 |
% 129.98/18.17 | DELTA: instantiating (2) with fresh symbols all_57_0, all_57_1, all_57_2,
% 129.98/18.17 | all_57_3, all_57_4, all_57_5, all_57_6, all_57_7, all_57_8, all_57_9,
% 129.98/18.17 | all_57_10, all_57_11, all_57_12, all_57_13, all_57_14, all_57_15 gives:
% 129.98/18.18 | (207) ((all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 129.98/18.18 | e3) | (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3,
% 129.98/18.18 | e0) = e3)) & ((all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 =
% 129.98/18.18 | e3 & op(e2, e3) = e3) | (all_57_6 = e3 & op(e1, e3) = e3) |
% 129.98/18.18 | (all_57_12 = e3 & op(e0, e3) = e3)) & ((all_57_0 = e2 & op(e3, e3)
% 129.98/18.18 | = e2) | (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_4 = e2 &
% 129.98/18.18 | op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)) &
% 129.98/18.18 | ((all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) =
% 129.98/18.18 | e2) | (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 &
% 129.98/18.18 | op(e0, e3) = e2)) & ((all_57_0 = e1 & op(e3, e3) = e1) |
% 129.98/18.18 | (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_4 = e1 & op(e3, e1) =
% 129.98/18.18 | e1) | (all_57_9 = e1 & op(e3, e0) = e1)) & ((all_57_0 = e1 &
% 129.98/18.18 | op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_6
% 129.98/18.18 | = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)) &
% 129.98/18.18 | ((all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 129.98/18.18 | e0) | (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3,
% 129.98/18.18 | e0) = e0)) & ((all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 =
% 129.98/18.18 | e0 & op(e2, e3) = e0) | (all_57_6 = e0 & op(e1, e3) = e0) |
% 129.98/18.18 | (all_57_12 = e0 & op(e0, e3) = e0)) & ((all_57_1 = e3 & op(e3, e2)
% 129.98/18.18 | = e3) | (all_57_3 = e3 & op(e2, e2) = e3) | (all_57_7 = e3 &
% 129.98/18.18 | op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)) &
% 129.98/18.18 | ((all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 129.98/18.18 | e2) | (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 &
% 129.98/18.18 | op(e0, e2) = e2)) & ((all_57_1 = e1 & op(e3, e2) = e1) |
% 129.98/18.18 | (all_57_3 = e1 & op(e2, e2) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 129.98/18.18 | e1) | (all_57_13 = e1 & op(e0, e2) = e1)) & ((all_57_1 = e0 &
% 129.98/18.18 | op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | (all_57_7
% 129.98/18.18 | = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)) &
% 129.98/18.18 | ((all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 129.98/18.18 | e3) | (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 &
% 129.98/18.18 | op(e2, e0) = e3)) & ((all_57_2 = e2 & op(e2, e3) = e2) |
% 129.98/18.18 | (all_57_3 = e2 & op(e2, e2) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 129.98/18.18 | e2) | (all_57_10 = e2 & op(e2, e0) = e2)) & ((all_57_2 = e1 &
% 129.98/18.18 | op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | (all_57_5
% 129.98/18.18 | = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)) &
% 129.98/18.18 | ((all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 129.98/18.18 | e0) | (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 &
% 129.98/18.18 | op(e2, e0) = e0)) & ((all_57_4 = e3 & op(e3, e1) = e3) |
% 129.98/18.18 | (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_8 = e3 & op(e1, e1) =
% 129.98/18.18 | e3) | (all_57_14 = e3 & op(e0, e1) = e3)) & ((all_57_4 = e2 &
% 129.98/18.18 | op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_8
% 129.98/18.18 | = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)) &
% 129.98/18.18 | ((all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) =
% 129.98/18.18 | e1) | (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 &
% 129.98/18.18 | op(e0, e1) = e1)) & ((all_57_4 = e0 & op(e3, e1) = e0) |
% 129.98/18.18 | (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_8 = e0 & op(e1, e1) =
% 129.98/18.18 | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) & ((all_57_6 = e3 &
% 129.98/18.18 | op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_8
% 129.98/18.18 | = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)) &
% 129.98/18.18 | ((all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) =
% 129.98/18.18 | e2) | (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 &
% 129.98/18.18 | op(e1, e0) = e2)) & ((all_57_6 = e1 & op(e1, e3) = e1) |
% 129.98/18.18 | (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_8 = e1 & op(e1, e1) =
% 129.98/18.18 | e1) | (all_57_11 = e1 & op(e1, e0) = e1)) & ((all_57_6 = e0 &
% 129.98/18.18 | op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_8
% 129.98/18.18 | = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 129.98/18.18 | ((all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 129.98/18.18 | e3) | (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 &
% 129.98/18.18 | op(e0, e0) = e3)) & ((all_57_9 = e2 & op(e3, e0) = e2) |
% 129.98/18.18 | (all_57_10 = e2 & op(e2, e0) = e2) | (all_57_11 = e2 & op(e1, e0) =
% 129.98/18.18 | e2) | (all_57_15 = e2 & op(e0, e0) = e2)) & ((all_57_9 = e1 &
% 129.98/18.18 | op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 129.98/18.18 | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 129.98/18.18 | e1)) & ((all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 &
% 129.98/18.18 | op(e0, e2) = e3) | (all_57_14 = e3 & op(e0, e1) = e3) |
% 129.98/18.18 | (all_57_15 = e3 & op(e0, e0) = e3)) & ((all_57_12 = e2 & op(e0, e3)
% 129.98/18.18 | = e2) | (all_57_13 = e2 & op(e0, e2) = e2) | (all_57_14 = e2 &
% 129.98/18.18 | op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)) &
% 129.98/18.18 | ((all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 129.98/18.18 | e1) | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 &
% 129.98/18.18 | op(e0, e0) = e1)) & ((all_57_15 = e0 & op(e0, e0) = e0) |
% 129.98/18.18 | (((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0)
% 129.98/18.18 | = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 =
% 129.98/18.18 | e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 129.98/18.18 | (all_57_14 = e0 & op(e0, e1) = e0))))
% 129.98/18.18 |
% 129.98/18.18 | ALPHA: (207) implies:
% 129.98/18.19 | (208) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) =
% 129.98/18.19 | e0) | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 129.98/18.19 | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) |
% 129.98/18.19 | (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1)
% 129.98/18.19 | = e0)))
% 129.98/18.19 | (209) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 129.98/18.19 | e1) | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0,
% 129.98/18.19 | e0) = e1)
% 129.98/18.19 | (210) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 129.98/18.19 | e2) | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0,
% 129.98/18.19 | e0) = e2)
% 129.98/18.19 | (211) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 129.98/18.19 | e3) | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0,
% 129.98/18.19 | e0) = e3)
% 129.98/18.19 | (212) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 129.98/18.19 | e1) | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0,
% 129.98/18.19 | e0) = e1)
% 129.98/18.19 | (213) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 129.98/18.19 | e2) | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0,
% 129.98/18.19 | e0) = e2)
% 129.98/18.19 | (214) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 129.98/18.19 | e3) | (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0,
% 129.98/18.19 | e0) = e3)
% 129.98/18.19 | (215) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0)
% 129.98/18.19 | | (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 129.98/18.19 | e0)
% 129.98/18.19 | (216) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1)
% 129.98/18.19 | | (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 129.98/18.19 | e1)
% 129.98/18.19 | (217) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2)
% 129.98/18.19 | | (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) =
% 129.98/18.19 | e2)
% 129.98/18.19 | (218) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3)
% 129.98/18.19 | | (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 129.98/18.19 | e3)
% 129.98/18.19 | (219) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0)
% 129.98/18.19 | | (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 129.98/18.19 | e0)
% 129.98/18.19 | (220) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1)
% 129.98/18.19 | | (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) =
% 129.98/18.19 | e1)
% 129.98/18.19 | (221) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2)
% 129.98/18.19 | | (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 129.98/18.19 | e2)
% 129.98/18.19 | (222) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3)
% 129.98/18.19 | | (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 129.98/18.19 | e3)
% 129.98/18.19 | (223) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 129.98/18.19 | | (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 129.98/18.19 | e0)
% 129.98/18.19 | (224) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 129.98/18.19 | | (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 129.98/18.19 | e1)
% 129.98/18.19 | (225) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 129.98/18.19 | | (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 129.98/18.19 | e2)
% 129.98/18.19 | (226) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 129.98/18.19 | | (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 129.98/18.19 | e3)
% 129.98/18.19 | (227) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 129.98/18.19 | | (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 129.98/18.19 | e0)
% 129.98/18.19 | (228) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 129.98/18.19 | | (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 129.98/18.19 | e1)
% 129.98/18.19 | (229) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 129.98/18.19 | | (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 129.98/18.19 | e2)
% 129.98/18.20 | (230) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 129.98/18.20 | | (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 129.98/18.20 | e3)
% 129.98/18.20 | (231) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0)
% 129.98/18.20 | | (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 129.98/18.20 | e0)
% 129.98/18.20 | (232) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0)
% 129.98/18.20 | | (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 129.98/18.20 | e0)
% 129.98/18.20 | (233) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1)
% 129.98/18.20 | | (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 129.98/18.20 | e1)
% 129.98/18.20 | (234) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1)
% 129.98/18.20 | | (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 129.98/18.20 | e1)
% 129.98/18.20 | (235) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2)
% 129.98/18.20 | | (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) =
% 129.98/18.20 | e2)
% 129.98/18.20 | (236) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2)
% 129.98/18.20 | | (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) =
% 129.98/18.20 | e2)
% 129.98/18.20 | (237) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3)
% 129.98/18.20 | | (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 129.98/18.20 | e3)
% 129.98/18.20 | (238) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3)
% 129.98/18.20 | | (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 129.98/18.20 | e3)
% 129.98/18.20 |
% 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_20_2, all_26_2, e0, e0,
% 129.98/18.20 | simplifying with (60), (69) gives:
% 129.98/18.20 | (239) all_26_2 = all_20_2
% 129.98/18.20 |
% 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_12_2, all_26_2, e0, e0,
% 129.98/18.20 | simplifying with (48), (69) gives:
% 129.98/18.20 | (240) all_26_2 = all_12_2
% 129.98/18.20 |
% 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_20_2, all_34_2, e0, e0,
% 129.98/18.20 | simplifying with (60), (81) gives:
% 129.98/18.20 | (241) all_34_2 = all_20_2
% 129.98/18.20 |
% 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_44_2, all_52_15, e0, e0,
% 129.98/18.20 | simplifying with (96), (156) gives:
% 129.98/18.20 | (242) all_52_15 = all_44_2
% 129.98/18.20 |
% 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_34_2, all_52_15, e0, e0,
% 129.98/18.20 | simplifying with (81), (156) gives:
% 129.98/18.20 | (243) all_52_15 = all_34_2
% 129.98/18.20 |
% 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_52_15, all_54_15, e0,
% 129.98/18.20 | e0, simplifying with (156), (173) gives:
% 129.98/18.20 | (244) all_54_15 = all_52_15
% 129.98/18.20 |
% 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_4_2, all_54_15, e0, e0,
% 129.98/18.20 | simplifying with (36), (173) gives:
% 129.98/18.20 | (245) all_54_15 = all_4_2
% 129.98/18.20 |
% 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_52_11, all_54_14, e1,
% 129.98/18.20 | e0, simplifying with (157), (174) gives:
% 129.98/18.20 | (246) all_54_14 = all_52_11
% 129.98/18.20 |
% 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_52_7, all_54_13, e2, e0,
% 129.98/18.20 | simplifying with (158), (175) gives:
% 129.98/18.20 | (247) all_54_13 = all_52_7
% 129.98/18.20 |
% 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_52_3, all_54_12, e3, e0,
% 129.98/18.20 | simplifying with (159), (176) gives:
% 129.98/18.20 | (248) all_54_12 = all_52_3
% 129.98/18.20 |
% 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_52_14, all_54_11, e0,
% 129.98/18.20 | e1, simplifying with (160), (177) gives:
% 129.98/18.20 | (249) all_54_11 = all_52_14
% 129.98/18.20 |
% 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_46_2, all_52_10, e1, e1,
% 129.98/18.20 | simplifying with (99), (161) gives:
% 129.98/18.20 | (250) all_52_10 = all_46_2
% 129.98/18.20 |
% 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_36_2, all_52_10, e1, e1,
% 129.98/18.20 | simplifying with (84), (161) gives:
% 129.98/18.20 | (251) all_52_10 = all_36_2
% 129.98/18.20 |
% 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_28_2, all_52_10, e1, e1,
% 129.98/18.20 | simplifying with (72), (161) gives:
% 129.98/18.20 | (252) all_52_10 = all_28_2
% 129.98/18.20 |
% 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_6_2, all_52_10, e1, e1,
% 129.98/18.20 | simplifying with (39), (161) gives:
% 129.98/18.20 | (253) all_52_10 = all_6_2
% 129.98/18.20 |
% 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_52_10, all_54_10, e1,
% 129.98/18.20 | e1, simplifying with (161), (178) gives:
% 129.98/18.20 | (254) all_54_10 = all_52_10
% 129.98/18.20 |
% 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_40_2, all_54_10, e1, e1,
% 129.98/18.20 | simplifying with (90), (178) gives:
% 129.98/18.20 | (255) all_54_10 = all_40_2
% 129.98/18.20 |
% 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_18_2, all_54_10, e1, e1,
% 129.98/18.20 | simplifying with (57), (178) gives:
% 129.98/18.20 | (256) all_54_10 = all_18_2
% 129.98/18.20 |
% 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_52_6, all_54_9, e2, e1,
% 129.98/18.20 | simplifying with (162), (179) gives:
% 129.98/18.20 | (257) all_54_9 = all_52_6
% 129.98/18.20 |
% 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_52_2, all_54_8, e3, e1,
% 129.98/18.20 | simplifying with (163), (180) gives:
% 129.98/18.20 | (258) all_54_8 = all_52_2
% 129.98/18.20 |
% 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_52_13, all_54_7, e0, e2,
% 129.98/18.20 | simplifying with (164), (181) gives:
% 129.98/18.20 | (259) all_54_7 = all_52_13
% 129.98/18.20 |
% 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_52_9, all_54_6, e1, e2,
% 129.98/18.21 | simplifying with (165), (182) gives:
% 129.98/18.21 | (260) all_54_6 = all_52_9
% 129.98/18.21 |
% 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_14_2, all_22_2, e2, e2,
% 129.98/18.21 | simplifying with (51), (63) gives:
% 129.98/18.21 | (261) all_22_2 = all_14_2
% 129.98/18.21 |
% 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_22_2, all_30_2, e2, e2,
% 129.98/18.21 | simplifying with (63), (75) gives:
% 129.98/18.21 | (262) all_30_2 = all_22_2
% 129.98/18.21 |
% 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_30_2, all_42_2, e2, e2,
% 129.98/18.21 | simplifying with (75), (93) gives:
% 129.98/18.21 | (263) all_42_2 = all_30_2
% 129.98/18.21 |
% 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_48_2, all_52_5, e2, e2,
% 129.98/18.21 | simplifying with (102), (166) gives:
% 129.98/18.21 | (264) all_52_5 = all_48_2
% 129.98/18.21 |
% 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_42_2, all_52_5, e2, e2,
% 129.98/18.21 | simplifying with (93), (166) gives:
% 129.98/18.21 | (265) all_52_5 = all_42_2
% 129.98/18.21 |
% 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_52_5, all_54_5, e2, e2,
% 129.98/18.21 | simplifying with (166), (183) gives:
% 129.98/18.21 | (266) all_54_5 = all_52_5
% 129.98/18.21 |
% 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_8_2, all_54_5, e2, e2,
% 129.98/18.21 | simplifying with (42), (183) gives:
% 129.98/18.21 | (267) all_54_5 = all_8_2
% 129.98/18.21 |
% 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_52_1, all_54_4, e3, e2,
% 129.98/18.21 | simplifying with (167), (184) gives:
% 129.98/18.21 | (268) all_54_4 = all_52_1
% 129.98/18.21 |
% 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_52_12, all_54_3, e0, e3,
% 129.98/18.21 | simplifying with (168), (185) gives:
% 129.98/18.21 | (269) all_54_3 = all_52_12
% 129.98/18.21 |
% 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_52_8, all_54_2, e1, e3,
% 129.98/18.21 | simplifying with (169), (186) gives:
% 129.98/18.21 | (270) all_54_2 = all_52_8
% 129.98/18.21 |
% 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_52_4, all_54_1, e2, e3,
% 129.98/18.21 | simplifying with (170), (187) gives:
% 129.98/18.21 | (271) all_54_1 = all_52_4
% 129.98/18.21 |
% 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_32_2, all_38_2, e3, e3,
% 129.98/18.21 | simplifying with (78), (87) gives:
% 129.98/18.21 | (272) all_38_2 = all_32_2
% 129.98/18.21 |
% 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_24_2, all_38_2, e3, e3,
% 129.98/18.21 | simplifying with (66), (87) gives:
% 129.98/18.21 | (273) all_38_2 = all_24_2
% 129.98/18.21 |
% 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_38_2, all_50_2, e3, e3,
% 129.98/18.21 | simplifying with (87), (105) gives:
% 129.98/18.21 | (274) all_50_2 = all_38_2
% 129.98/18.21 |
% 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_38_2, all_52_0, e3, e3,
% 129.98/18.21 | simplifying with (87), (171) gives:
% 129.98/18.21 | (275) all_52_0 = all_38_2
% 129.98/18.21 |
% 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_16_2, all_52_0, e3, e3,
% 129.98/18.21 | simplifying with (54), (171) gives:
% 129.98/18.21 | (276) all_52_0 = all_16_2
% 129.98/18.21 |
% 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_50_2, all_54_0, e3, e3,
% 129.98/18.21 | simplifying with (105), (188) gives:
% 129.98/18.21 | (277) all_54_0 = all_50_2
% 129.98/18.21 |
% 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_10_2, all_54_0, e3, e3,
% 129.98/18.21 | simplifying with (45), (188) gives:
% 129.98/18.21 | (278) all_54_0 = all_10_2
% 129.98/18.21 |
% 129.98/18.21 | COMBINE_EQS: (277), (278) imply:
% 129.98/18.21 | (279) all_50_2 = all_10_2
% 129.98/18.21 |
% 129.98/18.21 | SIMP: (279) implies:
% 129.98/18.21 | (280) all_50_2 = all_10_2
% 129.98/18.21 |
% 129.98/18.21 | COMBINE_EQS: (266), (267) imply:
% 129.98/18.21 | (281) all_52_5 = all_8_2
% 129.98/18.21 |
% 129.98/18.21 | SIMP: (281) implies:
% 129.98/18.21 | (282) all_52_5 = all_8_2
% 129.98/18.21 |
% 129.98/18.21 | COMBINE_EQS: (255), (256) imply:
% 129.98/18.21 | (283) all_40_2 = all_18_2
% 129.98/18.21 |
% 129.98/18.21 | COMBINE_EQS: (254), (255) imply:
% 129.98/18.21 | (284) all_52_10 = all_40_2
% 129.98/18.21 |
% 129.98/18.21 | SIMP: (284) implies:
% 129.98/18.21 | (285) all_52_10 = all_40_2
% 129.98/18.21 |
% 129.98/18.21 | COMBINE_EQS: (244), (245) imply:
% 129.98/18.21 | (286) all_52_15 = all_4_2
% 129.98/18.21 |
% 129.98/18.21 | SIMP: (286) implies:
% 129.98/18.21 | (287) all_52_15 = all_4_2
% 129.98/18.21 |
% 129.98/18.21 | COMBINE_EQS: (275), (276) imply:
% 129.98/18.21 | (288) all_38_2 = all_16_2
% 129.98/18.21 |
% 129.98/18.21 | SIMP: (288) implies:
% 129.98/18.21 | (289) all_38_2 = all_16_2
% 129.98/18.21 |
% 129.98/18.21 | COMBINE_EQS: (264), (265) imply:
% 129.98/18.21 | (290) all_48_2 = all_42_2
% 129.98/18.21 |
% 129.98/18.21 | COMBINE_EQS: (264), (282) imply:
% 129.98/18.21 | (291) all_48_2 = all_8_2
% 129.98/18.21 |
% 129.98/18.21 | COMBINE_EQS: (250), (251) imply:
% 129.98/18.21 | (292) all_46_2 = all_36_2
% 129.98/18.21 |
% 129.98/18.21 | COMBINE_EQS: (250), (252) imply:
% 129.98/18.21 | (293) all_46_2 = all_28_2
% 129.98/18.21 |
% 129.98/18.21 | COMBINE_EQS: (250), (285) imply:
% 129.98/18.21 | (294) all_46_2 = all_40_2
% 129.98/18.21 |
% 129.98/18.21 | COMBINE_EQS: (250), (253) imply:
% 129.98/18.21 | (295) all_46_2 = all_6_2
% 129.98/18.21 |
% 129.98/18.21 | COMBINE_EQS: (242), (243) imply:
% 129.98/18.21 | (296) all_44_2 = all_34_2
% 129.98/18.21 |
% 129.98/18.21 | COMBINE_EQS: (242), (287) imply:
% 129.98/18.21 | (297) all_44_2 = all_4_2
% 129.98/18.21 |
% 129.98/18.21 | COMBINE_EQS: (274), (280) imply:
% 129.98/18.21 | (298) all_38_2 = all_10_2
% 129.98/18.21 |
% 129.98/18.21 | SIMP: (298) implies:
% 129.98/18.21 | (299) all_38_2 = all_10_2
% 129.98/18.21 |
% 129.98/18.21 | COMBINE_EQS: (290), (291) imply:
% 129.98/18.21 | (300) all_42_2 = all_8_2
% 129.98/18.21 |
% 129.98/18.21 | SIMP: (300) implies:
% 129.98/18.21 | (301) all_42_2 = all_8_2
% 129.98/18.21 |
% 129.98/18.21 | COMBINE_EQS: (292), (295) imply:
% 129.98/18.21 | (302) all_36_2 = all_6_2
% 129.98/18.21 |
% 129.98/18.21 | COMBINE_EQS: (292), (293) imply:
% 129.98/18.21 | (303) all_36_2 = all_28_2
% 129.98/18.21 |
% 129.98/18.21 | COMBINE_EQS: (292), (294) imply:
% 129.98/18.21 | (304) all_40_2 = all_36_2
% 129.98/18.21 |
% 129.98/18.21 | SIMP: (304) implies:
% 129.98/18.21 | (305) all_40_2 = all_36_2
% 129.98/18.21 |
% 129.98/18.21 | COMBINE_EQS: (296), (297) imply:
% 129.98/18.21 | (306) all_34_2 = all_4_2
% 129.98/18.21 |
% 129.98/18.21 | SIMP: (306) implies:
% 129.98/18.21 | (307) all_34_2 = all_4_2
% 129.98/18.21 |
% 129.98/18.21 | COMBINE_EQS: (263), (301) imply:
% 129.98/18.21 | (308) all_30_2 = all_8_2
% 129.98/18.21 |
% 129.98/18.21 | SIMP: (308) implies:
% 129.98/18.21 | (309) all_30_2 = all_8_2
% 129.98/18.21 |
% 129.98/18.21 | COMBINE_EQS: (283), (305) imply:
% 129.98/18.21 | (310) all_36_2 = all_18_2
% 129.98/18.21 |
% 129.98/18.21 | SIMP: (310) implies:
% 129.98/18.21 | (311) all_36_2 = all_18_2
% 129.98/18.21 |
% 129.98/18.21 | COMBINE_EQS: (272), (299) imply:
% 129.98/18.21 | (312) all_32_2 = all_10_2
% 129.98/18.21 |
% 129.98/18.21 | COMBINE_EQS: (272), (273) imply:
% 129.98/18.21 | (313) all_32_2 = all_24_2
% 129.98/18.21 |
% 129.98/18.21 | COMBINE_EQS: (272), (289) imply:
% 129.98/18.21 | (314) all_32_2 = all_16_2
% 129.98/18.21 |
% 129.98/18.21 | COMBINE_EQS: (303), (311) imply:
% 129.98/18.21 | (315) all_28_2 = all_18_2
% 129.98/18.21 |
% 129.98/18.21 | COMBINE_EQS: (302), (303) imply:
% 129.98/18.21 | (316) all_28_2 = all_6_2
% 129.98/18.21 |
% 129.98/18.21 | COMBINE_EQS: (241), (307) imply:
% 129.98/18.21 | (317) all_20_2 = all_4_2
% 129.98/18.21 |
% 129.98/18.21 | SIMP: (317) implies:
% 129.98/18.21 | (318) all_20_2 = all_4_2
% 129.98/18.21 |
% 129.98/18.21 | COMBINE_EQS: (312), (313) imply:
% 129.98/18.21 | (319) all_24_2 = all_10_2
% 129.98/18.21 |
% 129.98/18.21 | COMBINE_EQS: (313), (314) imply:
% 129.98/18.21 | (320) all_24_2 = all_16_2
% 129.98/18.21 |
% 129.98/18.21 | COMBINE_EQS: (262), (309) imply:
% 129.98/18.21 | (321) all_22_2 = all_8_2
% 129.98/18.21 |
% 129.98/18.22 | SIMP: (321) implies:
% 129.98/18.22 | (322) all_22_2 = all_8_2
% 129.98/18.22 |
% 129.98/18.22 | COMBINE_EQS: (315), (316) imply:
% 129.98/18.22 | (323) all_18_2 = all_6_2
% 129.98/18.22 |
% 129.98/18.22 | SIMP: (323) implies:
% 129.98/18.22 | (324) all_18_2 = all_6_2
% 129.98/18.22 |
% 129.98/18.22 | COMBINE_EQS: (239), (240) imply:
% 129.98/18.22 | (325) all_20_2 = all_12_2
% 129.98/18.22 |
% 129.98/18.22 | SIMP: (325) implies:
% 129.98/18.22 | (326) all_20_2 = all_12_2
% 129.98/18.22 |
% 129.98/18.22 | COMBINE_EQS: (319), (320) imply:
% 129.98/18.22 | (327) all_16_2 = all_10_2
% 129.98/18.22 |
% 129.98/18.22 | COMBINE_EQS: (261), (322) imply:
% 129.98/18.22 | (328) all_14_2 = all_8_2
% 129.98/18.22 |
% 129.98/18.22 | SIMP: (328) implies:
% 129.98/18.22 | (329) all_14_2 = all_8_2
% 129.98/18.22 |
% 129.98/18.22 | COMBINE_EQS: (318), (326) imply:
% 129.98/18.22 | (330) all_12_2 = all_4_2
% 129.98/18.22 |
% 129.98/18.22 | COMBINE_EQS: (240), (330) imply:
% 129.98/18.22 | (331) all_26_2 = all_4_2
% 129.98/18.22 |
% 129.98/18.22 | COMBINE_EQS: (283), (324) imply:
% 129.98/18.22 | (332) all_40_2 = all_6_2
% 129.98/18.22 |
% 129.98/18.22 | COMBINE_EQS: (276), (327) imply:
% 129.98/18.22 | (333) all_52_0 = all_10_2
% 129.98/18.22 |
% 129.98/18.22 | COMBINE_EQS: (255), (332) imply:
% 129.98/18.22 | (334) all_54_10 = all_6_2
% 129.98/18.22 |
% 129.98/18.22 | REDUCE: (155), (333) imply:
% 129.98/18.22 | (335) ~ (all_52_1 = all_10_2)
% 129.98/18.22 |
% 129.98/18.22 | SIMP: (335) implies:
% 129.98/18.22 | (336) ~ (all_52_1 = all_10_2)
% 129.98/18.22 |
% 129.98/18.22 | REDUCE: (154), (333) imply:
% 129.98/18.22 | (337) ~ (all_52_2 = all_10_2)
% 129.98/18.22 |
% 129.98/18.22 | SIMP: (337) implies:
% 129.98/18.22 | (338) ~ (all_52_2 = all_10_2)
% 129.98/18.22 |
% 129.98/18.22 | REDUCE: (153), (333) imply:
% 129.98/18.22 | (339) ~ (all_52_3 = all_10_2)
% 129.98/18.22 |
% 129.98/18.22 | SIMP: (339) implies:
% 129.98/18.22 | (340) ~ (all_52_3 = all_10_2)
% 129.98/18.22 |
% 129.98/18.22 | REDUCE: (152), (333) imply:
% 129.98/18.22 | (341) ~ (all_52_4 = all_10_2)
% 129.98/18.22 |
% 129.98/18.22 | SIMP: (341) implies:
% 129.98/18.22 | (342) ~ (all_52_4 = all_10_2)
% 129.98/18.22 |
% 129.98/18.22 | REDUCE: (151), (333) imply:
% 129.98/18.22 | (343) ~ (all_52_8 = all_10_2)
% 129.98/18.22 |
% 129.98/18.22 | SIMP: (343) implies:
% 129.98/18.22 | (344) ~ (all_52_8 = all_10_2)
% 129.98/18.22 |
% 129.98/18.22 | REDUCE: (150), (333) imply:
% 129.98/18.22 | (345) ~ (all_52_12 = all_10_2)
% 129.98/18.22 |
% 129.98/18.22 | SIMP: (345) implies:
% 129.98/18.22 | (346) ~ (all_52_12 = all_10_2)
% 129.98/18.22 |
% 129.98/18.22 | REDUCE: (147), (282) imply:
% 129.98/18.22 | (347) ~ (all_52_1 = all_8_2)
% 129.98/18.22 |
% 129.98/18.22 | REDUCE: (142), (253) imply:
% 129.98/18.22 | (348) ~ (all_52_2 = all_6_2)
% 129.98/18.22 |
% 129.98/18.22 | REDUCE: (138), (287) imply:
% 129.98/18.22 | (349) ~ (all_52_3 = all_4_2)
% 129.98/18.22 |
% 129.98/18.22 | REDUCE: (137), (282) imply:
% 129.98/18.22 | (350) ~ (all_52_4 = all_8_2)
% 129.98/18.22 |
% 129.98/18.22 | REDUCE: (132), (282) imply:
% 129.98/18.22 | (351) ~ (all_52_6 = all_8_2)
% 129.98/18.22 |
% 129.98/18.22 | SIMP: (351) implies:
% 129.98/18.22 | (352) ~ (all_52_6 = all_8_2)
% 129.98/18.22 |
% 129.98/18.22 | REDUCE: (131), (282) imply:
% 129.98/18.22 | (353) ~ (all_52_7 = all_8_2)
% 129.98/18.22 |
% 129.98/18.22 | SIMP: (353) implies:
% 129.98/18.22 | (354) ~ (all_52_7 = all_8_2)
% 129.98/18.22 |
% 129.98/18.22 | REDUCE: (130), (282) imply:
% 129.98/18.22 | (355) ~ (all_52_9 = all_8_2)
% 129.98/18.22 |
% 129.98/18.22 | SIMP: (355) implies:
% 129.98/18.22 | (356) ~ (all_52_9 = all_8_2)
% 129.98/18.22 |
% 129.98/18.22 | REDUCE: (129), (282) imply:
% 129.98/18.22 | (357) ~ (all_52_13 = all_8_2)
% 129.98/18.22 |
% 129.98/18.22 | SIMP: (357) implies:
% 129.98/18.22 | (358) ~ (all_52_13 = all_8_2)
% 129.98/18.22 |
% 129.98/18.22 | REDUCE: (127), (253) imply:
% 129.98/18.22 | (359) ~ (all_52_6 = all_6_2)
% 129.98/18.22 |
% 129.98/18.22 | REDUCE: (124), (287) imply:
% 129.98/18.22 | (360) ~ (all_52_7 = all_4_2)
% 129.98/18.22 |
% 129.98/18.22 | REDUCE: (122), (253) imply:
% 129.98/18.22 | (361) ~ (all_52_8 = all_6_2)
% 129.98/18.22 |
% 129.98/18.22 | REDUCE: (119), (253) imply:
% 129.98/18.22 | (362) ~ (all_52_9 = all_6_2)
% 129.98/18.22 |
% 129.98/18.22 | REDUCE: (116), (253) imply:
% 129.98/18.22 | (363) ~ (all_52_11 = all_6_2)
% 129.98/18.22 |
% 129.98/18.22 | SIMP: (363) implies:
% 129.98/18.22 | (364) ~ (all_52_11 = all_6_2)
% 129.98/18.22 |
% 129.98/18.22 | REDUCE: (115), (253) imply:
% 129.98/18.22 | (365) ~ (all_52_14 = all_6_2)
% 129.98/18.22 |
% 129.98/18.22 | SIMP: (365) implies:
% 129.98/18.22 | (366) ~ (all_52_14 = all_6_2)
% 129.98/18.22 |
% 129.98/18.22 | REDUCE: (114), (287) imply:
% 129.98/18.22 | (367) ~ (all_52_11 = all_4_2)
% 129.98/18.22 |
% 129.98/18.22 | REDUCE: (111), (287) imply:
% 129.98/18.22 | (368) ~ (all_52_12 = all_4_2)
% 129.98/18.22 |
% 129.98/18.22 | REDUCE: (109), (287) imply:
% 129.98/18.22 | (369) ~ (all_52_13 = all_4_2)
% 129.98/18.22 |
% 129.98/18.22 | REDUCE: (108), (287) imply:
% 129.98/18.22 | (370) ~ (all_52_14 = all_4_2)
% 129.98/18.22 |
% 129.98/18.22 | BETA: splitting (37) gives:
% 129.98/18.22 |
% 129.98/18.22 | Case 1:
% 129.98/18.22 | |
% 129.98/18.22 | | (371) ~ (all_4_2 = e1)
% 129.98/18.22 | |
% 129.98/18.22 | | BETA: splitting (40) gives:
% 129.98/18.22 | |
% 129.98/18.22 | | Case 1:
% 129.98/18.22 | | |
% 129.98/18.22 | | | (372) ~ (all_6_2 = e2)
% 129.98/18.22 | | |
% 129.98/18.22 | | | BETA: splitting (43) gives:
% 129.98/18.22 | | |
% 129.98/18.22 | | | Case 1:
% 129.98/18.22 | | | |
% 129.98/18.22 | | | | (373) ~ (all_8_2 = e1)
% 129.98/18.22 | | | |
% 129.98/18.22 | | | | BETA: splitting (46) gives:
% 129.98/18.22 | | | |
% 129.98/18.22 | | | | Case 1:
% 129.98/18.22 | | | | |
% 129.98/18.22 | | | | | (374) ~ (all_10_2 = e0)
% 129.98/18.22 | | | | |
% 129.98/18.22 | | | | | BETA: splitting (52) gives:
% 129.98/18.22 | | | | |
% 129.98/18.22 | | | | | Case 1:
% 129.98/18.22 | | | | | |
% 129.98/18.22 | | | | | | (375) ~ (all_14_2 = e3)
% 129.98/18.22 | | | | | |
% 129.98/18.22 | | | | | | REDUCE: (329), (375) imply:
% 129.98/18.22 | | | | | | (376) ~ (all_8_2 = e3)
% 129.98/18.22 | | | | | |
% 129.98/18.22 | | | | | | BETA: splitting (55) gives:
% 129.98/18.22 | | | | | |
% 129.98/18.22 | | | | | | Case 1:
% 129.98/18.22 | | | | | | |
% 129.98/18.22 | | | | | | | (377) ~ (all_16_2 = e2)
% 129.98/18.22 | | | | | | |
% 129.98/18.22 | | | | | | | REDUCE: (327), (377) imply:
% 129.98/18.22 | | | | | | | (378) ~ (all_10_2 = e2)
% 129.98/18.22 | | | | | | |
% 129.98/18.22 | | | | | | | BETA: splitting (61) gives:
% 129.98/18.22 | | | | | | |
% 129.98/18.22 | | | | | | | Case 1:
% 129.98/18.22 | | | | | | | |
% 129.98/18.22 | | | | | | | | (379) ~ (all_20_2 = e2)
% 129.98/18.22 | | | | | | | |
% 129.98/18.22 | | | | | | | | REDUCE: (318), (379) imply:
% 129.98/18.22 | | | | | | | | (380) ~ (all_4_2 = e2)
% 129.98/18.22 | | | | | | | |
% 129.98/18.22 | | | | | | | | BETA: splitting (73) gives:
% 129.98/18.22 | | | | | | | |
% 129.98/18.22 | | | | | | | | Case 1:
% 129.98/18.22 | | | | | | | | |
% 129.98/18.22 | | | | | | | | | (381) ~ (all_28_2 = e3)
% 129.98/18.22 | | | | | | | | |
% 129.98/18.22 | | | | | | | | | REDUCE: (316), (381) imply:
% 129.98/18.22 | | | | | | | | | (382) ~ (all_6_2 = e3)
% 129.98/18.22 | | | | | | | | |
% 129.98/18.22 | | | | | | | | | BETA: splitting (76) gives:
% 129.98/18.22 | | | | | | | | |
% 129.98/18.22 | | | | | | | | | Case 1:
% 129.98/18.22 | | | | | | | | | |
% 129.98/18.22 | | | | | | | | | | (383) ~ (all_30_2 = e0)
% 129.98/18.22 | | | | | | | | | |
% 129.98/18.22 | | | | | | | | | | REDUCE: (309), (383) imply:
% 129.98/18.22 | | | | | | | | | | (384) ~ (all_8_2 = e0)
% 129.98/18.22 | | | | | | | | | |
% 129.98/18.22 | | | | | | | | | | BETA: splitting (199) gives:
% 129.98/18.22 | | | | | | | | | |
% 129.98/18.22 | | | | | | | | | | Case 1:
% 129.98/18.22 | | | | | | | | | | |
% 129.98/18.22 | | | | | | | | | | | (385) all_54_5 = e3
% 129.98/18.22 | | | | | | | | | | |
% 129.98/18.22 | | | | | | | | | | | COMBINE_EQS: (267), (385) imply:
% 129.98/18.22 | | | | | | | | | | | (386) all_8_2 = e3
% 129.98/18.22 | | | | | | | | | | |
% 129.98/18.22 | | | | | | | | | | | REDUCE: (376), (386) imply:
% 129.98/18.22 | | | | | | | | | | | (387) $false
% 129.98/18.23 | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | CLOSE: (387) is inconsistent.
% 129.98/18.23 | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | Case 2:
% 129.98/18.23 | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | (388) ~ (all_54_5 = e3)
% 129.98/18.23 | | | | | | | | | | | (389) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 129.98/18.23 | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | BETA: splitting (389) gives:
% 129.98/18.23 | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | Case 1:
% 129.98/18.23 | | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | | (390) all_54_5 = e2
% 129.98/18.23 | | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | | COMBINE_EQS: (267), (390) imply:
% 129.98/18.23 | | | | | | | | | | | | (391) all_8_2 = e2
% 129.98/18.23 | | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | | REDUCE: (347), (391) imply:
% 129.98/18.23 | | | | | | | | | | | | (392) ~ (all_52_1 = e2)
% 129.98/18.23 | | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | | REDUCE: (350), (391) imply:
% 129.98/18.23 | | | | | | | | | | | | (393) ~ (all_52_4 = e2)
% 129.98/18.23 | | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | | REDUCE: (356), (391) imply:
% 129.98/18.23 | | | | | | | | | | | | (394) ~ (all_52_9 = e2)
% 129.98/18.23 | | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | | REDUCE: (358), (391) imply:
% 129.98/18.23 | | | | | | | | | | | | (395) ~ (all_52_13 = e2)
% 129.98/18.23 | | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | | REDUCE: (376), (391) imply:
% 129.98/18.23 | | | | | | | | | | | | (396) ~ (e3 = e2)
% 129.98/18.23 | | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | | BETA: splitting (225) gives:
% 129.98/18.23 | | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | | Case 1:
% 129.98/18.23 | | | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | | | (397) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 129.98/18.23 | | | | | | | | | | | | | & op(e2, e2) = e2)
% 129.98/18.23 | | | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | | | BETA: splitting (397) gives:
% 129.98/18.23 | | | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | | | Case 1:
% 129.98/18.23 | | | | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | | | | (398) all_57_2 = e2 & op(e2, e3) = e2
% 129.98/18.23 | | | | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | | | | ALPHA: (398) implies:
% 129.98/18.23 | | | | | | | | | | | | | | (399) op(e2, e3) = e2
% 129.98/18.23 | | | | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | | | | REF_CLOSE: (167), (392), (399), (function-axioms) are
% 129.98/18.23 | | | | | | | | | | | | | | inconsistent by sub-proof #779.
% 129.98/18.23 | | | | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | | | Case 2:
% 129.98/18.23 | | | | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | | | | (400) all_57_3 = e2 & op(e2, e2) = e2
% 129.98/18.23 | | | | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | | | | ALPHA: (400) implies:
% 129.98/18.23 | | | | | | | | | | | | | | (401) all_57_3 = e2
% 129.98/18.23 | | | | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 129.98/18.23 | | | | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | | | | Case 1:
% 129.98/18.23 | | | | | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | | | | | (402) ~ (all_32_2 = e1)
% 129.98/18.23 | | | | | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | | | | | REDUCE: (312), (402) imply:
% 129.98/18.23 | | | | | | | | | | | | | | | (403) ~ (all_10_2 = e1)
% 129.98/18.23 | | | | | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 129.98/18.23 | | | | | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | | | | | Case 1:
% 129.98/18.23 | | | | | | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | | | | | | (404) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 129.98/18.23 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 129.98/18.23 | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 129.98/18.23 | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 129.98/18.23 | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 129.98/18.23 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 129.98/18.23 | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 129.98/18.23 | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 129.98/18.23 | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 129.98/18.23 | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 129.98/18.23 | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 129.98/18.23 | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 129.98/18.23 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 129.98/18.23 | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 129.98/18.23 | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 129.98/18.23 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 129.98/18.23 | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 129.98/18.23 | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 129.98/18.23 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 129.98/18.23 | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 129.98/18.23 | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 129.98/18.23 | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 129.98/18.23 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 129.98/18.23 | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 129.98/18.23 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 129.98/18.23 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 129.98/18.23 | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 129.98/18.23 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 129.98/18.23 | | | | | | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | | | | | | BETA: splitting (404) gives:
% 129.98/18.23 | | | | | | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.23 | | | | | | | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | | | | | | | (405) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 129.98/18.23 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 129.98/18.23 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 129.98/18.23 | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 129.98/18.23 | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 129.98/18.23 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 129.98/18.23 | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 129.98/18.23 | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 129.98/18.23 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 129.98/18.23 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 129.98/18.23 | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 129.98/18.23 | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 129.98/18.23 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 129.98/18.23 | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 129.98/18.23 | | | | | | | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | | | | | | | BETA: splitting (405) gives:
% 129.98/18.23 | | | | | | | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.23 | | | | | | | | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | | | | | | | | (406) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 129.98/18.23 | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 129.98/18.23 | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 129.98/18.23 | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 129.98/18.23 | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 129.98/18.23 | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 129.98/18.23 | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 129.98/18.23 | | | | | | | | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | | | | | | | | ALPHA: (406) implies:
% 129.98/18.23 | | | | | | | | | | | | | | | | | | (407) op(e3, e3) = e2
% 129.98/18.23 | | | | | | | | | | | | | | | | | |
% 129.98/18.23 | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (204), (278), (374), (378), (403), (407),
% 129.98/18.23 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 129.98/18.23 | | | | | | | | | | | | | | | | | | #776.
% 129.98/18.23 | | | | | | | | | | | | | | | | | |
% 129.98/18.24 | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.24 | | | | | | | | | | | | | | | | | |
% 129.98/18.24 | | | | | | | | | | | | | | | | | | (408) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 129.98/18.24 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 129.98/18.24 | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 129.98/18.24 | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 129.98/18.24 | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 129.98/18.24 | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 129.98/18.24 | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 129.98/18.24 | | | | | | | | | | | | | | | | | |
% 129.98/18.24 | | | | | | | | | | | | | | | | | | ALPHA: (408) implies:
% 129.98/18.24 | | | | | | | | | | | | | | | | | | (409) op(e3, e3) = e1
% 129.98/18.24 | | | | | | | | | | | | | | | | | |
% 129.98/18.24 | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (204), (278), (374), (378), (403), (409),
% 129.98/18.24 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 129.98/18.24 | | | | | | | | | | | | | | | | | | #774.
% 129.98/18.24 | | | | | | | | | | | | | | | | | |
% 129.98/18.24 | | | | | | | | | | | | | | | | | End of split
% 129.98/18.24 | | | | | | | | | | | | | | | | |
% 129.98/18.24 | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.24 | | | | | | | | | | | | | | | | |
% 129.98/18.24 | | | | | | | | | | | | | | | | | (410) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 129.98/18.24 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 129.98/18.24 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 129.98/18.24 | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 129.98/18.24 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 129.98/18.24 | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 129.98/18.24 | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 129.98/18.24 | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 129.98/18.24 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 129.98/18.24 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 129.98/18.24 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 129.98/18.24 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 129.98/18.24 | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 129.98/18.24 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 129.98/18.24 | | | | | | | | | | | | | | | | |
% 129.98/18.24 | | | | | | | | | | | | | | | | | BETA: splitting (410) gives:
% 129.98/18.24 | | | | | | | | | | | | | | | | |
% 129.98/18.24 | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.24 | | | | | | | | | | | | | | | | | |
% 129.98/18.24 | | | | | | | | | | | | | | | | | | (411) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 129.98/18.24 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 129.98/18.24 | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3,
% 129.98/18.24 | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 129.98/18.24 | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 129.98/18.24 | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 129.98/18.24 | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 129.98/18.24 | | | | | | | | | | | | | | | | | |
% 129.98/18.24 | | | | | | | | | | | | | | | | | | ALPHA: (411) implies:
% 129.98/18.24 | | | | | | | | | | | | | | | | | | (412) op(e3, e3) = e0
% 129.98/18.24 | | | | | | | | | | | | | | | | | |
% 129.98/18.24 | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (204), (278), (374), (378), (403), (412),
% 129.98/18.24 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 129.98/18.24 | | | | | | | | | | | | | | | | | | #772.
% 129.98/18.24 | | | | | | | | | | | | | | | | | |
% 129.98/18.24 | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.24 | | | | | | | | | | | | | | | | | |
% 129.98/18.24 | | | | | | | | | | | | | | | | | | (413) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 129.98/18.24 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 129.98/18.24 | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 129.98/18.24 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 129.98/18.24 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2,
% 129.98/18.24 | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 129.98/18.24 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 129.98/18.24 | | | | | | | | | | | | | | | | | |
% 129.98/18.24 | | | | | | | | | | | | | | | | | | ALPHA: (413) implies:
% 129.98/18.24 | | | | | | | | | | | | | | | | | | (414) op(e2, e3) = e2
% 129.98/18.24 | | | | | | | | | | | | | | | | | |
% 129.98/18.24 | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (392), (414), (function-axioms) are
% 129.98/18.24 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #779.
% 129.98/18.24 | | | | | | | | | | | | | | | | | |
% 129.98/18.24 | | | | | | | | | | | | | | | | | End of split
% 129.98/18.24 | | | | | | | | | | | | | | | | |
% 129.98/18.24 | | | | | | | | | | | | | | | | End of split
% 129.98/18.24 | | | | | | | | | | | | | | | |
% 129.98/18.24 | | | | | | | | | | | | | | | Case 2:
% 129.98/18.24 | | | | | | | | | | | | | | | |
% 129.98/18.24 | | | | | | | | | | | | | | | | (415) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 129.98/18.24 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 129.98/18.24 | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 129.98/18.24 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 129.98/18.24 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 129.98/18.24 | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 129.98/18.24 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 129.98/18.24 | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 129.98/18.24 | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 129.98/18.24 | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 129.98/18.24 | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 129.98/18.24 | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 129.98/18.24 | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 129.98/18.24 | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 129.98/18.24 | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 129.98/18.24 | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 129.98/18.24 | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 129.98/18.24 | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 129.98/18.24 | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 129.98/18.24 | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 129.98/18.24 | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 129.98/18.24 | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 129.98/18.24 | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 129.98/18.24 | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 129.98/18.24 | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 129.98/18.24 | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 129.98/18.24 | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 129.98/18.24 | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 129.98/18.24 | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 129.98/18.24 | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 129.98/18.24 | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 129.98/18.24 | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 129.98/18.24 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 129.98/18.24 | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 129.98/18.24 | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 129.98/18.24 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 129.98/18.24 | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 129.98/18.24 | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 129.98/18.24 | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 129.98/18.24 | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 129.98/18.24 | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 129.98/18.24 | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 129.98/18.24 | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 129.98/18.24 | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 129.98/18.24 | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 129.98/18.24 | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 129.98/18.24 | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 129.98/18.24 | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 129.98/18.24 | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 129.98/18.24 | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 129.98/18.24 | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 129.98/18.24 | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 129.98/18.24 | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 129.98/18.24 | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 129.98/18.24 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 129.98/18.24 | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 129.98/18.24 | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 129.98/18.24 | | | | | | | | | | | | | | | |
% 129.98/18.24 | | | | | | | | | | | | | | | | BETA: splitting (415) gives:
% 129.98/18.24 | | | | | | | | | | | | | | | |
% 129.98/18.24 | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.24 | | | | | | | | | | | | | | | | |
% 129.98/18.24 | | | | | | | | | | | | | | | | | (416) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 129.98/18.24 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 129.98/18.24 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 129.98/18.24 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 129.98/18.24 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 129.98/18.24 | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 129.98/18.24 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 129.98/18.24 | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 129.98/18.24 | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 129.98/18.24 | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 129.98/18.24 | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 129.98/18.25 | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 129.98/18.25 | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 129.98/18.25 | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 129.98/18.25 | | | | | | | | | | | | | | | | |
% 129.98/18.25 | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (165), (382), (394), (416),
% 129.98/18.25 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 129.98/18.25 | | | | | | | | | | | | | | | | | #769.
% 129.98/18.25 | | | | | | | | | | | | | | | | |
% 129.98/18.25 | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.25 | | | | | | | | | | | | | | | | |
% 129.98/18.25 | | | | | | | | | | | | | | | | | (417) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 129.98/18.25 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 129.98/18.25 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 129.98/18.25 | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 129.98/18.25 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 129.98/18.25 | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 129.98/18.25 | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 129.98/18.25 | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 129.98/18.25 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 129.98/18.25 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 129.98/18.25 | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 129.98/18.25 | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 129.98/18.25 | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 129.98/18.25 | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 129.98/18.25 | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 129.98/18.25 | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 129.98/18.25 | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 129.98/18.25 | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 129.98/18.25 | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 129.98/18.25 | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 129.98/18.25 | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 129.98/18.25 | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 129.98/18.25 | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 129.98/18.25 | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 129.98/18.25 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 129.98/18.25 | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 129.98/18.25 | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 129.98/18.25 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 129.98/18.25 | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 129.98/18.25 | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 129.98/18.25 | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 129.98/18.25 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 129.98/18.25 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 129.98/18.25 | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 129.98/18.25 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 129.98/18.25 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 129.98/18.25 | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 129.98/18.25 | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 129.98/18.25 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 129.98/18.25 | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 129.98/18.25 | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 129.98/18.25 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 129.98/18.25 | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 129.98/18.25 | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 129.98/18.25 | | | | | | | | | | | | | | | | |
% 129.98/18.25 | | | | | | | | | | | | | | | | | BETA: splitting (417) gives:
% 129.98/18.25 | | | | | | | | | | | | | | | | |
% 129.98/18.25 | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.25 | | | | | | | | | | | | | | | | | |
% 129.98/18.25 | | | | | | | | | | | | | | | | | | (418) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 129.98/18.25 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 129.98/18.25 | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 129.98/18.25 | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 129.98/18.25 | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 129.98/18.25 | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 129.98/18.25 | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 129.98/18.25 | | | | | | | | | | | | | | | | | |
% 129.98/18.25 | | | | | | | | | | | | | | | | | | ALPHA: (418) implies:
% 129.98/18.25 | | | | | | | | | | | | | | | | | | (419) op(e2, e0) = e2
% 129.98/18.25 | | | | | | | | | | | | | | | | | |
% 129.98/18.25 | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (395), (419), (function-axioms) are
% 129.98/18.25 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 129.98/18.25 | | | | | | | | | | | | | | | | | |
% 129.98/18.25 | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.25 | | | | | | | | | | | | | | | | | |
% 129.98/18.25 | | | | | | | | | | | | | | | | | | (420) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 129.98/18.25 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 129.98/18.25 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 129.98/18.25 | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 129.98/18.25 | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 129.98/18.25 | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 129.98/18.25 | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 129.98/18.25 | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 129.98/18.25 | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 129.98/18.25 | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 129.98/18.25 | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 129.98/18.25 | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 129.98/18.25 | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 129.98/18.25 | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 129.98/18.25 | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 129.98/18.25 | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 129.98/18.25 | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 129.98/18.25 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 129.98/18.25 | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 129.98/18.25 | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 129.98/18.25 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 129.98/18.25 | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 129.98/18.25 | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 129.98/18.25 | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 129.98/18.25 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 129.98/18.25 | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 129.98/18.25 | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 129.98/18.25 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 129.98/18.25 | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 129.98/18.25 | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 129.98/18.25 | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 129.98/18.25 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 129.98/18.25 | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 129.98/18.25 | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 129.98/18.25 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 129.98/18.25 | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 129.98/18.25 | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 129.98/18.25 | | | | | | | | | | | | | | | | | |
% 129.98/18.25 | | | | | | | | | | | | | | | | | | BETA: splitting (420) gives:
% 129.98/18.25 | | | | | | | | | | | | | | | | | |
% 129.98/18.25 | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.25 | | | | | | | | | | | | | | | | | | |
% 129.98/18.25 | | | | | | | | | | | | | | | | | | | (421) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 129.98/18.25 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 129.98/18.25 | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 129.98/18.25 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 129.98/18.25 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 129.98/18.25 | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 129.98/18.25 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 129.98/18.25 | | | | | | | | | | | | | | | | | | |
% 129.98/18.25 | | | | | | | | | | | | | | | | | | | ALPHA: (421) implies:
% 129.98/18.25 | | | | | | | | | | | | | | | | | | | (422) op(e1, e1) = e2
% 129.98/18.25 | | | | | | | | | | | | | | | | | | |
% 129.98/18.25 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (422), (function-axioms) are
% 129.98/18.25 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 129.98/18.25 | | | | | | | | | | | | | | | | | | |
% 129.98/18.25 | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.25 | | | | | | | | | | | | | | | | | | |
% 129.98/18.25 | | | | | | | | | | | | | | | | | | | (423) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 129.98/18.25 | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 129.98/18.25 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 129.98/18.25 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 129.98/18.25 | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 129.98/18.25 | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 129.98/18.25 | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 129.98/18.25 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 129.98/18.25 | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 129.98/18.26 | | | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | ALPHA: (423) implies:
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | (424) op(e0, e0) = all_56_31
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | (425) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 129.98/18.26 | | | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (39), (45), (100), (118), (157), (160),
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | (163), (164), (165), (167), (189), (190), (204),
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | (218), (226), (245), (246), (278), (295), (336),
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | (338), (364), (369), (370), (371), (374), (378),
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | (380), (401), (403), (424), (425),
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | #744.
% 129.98/18.26 | | | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.26 | | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | | End of split
% 129.98/18.26 | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | End of split
% 129.98/18.26 | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | End of split
% 129.98/18.26 | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | Case 2:
% 129.98/18.26 | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | (426) all_32_2 = e1
% 129.98/18.26 | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | COMBINE_EQS: (312), (426) imply:
% 129.98/18.26 | | | | | | | | | | | | | | | (427) all_10_2 = e1
% 129.98/18.26 | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | SIMP: (427) implies:
% 129.98/18.26 | | | | | | | | | | | | | | | (428) all_10_2 = e1
% 129.98/18.26 | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | COMBINE_EQS: (280), (428) imply:
% 129.98/18.26 | | | | | | | | | | | | | | | (429) all_50_2 = e1
% 129.98/18.26 | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | REDUCE: (336), (428) imply:
% 129.98/18.26 | | | | | | | | | | | | | | | (430) ~ (all_52_1 = e1)
% 129.98/18.26 | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | REDUCE: (338), (428) imply:
% 129.98/18.26 | | | | | | | | | | | | | | | (431) ~ (all_52_2 = e1)
% 129.98/18.26 | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | REDUCE: (342), (428) imply:
% 129.98/18.26 | | | | | | | | | | | | | | | (432) ~ (all_52_4 = e1)
% 129.98/18.26 | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | REDUCE: (344), (428) imply:
% 129.98/18.26 | | | | | | | | | | | | | | | (433) ~ (all_52_8 = e1)
% 129.98/18.26 | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | REDUCE: (346), (428) imply:
% 129.98/18.26 | | | | | | | | | | | | | | | (434) ~ (all_52_12 = e1)
% 129.98/18.26 | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | REDUCE: (378), (428) imply:
% 129.98/18.26 | | | | | | | | | | | | | | | (435) ~ (e2 = e1)
% 129.98/18.26 | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | REDUCE: (45), (428) imply:
% 129.98/18.26 | | | | | | | | | | | | | | | (436) op(e3, e3) = e1
% 129.98/18.26 | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 129.98/18.26 | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | Case 1:
% 129.98/18.26 | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | (437) ~ (all_34_2 = e3)
% 129.98/18.26 | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | REDUCE: (307), (437) imply:
% 129.98/18.26 | | | | | | | | | | | | | | | | (438) ~ (all_4_2 = e3)
% 129.98/18.26 | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 129.98/18.26 | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.26 | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | | (439) all_54_15 = e3
% 129.98/18.26 | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (439) imply:
% 129.98/18.26 | | | | | | | | | | | | | | | | | (440) all_4_2 = e3
% 129.98/18.26 | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | | REDUCE: (438), (440) imply:
% 129.98/18.26 | | | | | | | | | | | | | | | | | (441) $false
% 129.98/18.26 | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | | CLOSE: (441) is inconsistent.
% 129.98/18.26 | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.26 | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | | (442) ~ (all_54_15 = e3)
% 129.98/18.26 | | | | | | | | | | | | | | | | | (443) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 129.98/18.26 | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | | BETA: splitting (443) gives:
% 129.98/18.26 | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.26 | | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | | | (444) all_54_15 = e2
% 129.98/18.26 | | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (444) imply:
% 129.98/18.26 | | | | | | | | | | | | | | | | | | (445) all_4_2 = e2
% 129.98/18.26 | | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | | | REDUCE: (380), (445) imply:
% 129.98/18.26 | | | | | | | | | | | | | | | | | | (446) $false
% 129.98/18.26 | | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | | | CLOSE: (446) is inconsistent.
% 129.98/18.26 | | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.26 | | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | | | (447) ~ (all_54_15 = e2)
% 129.98/18.26 | | | | | | | | | | | | | | | | | | (448) all_54_15 = e1 | all_54_15 = e0
% 129.98/18.26 | | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | | | BETA: splitting (448) gives:
% 129.98/18.26 | | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.26 | | | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | (449) all_54_15 = e1
% 129.98/18.26 | | | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (449) imply:
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | (450) all_4_2 = e1
% 129.98/18.26 | | | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | REDUCE: (371), (450) imply:
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | (451) $false
% 129.98/18.26 | | | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | CLOSE: (451) is inconsistent.
% 129.98/18.26 | | | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.26 | | | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | (452) all_54_15 = e0
% 129.98/18.26 | | | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (452) imply:
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | (453) all_4_2 = e0
% 129.98/18.26 | | | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | REDUCE: (438), (453) imply:
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | (454) ~ (e3 = e0)
% 129.98/18.26 | | | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | REDUCE: (380), (453) imply:
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | (455) ~ (e2 = e0)
% 129.98/18.26 | | | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | REDUCE: (371), (453) imply:
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | (456) ~ (e1 = e0)
% 129.98/18.26 | | | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | REDUCE: (36), (453) imply:
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | (457) op(e0, e0) = e0
% 129.98/18.26 | | | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 129.98/18.26 | | | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | | (458) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | | BETA: splitting (458) gives:
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | |
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.26 | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | (459) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (459) gives:
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (460) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (460) implies:
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (461) op(e3, e3) = e2
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (436), (461), (function-axioms) are
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743.
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (462) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (462) implies:
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (463) ~ (all_56_21 = e1)
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (464) ~ (all_56_5 = e3)
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (465) op(e1, e1) = all_56_21
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (466) op(e1, e3) = all_56_5
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (467) op(e3, e1) = e3
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | all_56_21, e1, e1, simplifying with (39), (465)
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | gives:
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (468) all_56_21 = all_6_2
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2,
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | all_56_5, e3, e1, simplifying with (163), (466)
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | gives:
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (469) all_56_5 = all_52_2
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e3,
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (169), (467) gives:
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (470) all_52_8 = e3
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (463), (468) imply:
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (471) ~ (all_6_2 = e1)
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (470) imply:
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (472) ~ (all_52_4 = e3)
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (470) imply:
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (473) ~ (all_52_12 = e3)
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | SIMP: (473) implies:
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (474) ~ (all_52_12 = e3)
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (470) imply:
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (475) ~ (all_6_2 = e3)
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (39), (106), (163), (168), (170),
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (194), (203), (216), (217), (218), (228), (230),
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (238), (271), (334), (372), (382), (393), (401),
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (429), (431), (432), (436), (464), (466), (471),
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (472), (474), (function-axioms) are inconsistent
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #718.
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | (476) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (167), (392), (436), (476), (function-axioms)
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #716.
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | |
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | |
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | (477) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | |
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (39), (164), (165), (372), (382),
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | (394), (395), (457), (477), (function-axioms) are
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #708.
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | |
% 129.98/18.27 | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.27 | | | | | | | | | | | | | | | | | | |
% 129.98/18.27 | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.27 | | | | | | | | | | | | | | | | | |
% 129.98/18.27 | | | | | | | | | | | | | | | | | End of split
% 129.98/18.27 | | | | | | | | | | | | | | | | |
% 129.98/18.27 | | | | | | | | | | | | | | | | End of split
% 129.98/18.27 | | | | | | | | | | | | | | | |
% 129.98/18.27 | | | | | | | | | | | | | | | Case 2:
% 129.98/18.27 | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | (478) all_34_2 = e3
% 129.98/18.28 | | | | | | | | | | | | | | | | (479) ( ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 &
% 129.98/18.28 | | | | | | | | | | | | | | | | $i(all_34_0)) | ( ~ (all_34_1 = e1) & op(e3, e3)
% 129.98/18.28 | | | | | | | | | | | | | | | | = all_34_1 & $i(all_34_1))
% 129.98/18.28 | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (478) imply:
% 129.98/18.28 | | | | | | | | | | | | | | | | (480) all_4_2 = e3
% 129.98/18.28 | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | SIMP: (480) implies:
% 129.98/18.28 | | | | | | | | | | | | | | | | (481) all_4_2 = e3
% 129.98/18.28 | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | REDUCE: (349), (481) imply:
% 129.98/18.28 | | | | | | | | | | | | | | | | (482) ~ (all_52_3 = e3)
% 129.98/18.28 | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | REDUCE: (367), (481) imply:
% 129.98/18.28 | | | | | | | | | | | | | | | | (483) ~ (all_52_11 = e3)
% 129.98/18.28 | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | REDUCE: (368), (481) imply:
% 129.98/18.28 | | | | | | | | | | | | | | | | (484) ~ (all_52_12 = e3)
% 129.98/18.28 | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | REDUCE: (369), (481) imply:
% 129.98/18.28 | | | | | | | | | | | | | | | | (485) ~ (all_52_13 = e3)
% 129.98/18.28 | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | REDUCE: (370), (481) imply:
% 129.98/18.28 | | | | | | | | | | | | | | | | (486) ~ (all_52_14 = e3)
% 129.98/18.28 | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | REDUCE: (36), (481) imply:
% 129.98/18.28 | | | | | | | | | | | | | | | | (487) op(e0, e0) = e3
% 129.98/18.28 | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | BETA: splitting (479) gives:
% 129.98/18.28 | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.28 | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | (488) ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 &
% 129.98/18.28 | | | | | | | | | | | | | | | | | $i(all_34_0)
% 129.98/18.28 | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | ALPHA: (488) implies:
% 129.98/18.28 | | | | | | | | | | | | | | | | | (489) ~ (all_34_0 = e2)
% 129.98/18.28 | | | | | | | | | | | | | | | | | (490) op(e3, e0) = all_34_0
% 129.98/18.28 | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 129.98/18.28 | | | | | | | | | | | | | | | | | all_34_0, e0, e3, simplifying with (168), (490)
% 129.98/18.28 | | | | | | | | | | | | | | | | | gives:
% 129.98/18.28 | | | | | | | | | | | | | | | | | (491) all_52_12 = all_34_0
% 129.98/18.28 | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (491) imply:
% 129.98/18.28 | | | | | | | | | | | | | | | | | (492) all_54_3 = all_34_0
% 129.98/18.28 | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | REDUCE: (133), (491) imply:
% 129.98/18.28 | | | | | | | | | | | | | | | | | (493) ~ (all_52_4 = all_34_0)
% 129.98/18.28 | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | REDUCE: (113), (491) imply:
% 129.98/18.28 | | | | | | | | | | | | | | | | | (494) ~ (all_52_13 = all_34_0)
% 129.98/18.28 | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | SIMP: (494) implies:
% 129.98/18.28 | | | | | | | | | | | | | | | | | (495) ~ (all_52_13 = all_34_0)
% 129.98/18.28 | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | REDUCE: (484), (491) imply:
% 129.98/18.28 | | | | | | | | | | | | | | | | | (496) ~ (all_34_0 = e3)
% 129.98/18.28 | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | REDUCE: (434), (491) imply:
% 129.98/18.28 | | | | | | | | | | | | | | | | | (497) ~ (all_34_0 = e1)
% 129.98/18.28 | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 129.98/18.28 | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.28 | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | (498) all_54_3 = e3
% 129.98/18.28 | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (492), (498) imply:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | (499) all_34_0 = e3
% 129.98/18.28 | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | REDUCE: (496), (499) imply:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | (500) $false
% 129.98/18.28 | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | CLOSE: (500) is inconsistent.
% 129.98/18.28 | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.28 | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | (501) ~ (all_54_3 = e3)
% 129.98/18.28 | | | | | | | | | | | | | | | | | | (502) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 129.98/18.28 | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 129.98/18.28 | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | (503) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 129.98/18.28 | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | BETA: splitting (503) gives:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | (504) all_57_9 = e2 & op(e3, e0) = e2
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | ALPHA: (504) implies:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | (505) all_57_9 = e2
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | BETA: splitting (502) gives:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | (506) all_54_3 = e2
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (489), (492), (506) are inconsistent by sub-proof
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | #707.
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | (507) ~ (all_54_3 = e2)
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | (508) all_54_3 = e1 | all_54_3 = e0
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (508) gives:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | (509) all_54_3 = e1
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (492), (497), (509) are inconsistent by sub-proof
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | #706.
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | (510) all_54_3 = e0
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (492), (510) imply:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | (511) all_34_0 = e0
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | SIMP: (511) implies:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | (512) all_34_0 = e0
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (493), (512) imply:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | (513) ~ (all_52_4 = e0)
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (495), (512) imply:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | (514) ~ (all_52_13 = e0)
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (489), (512) imply:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | (515) ~ (e2 = e0)
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (497), (512) imply:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | (516) ~ (e1 = e0)
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | (517) all_54_1 = e3
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (517) imply:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | (518) all_52_4 = e3
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (518) imply:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | (519) ~ (all_52_6 = e3)
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (519) implies:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | (520) ~ (all_52_6 = e3)
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (518) imply:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | (521) ~ (all_52_8 = e3)
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (521) implies:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | (522) ~ (all_52_8 = e3)
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | (523) all_54_7 = e3
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (523) imply:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | (524) all_52_13 = e3
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (485), (524) imply:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | (525) $false
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (525) is inconsistent.
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | (526) ~ (all_54_7 = e3)
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | (527) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | (528) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (528) gives:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (529) all_57_0 = e3 & op(e3, e3) = e3
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (529) implies:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (530) op(e3, e3) = e3
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (436), (530), (function-axioms) are
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #775.
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (531) all_57_1 = e3 & op(e3, e2) = e3
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (531) implies:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (532) all_57_1 = e3
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (533) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (533) gives:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (534) all_57_4 = e3 & op(e3, e1) = e3
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (534) implies:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (535) op(e3, e1) = e3
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (522), (535), (function-axioms) are
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #705.
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (536) all_57_5 = e3 & op(e2, e1) = e3
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (536) implies:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (537) all_57_5 = e3
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (538) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (538) gives:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (539) all_57_6 = e3 & op(e1, e3) = e3
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (539) implies:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (540) all_57_6 = e3
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (527) gives:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (541) all_54_7 = e2
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (541) imply:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (542) all_52_13 = e2
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (395), (542) imply:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (543) $false
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (543) is inconsistent.
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (544) ~ (all_54_7 = e2)
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (545) all_54_7 = e1 | all_54_7 = e0
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (546) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (546) gives:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (547) all_57_6 = e2 & op(e1, e3) = e2
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (134), (168), (169), (203), (238),
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (271), (393), (432), (436), (484), (489), (492),
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (493), (497), (502), (532), (540), (547),
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #697.
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (548) all_57_7 = e2 & op(e1, e2) = e2
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (548) implies:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (549) all_57_7 = e2
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (550) all_57_15 = e0 & op(e0, e0) = e0
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (550) implies:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (551) op(e0, e0) = e0
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (487), (551), (function-axioms) are
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #715.
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (552) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (552) implies:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (553) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (554) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (554) gives:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (555) all_57_9 = e0 & op(e3, e0) = e0
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (555) implies:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (556) all_57_9 = e0
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (505), (556) are inconsistent by sub-proof
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #696.
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (557) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (557) gives:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (558) all_57_10 = e0 & op(e2, e0) = e0
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (558) implies:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (559) op(e2, e0) = e0
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (259), (514), (545), (559),
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #694.
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (560) all_57_11 = e0 & op(e1, e0) = e0
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (560) implies:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (561) all_57_11 = e0
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (562) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (562) gives:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (563) all_57_6 = e1 & op(e1, e3) = e1
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (563) implies:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (564) op(e1, e3) = e1
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (431), (564), (function-axioms) are
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #725.
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (565) all_57_7 = e1 & op(e1, e2) = e1
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (236),
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (436), (505), (513), (549), (565),
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #685.
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (566) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (566) gives:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (567) all_57_8 = e1 & op(e1, e1) = e1
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (567) implies:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (568) op(e1, e1) = e1
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (569) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (569) gives:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (570) all_57_2 = e0 & op(e2, e3) = e0
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (570) implies:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (571) all_57_2 = e0
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (572) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (572) gives:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (573) all_57_1 = e1 & op(e3, e2) = e1
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (432), (573), (function-axioms) are
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #684.
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (574) all_57_3 = e1 & op(e2, e2) = e1
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (574) implies:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (575) all_57_3 = e1
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (401), (575) imply:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (576) e2 = e1
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (505), (576) imply:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (577) all_57_9 = e1
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (236),
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (436), (513), (577), (function-axioms) are
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #686.
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (578) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (578) gives:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (579) all_57_7 = e1 & op(e1, e2) = e1
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (236),
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (436), (505), (513), (549), (579),
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #685.
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (580) all_57_13 = e1 & op(e0, e2) = e1
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (580) implies:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (581) all_57_13 = e1
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (582) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (167), (392), (436), (582), (function-axioms)
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #683.
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (583) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (583) gives:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (584) all_57_6 = e2 & op(e1, e3) = e2
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (134), (168), (169), (203), (238),
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (271), (393), (432), (436), (484), (489), (492),
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (493), (497), (502), (532), (540), (584),
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #697.
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (585) all_57_12 = e2 & op(e0, e3) = e2
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (585) implies:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (586) all_57_12 = e2
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (553) gives:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (587) all_57_12 = e0 & op(e0, e3) = e0
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (587) implies:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (588) all_57_12 = e0
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (586), (588) are inconsistent by sub-proof
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #682.
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (589) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (589) gives:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (590) all_57_13 = e0 & op(e0, e2) = e0
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (590) implies:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (591) all_57_13 = e0
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (581), (591) are inconsistent by sub-proof
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #681.
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (592) all_57_14 = e0 & op(e0, e1) = e0
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (592) implies:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (593) all_57_14 = e0
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (594) op(e0, e1) = e0
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (595) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (595) gives:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (596) all_57_4 = e2 & op(e3, e1) = e2
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (596) implies:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (597) all_57_4 = e2
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (598) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (598) gives:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (599) all_57_1 = e0 & op(e3, e2) = e0
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (513), (599), (function-axioms) are
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #693.
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (600) all_57_3 = e0 & op(e2, e2) = e0
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (600) implies:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (601) all_57_3 = e0
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (602) op(e2, e2) = e0
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (170), (224),
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225), (232), (236), (238), (430), (436), (513),
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (537), (571), (597), (601), (602),
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #665.
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (603) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (603) gives:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (604) all_57_7 = e0 & op(e1, e2) = e0
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (549), (604) are inconsistent by sub-proof
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #664.
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (605) all_57_13 = e0 & op(e0, e2) = e0
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (605) implies:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (606) all_57_13 = e0
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (581), (606) are inconsistent by sub-proof
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #681.
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (607) all_57_5 = e2 & op(e2, e1) = e2
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (607) implies:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (608) all_57_5 = e2
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (533) gives:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (609) all_57_4 = e3 & op(e3, e1) = e3
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (609) implies:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (610) op(e3, e1) = e3
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (522), (610), (function-axioms) are
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #705.
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (536), (608) are inconsistent by sub-proof
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #663.
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (611) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (611) gives:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (612) all_57_8 = e3 & op(e1, e1) = e3
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (612) implies:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (613) op(e1, e1) = e3
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (568), (613), (function-axioms) are
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #662.
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (614) all_57_14 = e3 & op(e0, e1) = e3
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (593), (614) are inconsistent by sub-proof
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #661.
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (615) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (39), (372), (594), (615), (function-axioms)
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #659.
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (616) all_57_3 = e0 & op(e2, e2) = e0
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (616) implies:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (617) all_57_3 = e0
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (401), (617) are inconsistent by sub-proof
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #679.
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (618) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (618) gives:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (619) all_57_5 = e0 & op(e2, e1) = e0
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (537), (619) are inconsistent by sub-proof
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #658.
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (620) all_57_10 = e0 & op(e2, e0) = e0
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (620) implies:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (621) op(e2, e0) = e0
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (259), (514), (545), (621),
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #694.
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (622) all_57_11 = e1 & op(e1, e0) = e1
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (622) implies:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (623) all_57_11 = e1
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (561), (623) imply:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (624) e1 = e0
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (624) imply:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (625) $false
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (625) is inconsistent.
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (626) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (626) gives:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (627) all_57_8 = e2 & op(e1, e1) = e2
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (627) implies:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (628) op(e1, e1) = e2
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (628), (function-axioms) are
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (629) all_57_11 = e2 & op(e1, e0) = e2
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (629) implies:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (630) all_57_11 = e2
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (164), (197), (208), (259), (395),
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (485), (487), (489), (492), (495), (497), (502),
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (505), (630), (function-axioms) are inconsistent
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #655.
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (631) all_57_7 = e3 & op(e1, e2) = e3
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (631) implies:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (632) op(e1, e2) = e3
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (520), (632), (function-axioms) are
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #654.
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (633) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (160), (382), (486), (633),
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #653.
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | (634) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (157), (382), (483), (634),
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | #651.
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | (635) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (169), (484), (522), (635),
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | #650.
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | (636) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (271), (393), (432), (513), (636) are inconsistent
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #701.
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | (637) all_57_10 = e2 & op(e2, e0) = e2
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | ALPHA: (637) implies:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | (638) op(e2, e0) = e2
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (395), (638), (function-axioms) are
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.31 | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | (639) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 129.98/18.31 | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | BETA: splitting (639) gives:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | (640) all_57_11 = e2 & op(e1, e0) = e2
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | ALPHA: (640) implies:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | (641) all_57_11 = e2
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | (642) op(e1, e0) = e2
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | (643) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (643) gives:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | (644) all_57_0 = e2 & op(e3, e3) = e2
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (644) implies:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | (645) op(e3, e3) = e2
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (436), (645), (function-axioms) are
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743.
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | (646) all_57_1 = e2 & op(e3, e2) = e2
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (646) implies:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | (647) all_57_1 = e2
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | (648) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (436), (647), (648), (function-axioms)
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #703.
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | (649) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (134), (168), (169), (203), (271), (393), (432),
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | (484), (489), (492), (493), (497), (502), (649),
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | #698.
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | (650) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (650) gives:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | (651) all_57_4 = e2 & op(e3, e1) = e2
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (651) implies:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | (652) all_57_4 = e2
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | (653) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (653) gives:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | (654) all_57_0 = e3 & op(e3, e3) = e3
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (654) implies:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | (655) op(e3, e3) = e3
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (436), (655), (function-axioms) are
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #775.
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | (656) all_57_1 = e3 & op(e3, e2) = e3
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (656) implies:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | (657) all_57_1 = e3
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | (658) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (658) gives:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (659) all_57_4 = e3 & op(e3, e1) = e3
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (134), (169), (203), (271), (393), (432), (489),
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (492), (493), (497), (502), (659),
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | #699.
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (660) all_57_5 = e3 & op(e2, e1) = e3
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (660) implies:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (661) all_57_5 = e3
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (502) gives:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (662) all_54_3 = e2
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (492), (662) imply:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (663) all_34_0 = e2
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (489), (663) imply:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (664) $false
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (664) is inconsistent.
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (665) ~ (all_54_3 = e2)
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (666) all_54_3 = e1 | all_54_3 = e0
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (667) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (436), (657), (667), (function-axioms)
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #648.
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (668) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (668) gives:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (669) all_57_4 = e0 & op(e3, e1) = e0
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (652), (669) are inconsistent by sub-proof
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #647.
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (670) all_57_9 = e0 & op(e3, e0) = e0
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (670) implies:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (671) all_57_9 = e0
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (672) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (672) gives:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (673) all_57_2 = e1 & op(e2, e3) = e1
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (430), (673), (function-axioms) are
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #676.
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (674) all_57_3 = e1 & op(e2, e2) = e1
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (674) implies:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (675) all_57_3 = e1
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (401), (675) imply:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (676) e2 = e1
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (652), (676) imply:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (677) all_57_4 = e1
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (236), (238), (436),
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (671), (677), (function-axioms) are inconsistent
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #668.
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (678) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (678) gives:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (679) all_57_5 = e1 & op(e2, e1) = e1
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (661), (679) are inconsistent by sub-proof
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #673.
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (680) all_57_10 = e1 & op(e2, e0) = e1
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (680) implies:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (681) op(e2, e0) = e1
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (682) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (682) gives:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (683) all_57_2 = e0 & op(e2, e3) = e0
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (683) implies:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (684) all_57_2 = e0
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (685) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (685) gives:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (686) all_57_0 = e3 & op(e3, e3) = e3
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (686) implies:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (687) op(e3, e3) = e3
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (436), (687), (function-axioms) are
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #775.
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (688) all_57_2 = e3 & op(e2, e3) = e3
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (688) implies:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (689) all_57_2 = e3
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (684), (689) imply:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (690) e3 = e0
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (690) imply:
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (691) $false
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (691) is inconsistent.
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (692) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (692) gives:
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (693) all_57_6 = e3 & op(e1, e3) = e3
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (693) implies:
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (694) all_57_6 = e3
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (695) op(e1, e3) = e3
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (696) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (167), (392), (436), (696), (function-axioms)
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #683.
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (697) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (697) gives:
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (698) all_57_6 = e2 & op(e1, e3) = e2
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (134), (168), (169), (203), (238),
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (271), (393), (432), (436), (484), (489), (492),
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (493), (497), (502), (657), (694), (698),
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #697.
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (699) all_57_12 = e2 & op(e0, e3) = e2
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (699) implies:
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (700) all_57_12 = e2
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (666) gives:
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (701) all_54_3 = e1
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (492), (497), (701) are inconsistent by sub-proof
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #706.
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (702) all_54_3 = e0
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (492), (702) imply:
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (703) all_34_0 = e0
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (703) implies:
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (704) all_34_0 = e0
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (495), (704) imply:
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (705) ~ (all_52_13 = e0)
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (496), (704) imply:
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (706) ~ (e3 = e0)
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (489), (704) imply:
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (707) ~ (e2 = e0)
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (497), (704) imply:
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (708) ~ (e1 = e0)
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (490), (704) imply:
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (709) op(e3, e0) = e0
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (710) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (710) gives:
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (711) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (711) gives:
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (712) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (712) implies:
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (713) op(e3, e3) = e2
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (233), (684), (694), (700), (713),
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #643.
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (714) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (714) implies:
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (715) ~ (all_56_5 = e3)
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (716) op(e1, e3) = all_56_5
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (695), (715), (716), (function-axioms) are
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #724.
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (717) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (39), (110), (160), (163), (164), (168),
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206), (208), (212), (214), (366), (436), (484),
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (485), (486), (489), (490), (641), (642), (681),
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (695), (705), (709), (717), (function-axioms) are
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #630.
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (718) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (718) gives:
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (719) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (719) gives:
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (720) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (720) implies:
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (721) ~ (all_56_25 = e0)
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (722) op(e3, e0) = all_56_25
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (709), (721), (722), (function-axioms) are
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #642.
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (723) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 =
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2,
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (723) implies:
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (724) op(e2, e1) = e2
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (394), (724), (function-axioms) are
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #770.
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (725) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (725) gives:
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (726) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (726) implies:
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (727) op(e2, e0) = e2
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (395), (727), (function-axioms) are
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (728) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (164), (208),
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212), (214), (372), (485), (641), (642), (695),
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (709), (728), (function-axioms) are inconsistent
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #629.
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (729) all_57_12 = e3 & op(e0, e3) = e3
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (482), (729), (function-axioms) are
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #628.
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (730) all_57_3 = e0 & op(e2, e2) = e0
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (401), (730) are inconsistent by sub-proof
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #627.
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (731) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (731) gives:
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (732) all_57_5 = e0 & op(e2, e1) = e0
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (661), (732) are inconsistent by sub-proof
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #658.
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (733) all_57_10 = e0 & op(e2, e0) = e0
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (733) implies:
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (734) op(e2, e0) = e0
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (681), (734), (function-axioms) are
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #695.
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | (735) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (157), (382), (483), (735),
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | #651.
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | (736) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (134), (168), (169), (203), (271), (393), (432),
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | (484), (489), (492), (493), (497), (502), (736),
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | #698.
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | (737) all_57_9 = e2 & op(e3, e0) = e2
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (737) implies:
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | (738) all_57_9 = e2
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (164), (197), (208), (259), (395),
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | (485), (487), (489), (492), (495), (497), (502),
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | (641), (738), (function-axioms) are inconsistent
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #655.
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | End of split
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | End of split
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | Case 2:
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | (739) all_57_15 = e2 & op(e0, e0) = e2
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | ALPHA: (739) implies:
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | (740) op(e0, e0) = e2
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (487), (740), (function-axioms) are
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #634.
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | | End of split
% 130.63/18.34 | | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | | End of split
% 130.63/18.34 | | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | End of split
% 130.63/18.34 | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | Case 2:
% 130.63/18.34 | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | (741) ~ (all_34_1 = e1) & op(e3, e3) = all_34_1 &
% 130.63/18.34 | | | | | | | | | | | | | | | | | $i(all_34_1)
% 130.63/18.34 | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | ALPHA: (741) implies:
% 130.63/18.34 | | | | | | | | | | | | | | | | | (742) ~ (all_34_1 = e1)
% 130.63/18.34 | | | | | | | | | | | | | | | | | (743) op(e3, e3) = all_34_1
% 130.63/18.34 | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | | REF_CLOSE: (436), (742), (743), (function-axioms) are
% 130.63/18.34 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #626.
% 130.63/18.34 | | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | End of split
% 130.63/18.34 | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | End of split
% 130.63/18.34 | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | End of split
% 130.63/18.34 | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | End of split
% 130.63/18.34 | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | Case 2:
% 130.63/18.34 | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | (744) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 130.63/18.34 | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 130.63/18.34 | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | REF_CLOSE: (164), (165), (394), (395), (744),
% 130.63/18.34 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 130.63/18.34 | | | | | | | | | | | | | #625.
% 130.63/18.34 | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | End of split
% 130.63/18.34 | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | Case 2:
% 130.63/18.34 | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | (745) all_54_5 = e1 | all_54_5 = e0
% 130.63/18.34 | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | REF_CLOSE: (267), (373), (384), (745) are inconsistent by
% 130.63/18.34 | | | | | | | | | | | | sub-proof #624.
% 130.63/18.34 | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | End of split
% 130.63/18.34 | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | End of split
% 130.63/18.34 | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | Case 2:
% 130.63/18.34 | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | (746) all_30_2 = e0
% 130.63/18.34 | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | COMBINE_EQS: (309), (746) imply:
% 130.63/18.34 | | | | | | | | | | (747) all_8_2 = e0
% 130.63/18.34 | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | SIMP: (747) implies:
% 130.63/18.34 | | | | | | | | | | (748) all_8_2 = e0
% 130.63/18.34 | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | COMBINE_EQS: (301), (748) imply:
% 130.63/18.34 | | | | | | | | | | (749) all_42_2 = e0
% 130.63/18.34 | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | REDUCE: (350), (748) imply:
% 130.63/18.34 | | | | | | | | | | (750) ~ (all_52_4 = e0)
% 130.63/18.34 | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | REDUCE: (352), (748) imply:
% 130.63/18.34 | | | | | | | | | | (751) ~ (all_52_6 = e0)
% 130.63/18.34 | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | REDUCE: (354), (748) imply:
% 130.63/18.34 | | | | | | | | | | (752) ~ (all_52_7 = e0)
% 130.63/18.34 | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | REDUCE: (356), (748) imply:
% 130.63/18.34 | | | | | | | | | | (753) ~ (all_52_9 = e0)
% 130.63/18.34 | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | REDUCE: (358), (748) imply:
% 130.63/18.34 | | | | | | | | | | (754) ~ (all_52_13 = e0)
% 130.63/18.34 | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | REDUCE: (376), (748) imply:
% 130.63/18.34 | | | | | | | | | | (755) ~ (e3 = e0)
% 130.63/18.34 | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | REDUCE: (373), (748) imply:
% 130.63/18.34 | | | | | | | | | | (756) ~ (e1 = e0)
% 130.63/18.34 | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | BETA: splitting (227) gives:
% 130.63/18.34 | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | Case 1:
% 130.63/18.34 | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | (757) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 130.63/18.34 | | | | | | | | | | | & op(e2, e2) = e0)
% 130.63/18.34 | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | BETA: splitting (757) gives:
% 130.63/18.34 | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | Case 1:
% 130.63/18.34 | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | (758) all_57_1 = e0 & op(e3, e2) = e0
% 130.63/18.34 | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | REF_CLOSE: (170), (750), (758), (function-axioms) are
% 130.63/18.34 | | | | | | | | | | | | inconsistent by sub-proof #693.
% 130.63/18.34 | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | Case 2:
% 130.63/18.34 | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | (759) all_57_3 = e0 & op(e2, e2) = e0
% 130.63/18.34 | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | ALPHA: (759) implies:
% 130.63/18.34 | | | | | | | | | | | | (760) all_57_3 = e0
% 130.63/18.34 | | | | | | | | | | | | (761) op(e2, e2) = e0
% 130.63/18.34 | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | BETA: splitting (79) gives:
% 130.63/18.34 | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | Case 1:
% 130.63/18.34 | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | (762) ~ (all_32_2 = e1)
% 130.63/18.34 | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | REDUCE: (312), (762) imply:
% 130.63/18.34 | | | | | | | | | | | | | (763) ~ (all_10_2 = e1)
% 130.63/18.34 | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | BETA: splitting (204) gives:
% 130.63/18.34 | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | Case 1:
% 130.63/18.34 | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | (764) all_54_0 = e3
% 130.63/18.34 | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | COMBINE_EQS: (278), (764) imply:
% 130.63/18.34 | | | | | | | | | | | | | | (765) all_10_2 = e3
% 130.63/18.34 | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | REDUCE: (338), (765) imply:
% 130.63/18.34 | | | | | | | | | | | | | | (766) ~ (all_52_2 = e3)
% 130.63/18.34 | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | REDUCE: (344), (765) imply:
% 130.63/18.34 | | | | | | | | | | | | | | (767) ~ (all_52_8 = e3)
% 130.63/18.34 | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | REDUCE: (346), (765) imply:
% 130.63/18.34 | | | | | | | | | | | | | | (768) ~ (all_52_12 = e3)
% 130.63/18.34 | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | REDUCE: (45), (765) imply:
% 130.63/18.34 | | | | | | | | | | | | | | (769) op(e3, e3) = e3
% 130.63/18.34 | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 130.63/18.34 | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | Case 1:
% 130.63/18.34 | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | (770) ~ (all_34_2 = e3)
% 130.63/18.34 | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | REDUCE: (307), (770) imply:
% 130.63/18.34 | | | | | | | | | | | | | | | (771) ~ (all_4_2 = e3)
% 130.63/18.34 | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 130.63/18.34 | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | Case 1:
% 130.63/18.34 | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | (772) all_54_15 = e3
% 130.63/18.34 | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (772) imply:
% 130.63/18.34 | | | | | | | | | | | | | | | | (773) all_4_2 = e3
% 130.63/18.34 | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | REDUCE: (771), (773) imply:
% 130.63/18.34 | | | | | | | | | | | | | | | | (774) $false
% 130.63/18.34 | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | CLOSE: (774) is inconsistent.
% 130.63/18.34 | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | Case 2:
% 130.63/18.34 | | | | | | | | | | | | | | | |
% 130.63/18.34 | | | | | | | | | | | | | | | | (775) ~ (all_54_15 = e3)
% 130.63/18.35 | | | | | | | | | | | | | | | | (776) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 130.63/18.35 | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | BETA: splitting (776) gives:
% 130.63/18.35 | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | Case 1:
% 130.63/18.35 | | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | | (777) all_54_15 = e2
% 130.63/18.35 | | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (777) imply:
% 130.63/18.35 | | | | | | | | | | | | | | | | | (778) all_4_2 = e2
% 130.63/18.35 | | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | | REDUCE: (380), (778) imply:
% 130.63/18.35 | | | | | | | | | | | | | | | | | (779) $false
% 130.63/18.35 | | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | | CLOSE: (779) is inconsistent.
% 130.63/18.35 | | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | Case 2:
% 130.63/18.35 | | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | | (780) ~ (all_54_15 = e2)
% 130.63/18.35 | | | | | | | | | | | | | | | | | (781) all_54_15 = e1 | all_54_15 = e0
% 130.63/18.35 | | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | | BETA: splitting (781) gives:
% 130.63/18.35 | | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | | Case 1:
% 130.63/18.35 | | | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | | | (782) all_54_15 = e1
% 130.63/18.35 | | | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (782) imply:
% 130.63/18.35 | | | | | | | | | | | | | | | | | | (783) all_4_2 = e1
% 130.63/18.35 | | | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | | | REDUCE: (371), (783) imply:
% 130.63/18.35 | | | | | | | | | | | | | | | | | | (784) $false
% 130.63/18.35 | | | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | | | CLOSE: (784) is inconsistent.
% 130.63/18.35 | | | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | | Case 2:
% 130.63/18.35 | | | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | | | (785) all_54_15 = e0
% 130.63/18.35 | | | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (785) imply:
% 130.63/18.35 | | | | | | | | | | | | | | | | | | (786) all_4_2 = e0
% 130.63/18.35 | | | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | | | REDUCE: (349), (786) imply:
% 130.63/18.35 | | | | | | | | | | | | | | | | | | (787) ~ (all_52_3 = e0)
% 130.63/18.35 | | | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | | | REDUCE: (368), (786) imply:
% 130.63/18.35 | | | | | | | | | | | | | | | | | | (788) ~ (all_52_12 = e0)
% 130.63/18.35 | | | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | | | REDUCE: (380), (786) imply:
% 130.63/18.35 | | | | | | | | | | | | | | | | | | (789) ~ (e2 = e0)
% 130.63/18.35 | | | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | | | REDUCE: (36), (786) imply:
% 130.63/18.35 | | | | | | | | | | | | | | | | | | (790) op(e0, e0) = e0
% 130.63/18.35 | | | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 130.63/18.35 | | | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | | | Case 1:
% 130.63/18.35 | | | | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | (791) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 130.63/18.35 | | | | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | BETA: splitting (791) gives:
% 130.63/18.35 | | | | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | Case 1:
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | | (792) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (769), (792), (function-axioms) are
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #623.
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | Case 2:
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | | (793) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (761), (768), (793), (function-axioms)
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #622.
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | End of split
% 130.63/18.35 | | | | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | | | Case 2:
% 130.63/18.35 | | | | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | (794) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 130.63/18.35 | | | | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | BETA: splitting (794) gives:
% 130.63/18.35 | | | | | | | | | | | | | | | | | | |
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | Case 1:
% 130.63/18.35 | | | | | | | | | | | | | | | | | | | |
% 130.63/18.36 | | | | | | | | | | | | | | | | | | | | (795) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 130.63/18.36 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 130.63/18.36 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 130.63/18.36 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 130.63/18.36 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 130.63/18.36 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 130.63/18.36 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 130.63/18.36 | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 130.63/18.36 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 130.63/18.36 | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 130.63/18.36 | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 130.63/18.36 | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 130.63/18.36 | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 130.63/18.36 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 130.63/18.36 | | | | | | | | | | | | | | | | | | | |
% 130.63/18.36 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (382), (761), (795), (function-axioms)
% 130.63/18.36 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #621.
% 130.63/18.36 | | | | | | | | | | | | | | | | | | | |
% 130.63/18.36 | | | | | | | | | | | | | | | | | | | Case 2:
% 130.63/18.36 | | | | | | | | | | | | | | | | | | | |
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | (796) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | |
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | BETA: splitting (796) gives:
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | |
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | Case 1:
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | (797) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | ALPHA: (797) implies:
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | (798) ~ (all_56_31 = e0)
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | (799) op(e0, e0) = all_56_31
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (790), (798), (799), (function-axioms) are
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #712.
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | (800) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (800) gives:
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | (801) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (801) implies:
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | (802) op(e1, e1) = e2
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (802), (function-axioms) are
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | (803) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (803) implies:
% 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | (804) op(e0, e0) = all_56_31
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | (805) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (805) gives:
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | (806) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27))
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (806) gives:
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | (807) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (807) implies:
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | (808) op(e0, e3) = e0
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (805) gives:
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (806) gives:
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (807) implies:
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (809) ~ (all_56_1 = e3)
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (810) op(e3, e3) = all_56_1
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (769), (809), (810), (function-axioms) are
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #766.
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (811) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27)
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (811) implies:
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (812) all_56_31 = e2
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (804), (812) imply:
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (813) op(e0, e0) = e2
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (790), (813), (function-axioms) are
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #714.
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | (814) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (814) gives:
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (815) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7)
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23)
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (815) implies:
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (816) op(e0, e3) = all_56_7
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (787), (808), (816), (function-axioms) are
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #620.
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (817) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (790), (804), (817), (function-axioms) are
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #711.
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | (818) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27)
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (818) implies:
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | (819) all_56_31 = e2
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (804), (819) imply:
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | (820) op(e0, e0) = e2
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (790), (820), (function-axioms) are
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #714.
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | (821) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (821) gives:
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | (822) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7)
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23)
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (822) implies:
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | (823) op(e1, e1) = e0
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | (824) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (824) gives:
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (825) all_57_0 = e0 & op(e3, e3) = e0
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (825) implies:
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (826) op(e3, e3) = e0
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (769), (826), (function-axioms) are
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #773.
% 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (827) all_57_1 = e0 & op(e3, e2) = e0
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (827) implies:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (828) op(e3, e2) = e0
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e0,
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (170), (828) gives:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (829) all_52_4 = e0
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (750), (829) imply:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (830) $false
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (830) is inconsistent.
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | (831) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (831) gives:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (832) all_57_4 = e0 & op(e3, e1) = e0
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (832) implies:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (833) op(e3, e1) = e0
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (169), (361), (823), (833),
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | #619.
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (834) all_57_9 = e0 & op(e3, e0) = e0
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (788), (834), (function-axioms) are
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #618.
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | (835) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (790), (804), (835), (function-axioms) are
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #711.
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | End of split
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | End of split
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | End of split
% 130.78/18.38 | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | End of split
% 130.78/18.38 | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | End of split
% 130.78/18.38 | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | End of split
% 130.78/18.38 | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | End of split
% 130.78/18.38 | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | Case 2:
% 130.78/18.38 | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | (836) all_34_2 = e3
% 130.78/18.38 | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | COMBINE_EQS: (307), (836) imply:
% 130.78/18.38 | | | | | | | | | | | | | | | (837) all_4_2 = e3
% 130.78/18.38 | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | SIMP: (837) implies:
% 130.78/18.38 | | | | | | | | | | | | | | | (838) all_4_2 = e3
% 130.78/18.38 | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | REDUCE: (360), (838) imply:
% 130.78/18.38 | | | | | | | | | | | | | | | (839) ~ (all_52_7 = e3)
% 130.78/18.38 | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | REDUCE: (367), (838) imply:
% 130.78/18.38 | | | | | | | | | | | | | | | (840) ~ (all_52_11 = e3)
% 130.78/18.38 | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | REDUCE: (370), (838) imply:
% 130.78/18.38 | | | | | | | | | | | | | | | (841) ~ (all_52_14 = e3)
% 130.78/18.38 | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | REDUCE: (36), (838) imply:
% 130.78/18.38 | | | | | | | | | | | | | | | (842) op(e0, e0) = e3
% 130.78/18.38 | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 130.78/18.38 | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | Case 1:
% 130.78/18.38 | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | (843) ~ (all_42_2 = e0)
% 130.78/18.38 | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | REDUCE: (749), (843) imply:
% 130.78/18.38 | | | | | | | | | | | | | | | | (844) $false
% 130.78/18.38 | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | CLOSE: (844) is inconsistent.
% 130.78/18.38 | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | Case 2:
% 130.78/18.38 | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | (845) ( ~ (all_42_0 = e1) & op(e0, e2) = all_42_0 &
% 130.78/18.38 | | | | | | | | | | | | | | | | $i(all_42_0)) | ( ~ (all_42_1 = e3) & op(e0, e0)
% 130.78/18.38 | | | | | | | | | | | | | | | | = all_42_1 & $i(all_42_1))
% 130.78/18.38 | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 130.78/18.38 | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | Case 1:
% 130.78/18.38 | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | (846) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 130.78/18.38 | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 130.78/18.38 | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | BETA: splitting (846) gives:
% 130.78/18.38 | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | Case 1:
% 130.78/18.38 | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | (847) all_57_6 = e3 & op(e1, e3) = e3
% 130.78/18.38 | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (766), (847), (function-axioms) are
% 130.78/18.38 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #761.
% 130.78/18.38 | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | Case 2:
% 130.78/18.38 | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | (848) all_57_7 = e3 & op(e1, e2) = e3
% 130.78/18.38 | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | ALPHA: (848) implies:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | (849) all_57_7 = e3
% 130.78/18.38 | | | | | | | | | | | | | | | | | | (850) op(e1, e2) = e3
% 130.78/18.38 | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | BETA: splitting (845) gives:
% 130.78/18.38 | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | Case 1:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | (851) ~ (all_42_0 = e1) & op(e0, e2) = all_42_0 &
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | $i(all_42_0)
% 130.78/18.38 | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | ALPHA: (851) implies:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | (852) ~ (all_42_0 = e1)
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | (853) op(e0, e2) = all_42_0
% 130.78/18.38 | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | Case 1:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | (854) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | BETA: splitting (854) gives:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | Case 1:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | (855) all_57_4 = e3 & op(e3, e1) = e3
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | ALPHA: (855) implies:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | (856) op(e3, e1) = e3
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (767), (856), (function-axioms) are
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #705.
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | (857) all_57_5 = e3 & op(e2, e1) = e3
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | ALPHA: (857) implies:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | (858) op(e2, e1) = e3
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7,
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | all_42_0, e2, e0, simplifying with (158), (853)
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | gives:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | (859) all_52_7 = all_42_0
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e3,
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | e2, e1, simplifying with (162), (850) gives:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | (860) all_52_6 = e3
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e3,
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (165), (858) gives:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | (861) all_52_9 = e3
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (859) imply:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | (862) all_54_13 = all_42_0
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (860) imply:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | (863) ~ (all_52_4 = e3)
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (859) imply:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | (864) ~ (all_52_4 = all_42_0)
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | REDUCE: (839), (859) imply:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | (865) ~ (all_42_0 = e3)
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | REDUCE: (752), (859) imply:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | (866) ~ (all_42_0 = e0)
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (861) imply:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | (867) ~ (all_52_11 = e3)
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (861) imply:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | (868) ~ (all_6_2 = e3)
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | (869) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (869) gives:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | (870) all_57_1 = e1 & op(e3, e2) = e1
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (870) implies:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | (871) all_57_1 = e1
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | (872) op(e3, e2) = e1
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | (873) all_54_13 = e3
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (862), (865), (873) are inconsistent by sub-proof
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | #617.
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | (874) ~ (all_54_13 = e3)
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | (875) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (875) gives:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | (876) all_54_13 = e2
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (862), (876) imply:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | (877) all_42_0 = e2
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (877) implies:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | (878) all_42_0 = e2
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (864), (878) imply:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | (879) ~ (all_52_4 = e2)
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (865), (878) imply:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | (880) ~ (e3 = e2)
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (853), (878) imply:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | (881) op(e0, e2) = e2
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (882) all_54_1 = e3
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (882) imply:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (883) all_52_4 = e3
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (863), (883) imply:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (884) $false
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (884) is inconsistent.
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (885) ~ (all_54_1 = e3)
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (886) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (887) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (887) gives:
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (888) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (888) gives:
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (889) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (889) implies:
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (890) op(e3, e3) = e2
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (769), (890), (function-axioms) are
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #778.
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (891) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (891) implies:
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (892) op(e3, e3) = e1
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (236),
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (863), (871), (872), (892),
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #610.
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (893) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (761), (768), (893), (function-axioms)
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #622.
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (894) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (894) gives:
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (895) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (382), (761), (895), (function-axioms)
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #621.
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (896) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (896) gives:
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (897) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (897) implies:
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (898) ~ (all_56_15 = e2)
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (899) op(e0, e2) = all_56_15
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (881), (898), (899), (function-axioms) are
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #609.
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (900) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (900) gives:
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (901) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (901) implies:
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (902) op(e1, e1) = e2
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (902), (function-axioms) are
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (903) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (903) implies:
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (904) op(e0, e0) = all_56_31
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (905) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (39), (100), (157), (190), (246), (271),
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (295), (364), (750), (769), (840), (842), (879),
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (886), (904), (905), (function-axioms) are
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #605.
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | (906) all_54_13 = e1 | all_54_13 = e0
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (852), (862), (866), (906) are inconsistent by
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #604.
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | (907) all_57_3 = e1 & op(e2, e2) = e1
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (907) implies:
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | (908) op(e2, e2) = e1
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (761), (908), (function-axioms) are
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675.
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | (909) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (909) gives:
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | (910) all_57_7 = e1 & op(e1, e2) = e1
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (849), (910) are inconsistent by sub-proof
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | #603.
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | (911) all_57_13 = e1 & op(e0, e2) = e1
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (911) implies:
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | (912) op(e0, e2) = e1
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | (913) all_54_13 = e3
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (862), (865), (913) are inconsistent by sub-proof
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | #617.
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | (914) ~ (all_54_13 = e3)
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | (915) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (915) gives:
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | (916) all_54_13 = e2
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (862), (916) imply:
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | (917) all_42_0 = e2
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (917) implies:
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | (918) all_42_0 = e2
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (864), (918) imply:
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | (919) ~ (all_52_4 = e2)
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (865), (918) imply:
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | (920) ~ (e3 = e2)
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (853), (918) imply:
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | (921) op(e0, e2) = e2
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | (922) all_54_1 = e3
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (922) imply:
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | (923) all_52_4 = e3
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (863), (923) imply:
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | (924) $false
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (924) is inconsistent.
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | (925) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (926) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (926) gives:
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (927) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (769), (927), (function-axioms) are
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #623.
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (928) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (761), (768), (928), (function-axioms)
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #622.
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (929) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (929) gives:
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (930) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (382), (761), (930), (function-axioms)
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #621.
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (931) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (931) gives:
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (932) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (932) implies:
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (933) op(e0, e2) = all_56_15
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15, e2, e0, simplifying with (921), (933)
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (934) all_56_15 = e2
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15, e2, e0, simplifying with (912), (933)
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (935) all_56_15 = e1
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (934), (935) imply:
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (936) e2 = e1
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (936) imply:
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (937) $false
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (937) is inconsistent.
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (938) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (938) gives:
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (939) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (939) implies:
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (940) op(e1, e1) = e2
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (940), (function-axioms) are
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (941) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (941) implies:
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (942) op(e0, e0) = all_56_31
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (943) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (39), (100), (157), (190), (246), (271),
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (295), (364), (750), (769), (840), (842), (919),
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (925), (942), (943), (function-axioms) are
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #605.
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | (944) all_54_13 = e1 | all_54_13 = e0
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (852), (862), (866), (944) are inconsistent by
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #604.
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | End of split
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | End of split
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | Case 2:
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | (945) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (157), (382), (840), (945),
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | | #651.
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | End of split
% 131.07/18.43 | | | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | | Case 2:
% 131.07/18.43 | | | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | (946) ~ (all_42_1 = e3) & op(e0, e0) = all_42_1 &
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | $i(all_42_1)
% 131.07/18.43 | | | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (842), (946), (function-axioms) are inconsistent
% 131.07/18.43 | | | | | | | | | | | | | | | | | | | by sub-proof #602.
% 131.07/18.43 | | | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | | End of split
% 131.07/18.43 | | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | End of split
% 131.07/18.43 | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | Case 2:
% 131.07/18.43 | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | (947) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 131.07/18.43 | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 131.07/18.43 | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (160), (382), (841), (947),
% 131.07/18.43 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.07/18.43 | | | | | | | | | | | | | | | | | #653.
% 131.07/18.43 | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | End of split
% 131.07/18.43 | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | End of split
% 131.07/18.43 | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | End of split
% 131.07/18.43 | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | Case 2:
% 131.07/18.43 | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | (948) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 131.07/18.43 | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | REF_CLOSE: (278), (374), (378), (763), (948) are inconsistent
% 131.07/18.43 | | | | | | | | | | | | | | by sub-proof #777.
% 131.07/18.43 | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | End of split
% 131.07/18.43 | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | Case 2:
% 131.07/18.43 | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | (949) all_32_2 = e1
% 131.07/18.43 | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | COMBINE_EQS: (312), (949) imply:
% 131.07/18.43 | | | | | | | | | | | | | (950) all_10_2 = e1
% 131.07/18.43 | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | REDUCE: (336), (950) imply:
% 131.07/18.43 | | | | | | | | | | | | | (951) ~ (all_52_1 = e1)
% 131.07/18.43 | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | REDUCE: (342), (950) imply:
% 131.07/18.43 | | | | | | | | | | | | | (952) ~ (all_52_4 = e1)
% 131.07/18.43 | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | REDUCE: (378), (950) imply:
% 131.07/18.43 | | | | | | | | | | | | | (953) ~ (e2 = e1)
% 131.07/18.43 | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | REDUCE: (45), (950) imply:
% 131.07/18.43 | | | | | | | | | | | | | (954) op(e3, e3) = e1
% 131.07/18.43 | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | BETA: splitting (82) gives:
% 131.07/18.43 | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | Case 1:
% 131.07/18.43 | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | (955) ~ (all_34_2 = e3)
% 131.07/18.43 | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | REDUCE: (307), (955) imply:
% 131.07/18.43 | | | | | | | | | | | | | | (956) ~ (all_4_2 = e3)
% 131.07/18.43 | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 131.07/18.43 | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | Case 1:
% 131.07/18.43 | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | (957) all_54_15 = e3
% 131.07/18.43 | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | REF_CLOSE: (245), (956), (957) are inconsistent by sub-proof
% 131.07/18.43 | | | | | | | | | | | | | | | #601.
% 131.07/18.43 | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | Case 2:
% 131.07/18.43 | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | (958) ~ (all_54_15 = e3)
% 131.07/18.43 | | | | | | | | | | | | | | | (959) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 131.07/18.43 | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (39), (168), (169), (170), (206),
% 131.07/18.43 | | | | | | | | | | | | | | | (232), (245), (368), (371), (372), (380), (382),
% 131.07/18.43 | | | | | | | | | | | | | | | (750), (761), (954), (956), (959),
% 131.07/18.43 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.07/18.43 | | | | | | | | | | | | | | | #594.
% 131.07/18.43 | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | End of split
% 131.07/18.43 | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | Case 2:
% 131.07/18.43 | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | (960) all_34_2 = e3
% 131.07/18.43 | | | | | | | | | | | | | | (961) ( ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 &
% 131.07/18.43 | | | | | | | | | | | | | | $i(all_34_0)) | ( ~ (all_34_1 = e1) & op(e3, e3)
% 131.07/18.43 | | | | | | | | | | | | | | = all_34_1 & $i(all_34_1))
% 131.07/18.43 | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | COMBINE_EQS: (307), (960) imply:
% 131.07/18.43 | | | | | | | | | | | | | | (962) all_4_2 = e3
% 131.07/18.43 | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | SIMP: (962) implies:
% 131.07/18.43 | | | | | | | | | | | | | | (963) all_4_2 = e3
% 131.07/18.43 | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | REDUCE: (360), (963) imply:
% 131.07/18.43 | | | | | | | | | | | | | | (964) ~ (all_52_7 = e3)
% 131.07/18.43 | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | REDUCE: (367), (963) imply:
% 131.07/18.43 | | | | | | | | | | | | | | (965) ~ (all_52_11 = e3)
% 131.07/18.43 | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | REDUCE: (368), (963) imply:
% 131.07/18.43 | | | | | | | | | | | | | | (966) ~ (all_52_12 = e3)
% 131.07/18.43 | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | REDUCE: (369), (963) imply:
% 131.07/18.43 | | | | | | | | | | | | | | (967) ~ (all_52_13 = e3)
% 131.07/18.43 | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | REDUCE: (370), (963) imply:
% 131.07/18.43 | | | | | | | | | | | | | | (968) ~ (all_52_14 = e3)
% 131.07/18.43 | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | REDUCE: (36), (963) imply:
% 131.07/18.43 | | | | | | | | | | | | | | (969) op(e0, e0) = e3
% 131.07/18.43 | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 131.07/18.43 | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | Case 1:
% 131.07/18.43 | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | (970) ~ (all_42_2 = e0)
% 131.07/18.43 | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | REDUCE: (749), (970) imply:
% 131.07/18.43 | | | | | | | | | | | | | | | (971) $false
% 131.07/18.43 | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | CLOSE: (971) is inconsistent.
% 131.07/18.43 | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | Case 2:
% 131.07/18.43 | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | (972) ( ~ (all_42_0 = e1) & op(e0, e2) = all_42_0 &
% 131.07/18.43 | | | | | | | | | | | | | | | $i(all_42_0)) | ( ~ (all_42_1 = e3) & op(e0, e0)
% 131.07/18.43 | | | | | | | | | | | | | | | = all_42_1 & $i(all_42_1))
% 131.07/18.43 | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | BETA: splitting (972) gives:
% 131.07/18.43 | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | Case 1:
% 131.07/18.43 | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | (973) ~ (all_42_0 = e1) & op(e0, e2) = all_42_0 &
% 131.07/18.43 | | | | | | | | | | | | | | | | $i(all_42_0)
% 131.07/18.43 | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | ALPHA: (973) implies:
% 131.07/18.43 | | | | | | | | | | | | | | | | (974) ~ (all_42_0 = e1)
% 131.07/18.43 | | | | | | | | | | | | | | | | (975) op(e0, e2) = all_42_0
% 131.07/18.43 | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | BETA: splitting (961) gives:
% 131.07/18.43 | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.43 | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | (976) ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 &
% 131.07/18.43 | | | | | | | | | | | | | | | | | $i(all_34_0)
% 131.07/18.43 | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | ALPHA: (976) implies:
% 131.07/18.43 | | | | | | | | | | | | | | | | | (977) ~ (all_34_0 = e2)
% 131.07/18.43 | | | | | | | | | | | | | | | | | (978) op(e3, e0) = all_34_0
% 131.07/18.43 | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7,
% 131.07/18.43 | | | | | | | | | | | | | | | | | all_42_0, e2, e0, simplifying with (158), (975)
% 131.07/18.43 | | | | | | | | | | | | | | | | | gives:
% 131.07/18.43 | | | | | | | | | | | | | | | | | (979) all_52_7 = all_42_0
% 131.07/18.43 | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 131.07/18.43 | | | | | | | | | | | | | | | | | all_34_0, e0, e3, simplifying with (168), (978)
% 131.07/18.43 | | | | | | | | | | | | | | | | | gives:
% 131.07/18.43 | | | | | | | | | | | | | | | | | (980) all_52_12 = all_34_0
% 131.07/18.43 | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (979) imply:
% 131.07/18.43 | | | | | | | | | | | | | | | | | (981) all_54_13 = all_42_0
% 131.07/18.43 | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | REDUCE: (135), (979) imply:
% 131.07/18.43 | | | | | | | | | | | | | | | | | (982) ~ (all_52_4 = all_42_0)
% 131.07/18.43 | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | REDUCE: (128), (979) imply:
% 131.07/18.43 | | | | | | | | | | | | | | | | | (983) ~ (all_52_6 = all_42_0)
% 131.07/18.43 | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | REDUCE: (964), (979) imply:
% 131.07/18.43 | | | | | | | | | | | | | | | | | (984) ~ (all_42_0 = e3)
% 131.07/18.43 | | | | | | | | | | | | | | | | |
% 131.07/18.43 | | | | | | | | | | | | | | | | | REDUCE: (752), (979) imply:
% 131.07/18.43 | | | | | | | | | | | | | | | | | (985) ~ (all_42_0 = e0)
% 131.07/18.43 | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 131.07/18.44 | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.44 | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | (986) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 131.07/18.44 | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 131.07/18.44 | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | BETA: splitting (986) gives:
% 131.07/18.44 | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | (987) all_57_12 = e1 & op(e0, e3) = e1
% 131.07/18.44 | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | ALPHA: (987) implies:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | (988) all_57_12 = e1
% 131.07/18.44 | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (235), (237),
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | (954), (988), (function-axioms) are inconsistent
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | by sub-proof #583.
% 131.07/18.44 | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | Case 2:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | (989) all_57_13 = e1 & op(e0, e2) = e1
% 131.07/18.44 | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | ALPHA: (989) implies:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | (990) all_57_13 = e1
% 131.07/18.44 | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | (991) all_54_13 = e3
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (981), (984), (991) are inconsistent by sub-proof
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | #617.
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | Case 2:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | (992) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | BETA: splitting (992) gives:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | (993) all_54_13 = e2
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (981), (993) imply:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | (994) all_42_0 = e2
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | SIMP: (994) implies:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | (995) all_42_0 = e2
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | REDUCE: (982), (995) imply:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | (996) ~ (all_52_4 = e2)
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | REDUCE: (983), (995) imply:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | (997) ~ (all_52_6 = e2)
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | (998) all_54_1 = e3
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (998) imply:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | (999) all_52_4 = e3
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (999) imply:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | (1000) ~ (all_52_6 = e3)
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1000) implies:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | (1001) ~ (all_52_6 = e3)
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (999) imply:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | (1002) ~ (all_52_8 = e3)
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1002) implies:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | (1003) ~ (all_52_8 = e3)
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | (1004) all_54_9 = e3
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (1004) imply:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | (1005) all_52_6 = e3
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1001), (1005) imply:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | (1006) $false
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1006) is inconsistent.
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | (1007) ~ (all_54_9 = e3)
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | (1008) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (39), (100), (157), (160),
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | (162), (167), (169), (170), (194), (208), (210),
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | (213), (215), (216), (218), (221), (222), (224),
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | (225), (231), (232), (236), (238), (257), (295),
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | (334), (359), (361), (372), (382), (750), (751),
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | (760), (761), (951), (954), (965), (968), (969),
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | (990), (997), (1001), (1003), (1008),
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | #565.
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | (1009) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (271), (750), (952), (996), (1009) are
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #701.
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | End of split
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | (1010) all_54_13 = e1 | all_54_13 = e0
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (974), (981), (985), (1010) are inconsistent by
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | sub-proof #604.
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | End of split
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | End of split
% 131.07/18.44 | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | End of split
% 131.07/18.44 | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | Case 2:
% 131.07/18.44 | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | (1011) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 131.07/18.44 | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 131.07/18.44 | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | BETA: splitting (1011) gives:
% 131.07/18.44 | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | (1012) all_57_14 = e1 & op(e0, e1) = e1
% 131.07/18.44 | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | ALPHA: (1012) implies:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | (1013) all_57_14 = e1
% 131.07/18.44 | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | (1014) all_54_13 = e3
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (981), (984), (1014) are inconsistent by sub-proof
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | #617.
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | Case 2:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | (1015) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1015) gives:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | (1016) all_54_13 = e2
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (981), (1016) imply:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | (1017) all_42_0 = e2
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | SIMP: (1017) implies:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | (1018) all_42_0 = e2
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | REDUCE: (982), (1018) imply:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | (1019) ~ (all_52_4 = e2)
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | REDUCE: (983), (1018) imply:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | (1020) ~ (all_52_6 = e2)
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | REDUCE: (975), (1018) imply:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | (1021) op(e0, e2) = e2
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | (1022) all_54_1 = e3
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (1022) imply:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | (1023) all_52_4 = e3
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (1023) imply:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | (1024) ~ (all_52_6 = e3)
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1024) implies:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | (1025) ~ (all_52_6 = e3)
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (1023) imply:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | (1026) ~ (all_52_8 = e3)
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1026) implies:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | (1027) ~ (all_52_8 = e3)
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | (1028) all_54_9 = e3
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (1028) imply:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | (1029) all_52_6 = e3
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1025), (1029) imply:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | (1030) $false
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1030) is inconsistent.
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | (1031) ~ (all_54_9 = e3)
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | (1032) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | (1033) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1033) gives:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | (1034) all_57_4 = e3 & op(e3, e1) = e3
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1034) implies:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | (1035) op(e3, e1) = e3
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (1027), (1035), (function-axioms) are
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #705.
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | (1036) all_57_5 = e3 & op(e2, e1) = e3
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1036) implies:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | (1037) all_57_5 = e3
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (1038) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1038) gives:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1039) all_57_6 = e3 & op(e1, e3) = e3
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1039) implies:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1040) all_57_6 = e3
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1041) op(e1, e3) = e3
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1042) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (170), (761), (952), (1042),
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #564.
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1043) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1043) gives:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1044) all_57_7 = e1 & op(e1, e2) = e1
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1044) implies:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1045) all_57_7 = e1
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1046) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1046) gives:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1047) all_57_1 = e3 & op(e3, e2) = e3
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1047) implies:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1048) all_57_1 = e3
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1049) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (954), (1048), (1049), (function-axioms)
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #562.
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1050) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1050) gives:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1051) all_57_4 = e2 & op(e3, e1) = e2
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1051) implies:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1052) all_57_4 = e2
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1053) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (170), (750), (954), (1053),
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #692.
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1054) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1054) gives:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1055) all_57_4 = e0 & op(e3, e1) = e0
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1055) implies:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1056) all_57_4 = e0
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (39), (221), (222),
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (382), (1013), (1056), (function-axioms)
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #558.
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1057) all_57_9 = e0 & op(e3, e0) = e0
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1057) implies:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1058) all_57_9 = e0
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1059) op(e3, e0) = e0
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1060) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1060) gives:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1061) all_57_6 = e2 & op(e1, e3) = e2
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1061) implies:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1062) all_57_6 = e2
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1040), (1062) are inconsistent by sub-proof
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #592.
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1063) all_57_7 = e2 & op(e1, e2) = e2
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1063) implies:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1064) all_57_7 = e2
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1045), (1064) imply:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1065) e2 = e1
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1052), (1065) imply:
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1066) all_57_4 = e1
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (236), (238), (954),
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1058), (1066), (function-axioms) are inconsistent
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #668.
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1067) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1067) gives:
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1068) all_57_8 = e2 & op(e1, e1) = e2
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1068) implies:
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1069) op(e1, e1) = e2
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (1069), (function-axioms) are
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1070) all_57_11 = e2 & op(e1, e0) = e2
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1070) implies:
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1071) all_57_11 = e2
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1072) op(e1, e0) = e2
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1073) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1073) gives:
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1074) all_57_9 = e1 & op(e3, e0) = e1
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1074) implies:
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1075) all_57_9 = e1
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (236),
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (750), (954), (1075), (function-axioms) are
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #686.
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1076) all_57_10 = e1 & op(e2, e0) = e1
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1076) implies:
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1077) op(e2, e0) = e1
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1078) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1078) gives:
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1079) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1079) gives:
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1080) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1080) implies:
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1081) op(e3, e3) = e2
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (954), (1081), (function-axioms) are
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743.
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1082) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1082) implies:
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1083) ~ (all_56_5 = e3)
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1084) op(e1, e3) = all_56_5
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (39), (218), (382), (1045), (1071),
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1083), (1084), (function-axioms) are inconsistent
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #722.
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1085) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (39), (110), (160), (163), (164), (168),
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206), (208), (212), (214), (366), (754), (954),
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (966), (967), (968), (977), (978), (1041), (1059),
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1071), (1072), (1077), (1085), (function-axioms)
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #630.
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1086) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1086) gives:
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1087) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1087) gives:
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1088) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1088) implies:
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1089) ~ (all_56_25 = e0)
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1090) op(e3, e0) = all_56_25
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1059), (1089), (1090), (function-axioms) are
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #642.
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1091) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 =
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2,
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1091) implies:
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1092) ~ (all_56_5 = e3)
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1093) op(e1, e3) = all_56_5
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (39), (218), (382), (1045), (1071),
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1092), (1093), (function-axioms) are inconsistent
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #722.
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1094) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1094) gives:
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1095) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1095) implies:
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1096) ~ (all_56_15 = e2)
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1097) op(e0, e2) = all_56_15
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1021), (1096), (1097), (function-axioms) are
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #609.
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1098) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (164), (208),
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212), (214), (372), (967), (1041), (1059),
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1071), (1072), (1098), (function-axioms) are
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #629.
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1099) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (969), (1072), (1099), (function-axioms)
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #557.
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1100) all_57_9 = e2 & op(e3, e0) = e2
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1100) implies:
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1101) all_57_9 = e2
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1102) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1102) gives:
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1103) all_57_4 = e2 & op(e3, e1) = e2
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1103) implies:
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1104) all_57_4 = e2
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1105) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (170), (750), (954), (1105),
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #692.
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1106) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1106) gives:
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1107) all_57_4 = e0 & op(e3, e1) = e0
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1107) implies:
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1108) all_57_4 = e0
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (39), (221), (222),
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (382), (1013), (1108), (function-axioms)
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #558.
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1109) all_57_9 = e0 & op(e3, e0) = e0
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1109) implies:
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1110) all_57_9 = e0
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1101), (1110) imply:
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1111) e2 = e0
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1104), (1111) imply:
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1112) all_57_4 = e0
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (39), (221), (222),
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (382), (1013), (1112), (function-axioms)
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #558.
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1113) all_57_5 = e2 & op(e2, e1) = e2
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1037), (1113) are inconsistent by sub-proof
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #677.
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1114) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1114) gives:
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1115) all_57_8 = e2 & op(e1, e1) = e2
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1115) implies:
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1116) op(e1, e1) = e2
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (1116), (function-axioms) are
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1117) all_57_14 = e2 & op(e0, e1) = e2
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1117) implies:
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1118) op(e0, e1) = e2
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (100), (194), (257), (295), (334), (359), (372),
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (382), (751), (969), (1020), (1032), (1118),
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #566.
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1119) all_57_3 = e3 & op(e2, e2) = e3
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1119) implies:
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1120) op(e2, e2) = e3
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (761), (1120), (function-axioms) are
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641.
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1121) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (964), (1025), (1121),
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #555.
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1122) all_57_13 = e1 & op(e0, e2) = e1
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1122) implies:
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1123) all_57_13 = e1
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (39), (100), (157), (160),
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (162), (167), (169), (170), (194), (208), (210),
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213), (215), (216), (218), (221), (222), (224),
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225), (231), (232), (236), (238), (257), (295),
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334), (359), (361), (372), (382), (750), (751),
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (760), (761), (951), (954), (965), (968), (969),
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1020), (1025), (1027), (1032), (1123),
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #565.
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1124) all_57_7 = e3 & op(e1, e2) = e3
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1124) implies:
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1125) op(e1, e2) = e3
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (1025), (1125), (function-axioms) are
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #654.
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (1126) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (160), (382), (968), (1126),
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | #653.
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | (1127) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (157), (382), (965), (1127),
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | #651.
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | (1128) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (271), (750), (952), (1019), (1128) are
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #701.
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | End of split
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | (1129) all_54_13 = e1 | all_54_13 = e0
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (974), (981), (985), (1129) are inconsistent by
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | sub-proof #604.
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | | End of split
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | End of split
% 131.23/18.47 | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.47 | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | (1130) all_57_15 = e1 & op(e0, e0) = e1
% 131.23/18.47 | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | ALPHA: (1130) implies:
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | (1131) op(e0, e0) = e1
% 131.23/18.47 | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (969), (1131), (function-axioms) are
% 131.23/18.47 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #606.
% 131.23/18.47 | | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | | End of split
% 131.23/18.47 | | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | End of split
% 131.23/18.47 | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.47 | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | (1132) ~ (all_34_1 = e1) & op(e3, e3) = all_34_1 &
% 131.23/18.47 | | | | | | | | | | | | | | | | | $i(all_34_1)
% 131.23/18.47 | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | ALPHA: (1132) implies:
% 131.23/18.47 | | | | | | | | | | | | | | | | | (1133) ~ (all_34_1 = e1)
% 131.23/18.47 | | | | | | | | | | | | | | | | | (1134) op(e3, e3) = all_34_1
% 131.23/18.47 | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | | REF_CLOSE: (954), (1133), (1134), (function-axioms) are
% 131.23/18.47 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #626.
% 131.23/18.47 | | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | End of split
% 131.23/18.47 | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | Case 2:
% 131.23/18.47 | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | (1135) ~ (all_42_1 = e3) & op(e0, e0) = all_42_1 &
% 131.23/18.47 | | | | | | | | | | | | | | | | $i(all_42_1)
% 131.23/18.47 | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | REF_CLOSE: (969), (1135), (function-axioms) are inconsistent
% 131.23/18.47 | | | | | | | | | | | | | | | | by sub-proof #602.
% 131.23/18.47 | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | End of split
% 131.23/18.47 | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | End of split
% 131.23/18.47 | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | End of split
% 131.23/18.47 | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | End of split
% 131.23/18.47 | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | End of split
% 131.23/18.47 | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | Case 2:
% 131.23/18.47 | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | (1136) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 131.23/18.47 | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 131.23/18.47 | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | BETA: splitting (1136) gives:
% 131.23/18.47 | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | Case 1:
% 131.23/18.47 | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | (1137) all_57_7 = e0 & op(e1, e2) = e0
% 131.23/18.47 | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | ALPHA: (1137) implies:
% 131.23/18.47 | | | | | | | | | | | | (1138) op(e1, e2) = e0
% 131.23/18.47 | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e0,
% 131.23/18.47 | | | | | | | | | | | | e2, e1, simplifying with (162), (1138) gives:
% 131.23/18.47 | | | | | | | | | | | | (1139) all_52_6 = e0
% 131.23/18.47 | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | REDUCE: (751), (1139) imply:
% 131.23/18.47 | | | | | | | | | | | | (1140) $false
% 131.23/18.47 | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | CLOSE: (1140) is inconsistent.
% 131.23/18.47 | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | Case 2:
% 131.23/18.47 | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | (1141) all_57_13 = e0 & op(e0, e2) = e0
% 131.23/18.47 | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | ALPHA: (1141) implies:
% 131.23/18.47 | | | | | | | | | | | | (1142) op(e0, e2) = e0
% 131.23/18.47 | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0,
% 131.23/18.47 | | | | | | | | | | | | e2, e0, simplifying with (158), (1142) gives:
% 131.23/18.47 | | | | | | | | | | | | (1143) all_52_7 = e0
% 131.23/18.47 | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | REDUCE: (752), (1143) imply:
% 131.23/18.47 | | | | | | | | | | | | (1144) $false
% 131.23/18.47 | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | CLOSE: (1144) is inconsistent.
% 131.23/18.47 | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | End of split
% 131.23/18.47 | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | End of split
% 131.23/18.47 | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | End of split
% 131.23/18.47 | | | | | | | | |
% 131.23/18.47 | | | | | | | | Case 2:
% 131.23/18.47 | | | | | | | | |
% 131.23/18.47 | | | | | | | | | (1145) all_28_2 = e3
% 131.23/18.47 | | | | | | | | |
% 131.23/18.47 | | | | | | | | | COMBINE_EQS: (316), (1145) imply:
% 131.23/18.47 | | | | | | | | | (1146) all_6_2 = e3
% 131.23/18.47 | | | | | | | | |
% 131.23/18.47 | | | | | | | | | SIMP: (1146) implies:
% 131.23/18.47 | | | | | | | | | (1147) all_6_2 = e3
% 131.23/18.47 | | | | | | | | |
% 131.23/18.47 | | | | | | | | | REDUCE: (359), (1147) imply:
% 131.23/18.47 | | | | | | | | | (1148) ~ (all_52_6 = e3)
% 131.23/18.47 | | | | | | | | |
% 131.23/18.47 | | | | | | | | | REDUCE: (361), (1147) imply:
% 131.23/18.47 | | | | | | | | | (1149) ~ (all_52_8 = e3)
% 131.23/18.47 | | | | | | | | |
% 131.23/18.47 | | | | | | | | | REDUCE: (362), (1147) imply:
% 131.23/18.47 | | | | | | | | | (1150) ~ (all_52_9 = e3)
% 131.23/18.47 | | | | | | | | |
% 131.23/18.47 | | | | | | | | | REDUCE: (39), (1147) imply:
% 131.23/18.47 | | | | | | | | | (1151) op(e1, e1) = e3
% 131.23/18.47 | | | | | | | | |
% 131.23/18.47 | | | | | | | | | BETA: splitting (76) gives:
% 131.23/18.47 | | | | | | | | |
% 131.23/18.47 | | | | | | | | | Case 1:
% 131.23/18.47 | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | (1152) ~ (all_30_2 = e0)
% 131.23/18.47 | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | REDUCE: (309), (1152) imply:
% 131.23/18.47 | | | | | | | | | | (1153) ~ (all_8_2 = e0)
% 131.23/18.47 | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | BETA: splitting (199) gives:
% 131.23/18.47 | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | Case 1:
% 131.23/18.47 | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | (1154) all_54_5 = e3
% 131.23/18.47 | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | REF_CLOSE: (267), (376), (1154) are inconsistent by sub-proof
% 131.23/18.47 | | | | | | | | | | | #554.
% 131.23/18.47 | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | Case 2:
% 131.23/18.47 | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | (1155) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 131.23/18.47 | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | BETA: splitting (1155) gives:
% 131.23/18.47 | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | Case 1:
% 131.23/18.47 | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | (1156) all_54_5 = e2
% 131.23/18.47 | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | COMBINE_EQS: (267), (1156) imply:
% 131.23/18.47 | | | | | | | | | | | | (1157) all_8_2 = e2
% 131.23/18.47 | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | SIMP: (1157) implies:
% 131.23/18.47 | | | | | | | | | | | | (1158) all_8_2 = e2
% 131.23/18.47 | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | REDUCE: (347), (1158) imply:
% 131.23/18.47 | | | | | | | | | | | | (1159) ~ (all_52_1 = e2)
% 131.23/18.47 | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | REDUCE: (350), (1158) imply:
% 131.23/18.47 | | | | | | | | | | | | (1160) ~ (all_52_4 = e2)
% 131.23/18.47 | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | REDUCE: (356), (1158) imply:
% 131.23/18.47 | | | | | | | | | | | | (1161) ~ (all_52_9 = e2)
% 131.23/18.47 | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | REDUCE: (358), (1158) imply:
% 131.23/18.47 | | | | | | | | | | | | (1162) ~ (all_52_13 = e2)
% 131.23/18.47 | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | BETA: splitting (225) gives:
% 131.23/18.47 | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | Case 1:
% 131.23/18.47 | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | (1163) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 131.23/18.47 | | | | | | | | | | | | | & op(e2, e2) = e2)
% 131.23/18.47 | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | BETA: splitting (1163) gives:
% 131.23/18.47 | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | Case 1:
% 131.23/18.47 | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | (1164) all_57_2 = e2 & op(e2, e3) = e2
% 131.23/18.47 | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | ALPHA: (1164) implies:
% 131.23/18.47 | | | | | | | | | | | | | | (1165) op(e2, e3) = e2
% 131.23/18.47 | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | REF_CLOSE: (167), (1159), (1165), (function-axioms) are
% 131.23/18.47 | | | | | | | | | | | | | | inconsistent by sub-proof #779.
% 131.23/18.47 | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | Case 2:
% 131.23/18.47 | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | (1166) all_57_3 = e2 & op(e2, e2) = e2
% 131.23/18.47 | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | ALPHA: (1166) implies:
% 131.23/18.47 | | | | | | | | | | | | | | (1167) all_57_3 = e2
% 131.23/18.47 | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 131.23/18.47 | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | Case 1:
% 131.23/18.47 | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | (1168) ~ (all_32_2 = e1)
% 131.23/18.47 | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | REDUCE: (312), (1168) imply:
% 131.23/18.47 | | | | | | | | | | | | | | | (1169) ~ (all_10_2 = e1)
% 131.23/18.47 | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 131.23/18.47 | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | Case 1:
% 131.23/18.47 | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | (1170) all_54_0 = e3
% 131.23/18.47 | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (1170) imply:
% 131.23/18.47 | | | | | | | | | | | | | | | | (1171) all_10_2 = e3
% 131.23/18.47 | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | SIMP: (1171) implies:
% 131.23/18.47 | | | | | | | | | | | | | | | | (1172) all_10_2 = e3
% 131.23/18.47 | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | REDUCE: (346), (1172) imply:
% 131.23/18.47 | | | | | | | | | | | | | | | | (1173) ~ (all_52_12 = e3)
% 131.23/18.47 | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | REDUCE: (45), (1172) imply:
% 131.23/18.47 | | | | | | | | | | | | | | | | (1174) op(e3, e3) = e3
% 131.23/18.47 | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 131.23/18.47 | | | | | | | | | | | | | | | |
% 131.23/18.47 | | | | | | | | | | | | | | | | Case 1:
% 131.23/18.47 | | | | | | | | | | | | | | | | |
% 131.23/18.48 | | | | | | | | | | | | | | | | | (1175) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 131.23/18.48 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.23/18.48 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 131.23/18.48 | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 131.23/18.48 | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 131.23/18.48 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 131.23/18.48 | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.23/18.48 | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 131.23/18.48 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 131.23/18.48 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 131.23/18.48 | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 131.23/18.48 | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 131.23/18.48 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 131.23/18.48 | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 131.23/18.48 | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 131.23/18.48 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 131.23/18.48 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 131.23/18.48 | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 131.23/18.48 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.23/18.48 | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 131.23/18.48 | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 131.23/18.48 | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 131.23/18.48 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.23/18.48 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.23/18.48 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.23/18.48 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 131.23/18.48 | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.23/18.48 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 131.23/18.48 | | | | | | | | | | | | | | | | |
% 131.23/18.48 | | | | | | | | | | | | | | | | | BETA: splitting (1175) gives:
% 131.23/18.48 | | | | | | | | | | | | | | | | |
% 131.23/18.48 | | | | | | | | | | | | | | | | | Case 1:
% 131.23/18.48 | | | | | | | | | | | | | | | | | |
% 131.23/18.48 | | | | | | | | | | | | | | | | | | (1176) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 131.23/18.48 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.23/18.48 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 131.23/18.48 | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 131.23/18.48 | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 131.23/18.48 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 131.23/18.48 | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.23/18.48 | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 131.23/18.48 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 131.23/18.48 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 131.23/18.48 | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 131.23/18.48 | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 131.23/18.48 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 131.23/18.48 | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 131.23/18.48 | | | | | | | | | | | | | | | | | |
% 131.23/18.48 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (1174), (1176), (function-axioms) are
% 131.23/18.48 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #623.
% 131.23/18.48 | | | | | | | | | | | | | | | | | |
% 131.23/18.48 | | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.48 | | | | | | | | | | | | | | | | | |
% 131.23/18.48 | | | | | | | | | | | | | | | | | | (1177) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 131.23/18.48 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 131.23/18.48 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 131.23/18.48 | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 131.23/18.48 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.23/18.48 | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 131.23/18.48 | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 131.23/18.48 | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 131.23/18.48 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.23/18.48 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.23/18.48 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.23/18.48 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 131.23/18.48 | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.23/18.48 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 131.23/18.48 | | | | | | | | | | | | | | | | | |
% 131.23/18.48 | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (1173), (1174), (1177), (function-axioms)
% 131.23/18.48 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #553.
% 131.23/18.48 | | | | | | | | | | | | | | | | | |
% 131.23/18.48 | | | | | | | | | | | | | | | | | End of split
% 131.23/18.48 | | | | | | | | | | | | | | | | |
% 131.23/18.48 | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.48 | | | | | | | | | | | | | | | | |
% 131.23/18.48 | | | | | | | | | | | | | | | | | (1178) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 131.23/18.48 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.23/18.48 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.23/18.48 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.23/18.48 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 131.23/18.48 | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.23/18.48 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 131.23/18.48 | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 131.23/18.48 | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 131.23/18.48 | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 131.23/18.48 | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 131.23/18.48 | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 131.23/18.48 | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 131.23/18.48 | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 131.23/18.48 | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 131.23/18.48 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.23/18.48 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 131.23/18.48 | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 131.23/18.48 | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 131.23/18.48 | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 131.23/18.48 | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 131.23/18.48 | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 131.23/18.48 | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 131.23/18.48 | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.23/18.48 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 131.23/18.48 | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 131.23/18.48 | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 131.23/18.48 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 131.23/18.48 | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 131.23/18.48 | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 131.23/18.48 | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 131.23/18.48 | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.23/18.48 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 131.23/18.48 | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 131.23/18.48 | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 131.23/18.48 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 131.23/18.48 | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 131.23/18.48 | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 131.23/18.48 | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.23/18.48 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.23/18.48 | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 131.23/18.48 | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 131.23/18.48 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 131.23/18.48 | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 131.23/18.48 | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 131.23/18.48 | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 131.23/18.48 | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 131.23/18.48 | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 131.23/18.48 | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 131.23/18.48 | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 131.23/18.48 | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 131.23/18.48 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 131.23/18.48 | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 131.23/18.48 | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 131.23/18.48 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 131.23/18.48 | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 131.23/18.48 | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 131.23/18.48 | | | | | | | | | | | | | | | | |
% 131.23/18.48 | | | | | | | | | | | | | | | | | BETA: splitting (1178) gives:
% 131.23/18.48 | | | | | | | | | | | | | | | | |
% 131.23/18.48 | | | | | | | | | | | | | | | | | Case 1:
% 131.23/18.48 | | | | | | | | | | | | | | | | | |
% 131.23/18.48 | | | | | | | | | | | | | | | | | | (1179) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 131.23/18.48 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.23/18.48 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.23/18.48 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.23/18.48 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 131.23/18.48 | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.23/18.48 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 131.23/18.48 | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 131.23/18.48 | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 131.23/18.48 | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 131.23/18.48 | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 131.23/18.48 | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 131.23/18.48 | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 131.23/18.48 | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 131.23/18.48 | | | | | | | | | | | | | | | | | |
% 131.23/18.48 | | | | | | | | | | | | | | | | | | BETA: splitting (1179) gives:
% 131.23/18.48 | | | | | | | | | | | | | | | | | |
% 131.23/18.48 | | | | | | | | | | | | | | | | | | Case 1:
% 131.23/18.48 | | | | | | | | | | | | | | | | | | |
% 131.23/18.48 | | | | | | | | | | | | | | | | | | | (1180) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 131.23/18.48 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 131.23/18.48 | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.23/18.48 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.23/18.48 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 131.23/18.48 | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.23/18.48 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 131.23/18.48 | | | | | | | | | | | | | | | | | | |
% 131.23/18.48 | | | | | | | | | | | | | | | | | | | ALPHA: (1180) implies:
% 131.23/18.48 | | | | | | | | | | | | | | | | | | | (1181) ~ (all_56_1 = e3)
% 131.23/18.48 | | | | | | | | | | | | | | | | | | | (1182) op(e3, e3) = all_56_1
% 131.23/18.48 | | | | | | | | | | | | | | | | | | |
% 131.23/18.48 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1174), (1181), (1182), (function-axioms) are
% 131.23/18.48 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #766.
% 131.23/18.48 | | | | | | | | | | | | | | | | | | |
% 131.23/18.48 | | | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.48 | | | | | | | | | | | | | | | | | | |
% 131.23/18.48 | | | | | | | | | | | | | | | | | | | (1183) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 =
% 131.23/18.48 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 131.23/18.48 | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2,
% 131.23/18.48 | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 131.23/18.48 | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 131.23/18.48 | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 131.23/18.48 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 131.23/18.48 | | | | | | | | | | | | | | | | | | |
% 131.23/18.48 | | | | | | | | | | | | | | | | | | | ALPHA: (1183) implies:
% 131.23/18.48 | | | | | | | | | | | | | | | | | | | (1184) op(e2, e1) = e2
% 131.23/18.48 | | | | | | | | | | | | | | | | | | |
% 131.23/18.48 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (1161), (1184), (function-axioms) are
% 131.23/18.48 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #770.
% 131.23/18.48 | | | | | | | | | | | | | | | | | | |
% 131.23/18.48 | | | | | | | | | | | | | | | | | | End of split
% 131.23/18.48 | | | | | | | | | | | | | | | | | |
% 131.23/18.48 | | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.48 | | | | | | | | | | | | | | | | | |
% 131.23/18.49 | | | | | | | | | | | | | | | | | | (1185) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 131.23/18.49 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 131.23/18.49 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 131.23/18.49 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 131.23/18.49 | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 131.23/18.49 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.23/18.49 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 131.23/18.49 | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.23/18.49 | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 131.23/18.49 | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.23/18.49 | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 131.23/18.49 | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 131.23/18.49 | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 131.23/18.49 | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 131.23/18.49 | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 131.23/18.49 | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 131.23/18.49 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 131.23/18.49 | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 131.23/18.49 | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 131.23/18.49 | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.23/18.49 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.23/18.49 | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 131.23/18.49 | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 131.23/18.49 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 131.23/18.49 | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 131.23/18.49 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 131.23/18.49 | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 131.23/18.49 | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 131.23/18.49 | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 131.23/18.49 | | | | | | | | | | | | | | | | | |
% 131.23/18.49 | | | | | | | | | | | | | | | | | | BETA: splitting (1185) gives:
% 131.23/18.49 | | | | | | | | | | | | | | | | | |
% 131.23/18.49 | | | | | | | | | | | | | | | | | | Case 1:
% 131.23/18.49 | | | | | | | | | | | | | | | | | | |
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | (1186) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 131.23/18.49 | | | | | | | | | | | | | | | | | | |
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | ALPHA: (1186) implies:
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | (1187) op(e2, e0) = e2
% 131.23/18.49 | | | | | | | | | | | | | | | | | | |
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (1162), (1187), (function-axioms) are
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 131.23/18.49 | | | | | | | | | | | | | | | | | | |
% 131.23/18.49 | | | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.49 | | | | | | | | | | | | | | | | | | |
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | (1188) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 131.23/18.49 | | | | | | | | | | | | | | | | | | |
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | BETA: splitting (1188) gives:
% 131.23/18.49 | | | | | | | | | | | | | | | | | | |
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | Case 1:
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | |
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (1189) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | |
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | ALPHA: (1189) implies:
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (1190) op(e1, e1) = e2
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | |
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (1190), (function-axioms) are
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | |
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | |
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (1191) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | |
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | ALPHA: (1191) implies:
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (1192) op(e0, e0) = all_56_31
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (1193) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | |
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (39), (45), (100), (118), (157), (160),
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (163), (164), (165), (167), (189), (190), (204),
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (218), (226), (245), (246), (278), (295), (336),
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (338), (364), (369), (370), (371), (374), (378),
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (380), (1167), (1169), (1192), (1193),
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | | #744.
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | |
% 131.23/18.49 | | | | | | | | | | | | | | | | | | | End of split
% 131.23/18.49 | | | | | | | | | | | | | | | | | | |
% 131.23/18.49 | | | | | | | | | | | | | | | | | | End of split
% 131.23/18.49 | | | | | | | | | | | | | | | | | |
% 131.23/18.49 | | | | | | | | | | | | | | | | | End of split
% 131.23/18.49 | | | | | | | | | | | | | | | | |
% 131.23/18.49 | | | | | | | | | | | | | | | | End of split
% 131.23/18.49 | | | | | | | | | | | | | | | |
% 131.23/18.49 | | | | | | | | | | | | | | | Case 2:
% 131.23/18.49 | | | | | | | | | | | | | | | |
% 131.23/18.49 | | | | | | | | | | | | | | | | (1194) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 131.23/18.49 | | | | | | | | | | | | | | | |
% 131.23/18.49 | | | | | | | | | | | | | | | | REF_CLOSE: (278), (374), (378), (1169), (1194) are
% 131.23/18.49 | | | | | | | | | | | | | | | | inconsistent by sub-proof #777.
% 131.23/18.49 | | | | | | | | | | | | | | | |
% 131.23/18.49 | | | | | | | | | | | | | | | End of split
% 131.23/18.49 | | | | | | | | | | | | | | |
% 131.23/18.49 | | | | | | | | | | | | | | Case 2:
% 131.23/18.49 | | | | | | | | | | | | | | |
% 131.23/18.49 | | | | | | | | | | | | | | | (1195) all_32_2 = e1
% 131.23/18.49 | | | | | | | | | | | | | | |
% 131.23/18.49 | | | | | | | | | | | | | | | COMBINE_EQS: (312), (1195) imply:
% 131.23/18.49 | | | | | | | | | | | | | | | (1196) all_10_2 = e1
% 131.23/18.49 | | | | | | | | | | | | | | |
% 131.23/18.49 | | | | | | | | | | | | | | | SIMP: (1196) implies:
% 131.23/18.49 | | | | | | | | | | | | | | | (1197) all_10_2 = e1
% 131.23/18.49 | | | | | | | | | | | | | | |
% 131.23/18.49 | | | | | | | | | | | | | | | REDUCE: (338), (1197) imply:
% 131.23/18.49 | | | | | | | | | | | | | | | (1198) ~ (all_52_2 = e1)
% 131.23/18.49 | | | | | | | | | | | | | | |
% 131.23/18.49 | | | | | | | | | | | | | | | REDUCE: (340), (1197) imply:
% 131.23/18.49 | | | | | | | | | | | | | | | (1199) ~ (all_52_3 = e1)
% 131.23/18.49 | | | | | | | | | | | | | | |
% 131.23/18.49 | | | | | | | | | | | | | | | REDUCE: (378), (1197) imply:
% 131.23/18.49 | | | | | | | | | | | | | | | (1200) ~ (e2 = e1)
% 131.23/18.49 | | | | | | | | | | | | | | |
% 131.23/18.49 | | | | | | | | | | | | | | | REDUCE: (45), (1197) imply:
% 131.23/18.49 | | | | | | | | | | | | | | | (1201) op(e3, e3) = e1
% 131.23/18.49 | | | | | | | | | | | | | | |
% 131.23/18.49 | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 131.23/18.49 | | | | | | | | | | | | | | |
% 131.23/18.49 | | | | | | | | | | | | | | | Case 1:
% 131.23/18.49 | | | | | | | | | | | | | | | |
% 131.23/18.50 | | | | | | | | | | | | | | | | (1202) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 131.23/18.50 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.23/18.50 | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 131.23/18.50 | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 131.23/18.50 | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 131.23/18.50 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 131.23/18.50 | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.23/18.50 | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 131.23/18.50 | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 131.23/18.50 | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 131.23/18.50 | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 131.23/18.50 | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 131.23/18.50 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 131.23/18.50 | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 131.23/18.50 | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 131.23/18.50 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 131.23/18.50 | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 131.23/18.50 | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 131.23/18.50 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.23/18.50 | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 131.23/18.50 | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 131.23/18.50 | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 131.23/18.50 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.23/18.50 | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.23/18.50 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.23/18.50 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 131.23/18.50 | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.23/18.50 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 131.23/18.50 | | | | | | | | | | | | | | | |
% 131.23/18.50 | | | | | | | | | | | | | | | | BETA: splitting (1202) gives:
% 131.23/18.50 | | | | | | | | | | | | | | | |
% 131.23/18.50 | | | | | | | | | | | | | | | | Case 1:
% 131.23/18.50 | | | | | | | | | | | | | | | | |
% 131.23/18.50 | | | | | | | | | | | | | | | | | (1203) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 131.23/18.50 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.23/18.50 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 131.23/18.50 | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 131.23/18.50 | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 131.23/18.50 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 131.23/18.50 | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.23/18.50 | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 131.23/18.50 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 131.23/18.50 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 131.23/18.50 | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 131.23/18.50 | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 131.23/18.50 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 131.23/18.50 | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 131.23/18.50 | | | | | | | | | | | | | | | | |
% 131.23/18.50 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (169), (1149), (1201), (1203),
% 131.23/18.50 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.23/18.50 | | | | | | | | | | | | | | | | | #552.
% 131.23/18.50 | | | | | | | | | | | | | | | | |
% 131.23/18.50 | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.50 | | | | | | | | | | | | | | | | |
% 131.23/18.50 | | | | | | | | | | | | | | | | | (1204) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 131.23/18.50 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 131.23/18.50 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 131.23/18.50 | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 131.23/18.50 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.23/18.50 | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 131.23/18.50 | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 131.23/18.50 | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 131.23/18.50 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.23/18.50 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.23/18.50 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.23/18.50 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 131.23/18.50 | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.23/18.50 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 131.23/18.50 | | | | | | | | | | | | | | | | |
% 131.23/18.50 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (167), (1159), (1201), (1204),
% 131.23/18.50 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.23/18.50 | | | | | | | | | | | | | | | | | #716.
% 131.23/18.50 | | | | | | | | | | | | | | | | |
% 131.23/18.50 | | | | | | | | | | | | | | | | End of split
% 131.23/18.50 | | | | | | | | | | | | | | | |
% 131.23/18.50 | | | | | | | | | | | | | | | Case 2:
% 131.23/18.50 | | | | | | | | | | | | | | | |
% 131.23/18.50 | | | | | | | | | | | | | | | | (1205) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 131.23/18.50 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.23/18.50 | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.23/18.50 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.23/18.50 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 131.23/18.50 | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.23/18.50 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 131.23/18.50 | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 131.23/18.50 | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 131.23/18.50 | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 131.23/18.50 | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 131.23/18.50 | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 131.23/18.50 | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 131.23/18.50 | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 131.23/18.50 | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 131.23/18.50 | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.23/18.50 | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 131.23/18.50 | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 131.23/18.50 | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 131.23/18.50 | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 131.23/18.50 | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 131.23/18.50 | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 131.23/18.50 | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 131.23/18.50 | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.23/18.50 | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 131.23/18.50 | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 131.23/18.50 | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 131.23/18.50 | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 131.23/18.50 | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 131.23/18.50 | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 131.23/18.50 | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 131.23/18.50 | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.23/18.50 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 131.23/18.50 | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 131.23/18.50 | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 131.23/18.50 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 131.23/18.50 | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 131.23/18.50 | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 131.23/18.50 | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.23/18.50 | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.23/18.50 | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 131.23/18.50 | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 131.23/18.50 | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 131.23/18.50 | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 131.23/18.50 | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 131.23/18.50 | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 131.23/18.50 | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 131.23/18.50 | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 131.23/18.50 | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 131.23/18.50 | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 131.23/18.50 | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 131.23/18.50 | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 131.23/18.50 | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 131.23/18.50 | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 131.23/18.50 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 131.23/18.50 | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 131.23/18.50 | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 131.23/18.50 | | | | | | | | | | | | | | | |
% 131.23/18.50 | | | | | | | | | | | | | | | | BETA: splitting (1205) gives:
% 131.23/18.50 | | | | | | | | | | | | | | | |
% 131.23/18.50 | | | | | | | | | | | | | | | | Case 1:
% 131.23/18.50 | | | | | | | | | | | | | | | | |
% 131.23/18.50 | | | | | | | | | | | | | | | | | (1206) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 131.23/18.50 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.23/18.50 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.23/18.50 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.23/18.50 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 131.23/18.50 | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.23/18.50 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 131.23/18.50 | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 131.23/18.50 | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 131.23/18.50 | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 131.23/18.50 | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 131.23/18.50 | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 131.23/18.50 | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 131.23/18.50 | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 131.23/18.50 | | | | | | | | | | | | | | | | |
% 131.23/18.50 | | | | | | | | | | | | | | | | | BETA: splitting (1206) gives:
% 131.23/18.50 | | | | | | | | | | | | | | | | |
% 131.23/18.50 | | | | | | | | | | | | | | | | | Case 1:
% 131.23/18.50 | | | | | | | | | | | | | | | | | |
% 131.23/18.50 | | | | | | | | | | | | | | | | | | (1207) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 131.23/18.50 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 131.23/18.50 | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.23/18.50 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.23/18.50 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 131.23/18.50 | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.23/18.50 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 131.23/18.50 | | | | | | | | | | | | | | | | | |
% 131.23/18.50 | | | | | | | | | | | | | | | | | | ALPHA: (1207) implies:
% 131.23/18.50 | | | | | | | | | | | | | | | | | | (1208) op(e1, e3) = e1
% 131.23/18.50 | | | | | | | | | | | | | | | | | |
% 131.23/18.50 | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (1198), (1208), (function-axioms) are
% 131.23/18.50 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #725.
% 131.23/18.50 | | | | | | | | | | | | | | | | | |
% 131.23/18.50 | | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.50 | | | | | | | | | | | | | | | | | |
% 131.23/18.50 | | | | | | | | | | | | | | | | | | (1209) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 =
% 131.23/18.50 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 131.23/18.50 | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2,
% 131.23/18.50 | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 131.23/18.50 | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 131.23/18.50 | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 131.23/18.50 | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 131.23/18.50 | | | | | | | | | | | | | | | | | |
% 131.23/18.50 | | | | | | | | | | | | | | | | | | ALPHA: (1209) implies:
% 131.23/18.50 | | | | | | | | | | | | | | | | | | (1210) op(e2, e1) = e2
% 131.23/18.50 | | | | | | | | | | | | | | | | | |
% 131.23/18.50 | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (1161), (1210), (function-axioms) are
% 131.23/18.50 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #770.
% 131.23/18.50 | | | | | | | | | | | | | | | | | |
% 131.23/18.50 | | | | | | | | | | | | | | | | | End of split
% 131.23/18.50 | | | | | | | | | | | | | | | | |
% 131.23/18.50 | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.50 | | | | | | | | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | | | | | | | | (1211) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 131.23/18.51 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 131.23/18.51 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 131.23/18.51 | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 131.23/18.51 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.23/18.51 | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 131.23/18.51 | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 131.23/18.51 | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 131.23/18.51 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.23/18.51 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 131.23/18.51 | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.23/18.51 | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 131.23/18.51 | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 131.23/18.51 | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.23/18.51 | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 131.23/18.51 | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 131.23/18.51 | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 131.23/18.51 | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 131.23/18.51 | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 131.23/18.51 | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 131.23/18.51 | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 131.23/18.51 | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 131.23/18.51 | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 131.23/18.51 | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 131.23/18.51 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 131.23/18.51 | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 131.23/18.51 | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 131.23/18.51 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 131.23/18.51 | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 131.23/18.51 | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 131.23/18.51 | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.23/18.51 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.23/18.51 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 131.23/18.51 | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 131.23/18.51 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.23/18.51 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 131.23/18.51 | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 131.23/18.51 | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 131.23/18.51 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 131.23/18.51 | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 131.23/18.51 | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 131.23/18.51 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 131.23/18.51 | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 131.23/18.51 | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 131.23/18.51 | | | | | | | | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | | | | | | | | BETA: splitting (1211) gives:
% 131.23/18.51 | | | | | | | | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | | | | | | | | Case 1:
% 131.23/18.51 | | | | | | | | | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | | | | | | | | | (1212) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 131.23/18.51 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 131.23/18.51 | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 131.23/18.51 | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 131.23/18.51 | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 131.23/18.51 | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 131.23/18.51 | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 131.23/18.51 | | | | | | | | | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | | | | | | | | | ALPHA: (1212) implies:
% 131.23/18.51 | | | | | | | | | | | | | | | | | | (1213) op(e2, e0) = e2
% 131.23/18.51 | | | | | | | | | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (1162), (1213), (function-axioms) are
% 131.23/18.51 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 131.23/18.51 | | | | | | | | | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.51 | | | | | | | | | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | | | | | | | | | (1214) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 131.23/18.51 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.23/18.51 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 131.23/18.51 | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.23/18.51 | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 131.23/18.51 | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 131.23/18.51 | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.23/18.51 | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 131.23/18.51 | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 131.23/18.51 | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 131.23/18.51 | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 131.23/18.51 | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 131.23/18.51 | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 131.23/18.51 | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 131.23/18.51 | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 131.23/18.51 | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 131.23/18.51 | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 131.23/18.51 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 131.23/18.51 | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 131.23/18.51 | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 131.23/18.51 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 131.23/18.51 | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 131.23/18.51 | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 131.23/18.51 | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.23/18.51 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.23/18.51 | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 131.23/18.51 | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 131.23/18.51 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.23/18.51 | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 131.23/18.51 | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 131.23/18.51 | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 131.23/18.51 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 131.23/18.51 | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 131.23/18.51 | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 131.23/18.51 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 131.23/18.51 | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 131.23/18.51 | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 131.23/18.51 | | | | | | | | | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | | | | | | | | | BETA: splitting (1214) gives:
% 131.23/18.51 | | | | | | | | | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | | | | | | | | | Case 1:
% 131.23/18.51 | | | | | | | | | | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | (1215) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 131.23/18.51 | | | | | | | | | | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | ALPHA: (1215) implies:
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | (1216) op(e1, e1) = e2
% 131.23/18.51 | | | | | | | | | | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (1216), (function-axioms) are
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 131.23/18.51 | | | | | | | | | | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.51 | | | | | | | | | | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | (1217) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 131.23/18.51 | | | | | | | | | | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | ALPHA: (1217) implies:
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | (1218) op(e0, e0) = all_56_31
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | (1219) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 131.23/18.51 | | | | | | | | | | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (36), (82), (159), (168), (169),
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | (170), (232), (236), (238), (307), (349), (368),
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | (371), (380), (1149), (1151), (1160), (1199),
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | (1201), (1218), (1219), (function-axioms) are
% 131.23/18.51 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #548.
% 131.23/18.51 | | | | | | | | | | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | | | | | | | | | End of split
% 131.23/18.51 | | | | | | | | | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | | | | | | | | End of split
% 131.23/18.51 | | | | | | | | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | | | | | | | End of split
% 131.23/18.51 | | | | | | | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | | | | | | End of split
% 131.23/18.51 | | | | | | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | | | | | End of split
% 131.23/18.51 | | | | | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | | | | End of split
% 131.23/18.51 | | | | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | | | Case 2:
% 131.23/18.51 | | | | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | | | | (1220) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 131.23/18.51 | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 131.23/18.51 | | | | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | | | | REF_CLOSE: (164), (165), (1161), (1162), (1220),
% 131.23/18.51 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.23/18.51 | | | | | | | | | | | | | #625.
% 131.23/18.51 | | | | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | | | End of split
% 131.23/18.51 | | | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | | Case 2:
% 131.23/18.51 | | | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | | | (1221) all_54_5 = e1 | all_54_5 = e0
% 131.23/18.51 | | | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | | | REF_CLOSE: (267), (373), (1153), (1221) are inconsistent by
% 131.23/18.51 | | | | | | | | | | | | sub-proof #624.
% 131.23/18.51 | | | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | | End of split
% 131.23/18.51 | | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | End of split
% 131.23/18.51 | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | Case 2:
% 131.23/18.51 | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | (1222) all_30_2 = e0
% 131.23/18.51 | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | COMBINE_EQS: (309), (1222) imply:
% 131.23/18.51 | | | | | | | | | | (1223) all_8_2 = e0
% 131.23/18.51 | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | COMBINE_EQS: (301), (1223) imply:
% 131.23/18.51 | | | | | | | | | | (1224) all_42_2 = e0
% 131.23/18.51 | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | REDUCE: (350), (1223) imply:
% 131.23/18.51 | | | | | | | | | | (1225) ~ (all_52_4 = e0)
% 131.23/18.51 | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | REDUCE: (354), (1223) imply:
% 131.23/18.51 | | | | | | | | | | (1226) ~ (all_52_7 = e0)
% 131.23/18.51 | | | | | | | | | |
% 131.23/18.51 | | | | | | | | | | REDUCE: (376), (1223) imply:
% 131.23/18.52 | | | | | | | | | | (1227) ~ (e3 = e0)
% 131.23/18.52 | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | REDUCE: (373), (1223) imply:
% 131.23/18.52 | | | | | | | | | | (1228) ~ (e1 = e0)
% 131.23/18.52 | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | REDUCE: (42), (1223) imply:
% 131.23/18.52 | | | | | | | | | | (1229) op(e2, e2) = e0
% 131.23/18.52 | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | BETA: splitting (79) gives:
% 131.23/18.52 | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | Case 1:
% 131.23/18.52 | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | (1230) ~ (all_32_2 = e1)
% 131.23/18.52 | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | REDUCE: (312), (1230) imply:
% 131.23/18.52 | | | | | | | | | | | (1231) ~ (all_10_2 = e1)
% 131.23/18.52 | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | REF_CLOSE: (4), (36), (39), (45), (158), (164), (165), (167),
% 131.23/18.52 | | | | | | | | | | | (168), (204), (206), (226), (278), (336), (346),
% 131.23/18.52 | | | | | | | | | | | (371), (372), (374), (378), (1150), (1151),
% 131.23/18.52 | | | | | | | | | | | (1226), (1229), (1231), (function-axioms) are
% 131.23/18.52 | | | | | | | | | | | inconsistent by sub-proof #541.
% 131.23/18.52 | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | Case 2:
% 131.23/18.52 | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | (1232) all_32_2 = e1
% 131.23/18.52 | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | COMBINE_EQS: (312), (1232) imply:
% 131.23/18.52 | | | | | | | | | | | (1233) all_10_2 = e1
% 131.23/18.52 | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | SIMP: (1233) implies:
% 131.23/18.52 | | | | | | | | | | | (1234) all_10_2 = e1
% 131.23/18.52 | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | REDUCE: (338), (1234) imply:
% 131.23/18.52 | | | | | | | | | | | (1235) ~ (all_52_2 = e1)
% 131.23/18.52 | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | REDUCE: (342), (1234) imply:
% 131.23/18.52 | | | | | | | | | | | (1236) ~ (all_52_4 = e1)
% 131.23/18.52 | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | REDUCE: (346), (1234) imply:
% 131.23/18.52 | | | | | | | | | | | (1237) ~ (all_52_12 = e1)
% 131.23/18.52 | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | REDUCE: (378), (1234) imply:
% 131.23/18.52 | | | | | | | | | | | (1238) ~ (e2 = e1)
% 131.23/18.52 | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | REDUCE: (45), (1234) imply:
% 131.23/18.52 | | | | | | | | | | | (1239) op(e3, e3) = e1
% 131.23/18.52 | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | BETA: splitting (82) gives:
% 131.23/18.52 | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | Case 1:
% 131.23/18.52 | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | (1240) ~ (all_34_2 = e3)
% 131.23/18.52 | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | REDUCE: (307), (1240) imply:
% 131.23/18.52 | | | | | | | | | | | | (1241) ~ (all_4_2 = e3)
% 131.23/18.52 | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | BETA: splitting (189) gives:
% 131.23/18.52 | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | Case 1:
% 131.23/18.52 | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | (1242) all_54_15 = e3
% 131.23/18.52 | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | COMBINE_EQS: (245), (1242) imply:
% 131.23/18.52 | | | | | | | | | | | | | (1243) all_4_2 = e3
% 131.23/18.52 | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | REDUCE: (1241), (1243) imply:
% 131.23/18.52 | | | | | | | | | | | | | (1244) $false
% 131.23/18.52 | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | CLOSE: (1244) is inconsistent.
% 131.23/18.52 | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | Case 2:
% 131.23/18.52 | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | (1245) ~ (all_54_15 = e3)
% 131.23/18.52 | | | | | | | | | | | | | (1246) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 131.23/18.52 | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | BETA: splitting (1246) gives:
% 131.23/18.52 | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | Case 1:
% 131.23/18.52 | | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | | (1247) all_54_15 = e2
% 131.23/18.52 | | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | | COMBINE_EQS: (245), (1247) imply:
% 131.23/18.52 | | | | | | | | | | | | | | (1248) all_4_2 = e2
% 131.23/18.52 | | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | | REDUCE: (380), (1248) imply:
% 131.23/18.52 | | | | | | | | | | | | | | (1249) $false
% 131.23/18.52 | | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | | CLOSE: (1249) is inconsistent.
% 131.23/18.52 | | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | Case 2:
% 131.23/18.52 | | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | | (1250) ~ (all_54_15 = e2)
% 131.23/18.52 | | | | | | | | | | | | | | (1251) all_54_15 = e1 | all_54_15 = e0
% 131.23/18.52 | | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | | BETA: splitting (1251) gives:
% 131.23/18.52 | | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | | Case 1:
% 131.23/18.52 | | | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | | | (1252) all_54_15 = e1
% 131.23/18.52 | | | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | | | COMBINE_EQS: (245), (1252) imply:
% 131.23/18.52 | | | | | | | | | | | | | | | (1253) all_4_2 = e1
% 131.23/18.52 | | | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | | | REDUCE: (371), (1253) imply:
% 131.23/18.52 | | | | | | | | | | | | | | | (1254) $false
% 131.23/18.52 | | | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | | | CLOSE: (1254) is inconsistent.
% 131.23/18.52 | | | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | | Case 2:
% 131.23/18.52 | | | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | | | (1255) all_54_15 = e0
% 131.23/18.52 | | | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | | | COMBINE_EQS: (245), (1255) imply:
% 131.23/18.52 | | | | | | | | | | | | | | | (1256) all_4_2 = e0
% 131.23/18.52 | | | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | | | REDUCE: (368), (1256) imply:
% 131.23/18.52 | | | | | | | | | | | | | | | (1257) ~ (all_52_12 = e0)
% 131.23/18.52 | | | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | | | REDUCE: (380), (1256) imply:
% 131.23/18.52 | | | | | | | | | | | | | | | (1258) ~ (e2 = e0)
% 131.23/18.52 | | | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | | | REDUCE: (36), (1256) imply:
% 131.23/18.52 | | | | | | | | | | | | | | | (1259) op(e0, e0) = e0
% 131.23/18.52 | | | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 131.23/18.52 | | | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | | | Case 1:
% 131.23/18.52 | | | | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | | | | (1260) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 131.23/18.52 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.23/18.52 | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 131.23/18.52 | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 131.23/18.52 | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 131.23/18.52 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 131.23/18.52 | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.23/18.52 | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 131.23/18.52 | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 131.23/18.52 | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 131.23/18.52 | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 131.23/18.52 | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 131.23/18.52 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 131.23/18.52 | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 131.23/18.52 | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 131.23/18.52 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 131.23/18.52 | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 131.23/18.52 | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 131.23/18.52 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.23/18.52 | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 131.23/18.52 | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 131.23/18.52 | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 131.23/18.52 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.23/18.52 | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.23/18.52 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.23/18.52 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 131.23/18.52 | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.23/18.52 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 131.23/18.52 | | | | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (168), (169), (170), (232), (1225),
% 131.23/18.52 | | | | | | | | | | | | | | | | (1229), (1239), (1257), (1260), (function-axioms)
% 131.23/18.52 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #597.
% 131.23/18.52 | | | | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | | | Case 2:
% 131.23/18.52 | | | | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | | | | (1261) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 131.23/18.52 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.23/18.52 | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.23/18.52 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.23/18.52 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 131.23/18.52 | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.23/18.52 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 131.23/18.52 | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 131.23/18.52 | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 131.23/18.52 | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 131.23/18.52 | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 131.23/18.52 | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 131.23/18.52 | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 131.23/18.52 | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 131.23/18.52 | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 131.23/18.52 | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.23/18.52 | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 131.23/18.52 | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 131.23/18.52 | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 131.23/18.52 | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 131.23/18.52 | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 131.23/18.52 | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 131.23/18.52 | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 131.23/18.52 | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.23/18.52 | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 131.23/18.52 | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 131.23/18.52 | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 131.23/18.52 | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 131.23/18.52 | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 131.23/18.52 | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 131.23/18.52 | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 131.23/18.52 | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.23/18.52 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 131.23/18.52 | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 131.23/18.52 | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 131.23/18.52 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 131.23/18.52 | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 131.23/18.52 | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 131.23/18.52 | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.23/18.52 | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.23/18.52 | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 131.23/18.52 | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 131.23/18.52 | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 131.23/18.52 | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 131.23/18.52 | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 131.23/18.52 | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 131.23/18.52 | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 131.23/18.52 | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 131.23/18.52 | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 131.23/18.52 | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 131.23/18.52 | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 131.23/18.52 | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 131.23/18.52 | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 131.23/18.52 | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 131.23/18.52 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 131.23/18.52 | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 131.23/18.52 | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 131.23/18.52 | | | | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | | | | BETA: splitting (1261) gives:
% 131.23/18.52 | | | | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | | | | Case 1:
% 131.23/18.52 | | | | | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | | | | | (1262) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 131.23/18.52 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.23/18.52 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.23/18.52 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.23/18.52 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 131.23/18.52 | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.23/18.52 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 131.23/18.52 | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 131.23/18.52 | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 131.23/18.52 | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 131.23/18.52 | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 131.23/18.52 | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 131.23/18.52 | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 131.23/18.52 | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 131.23/18.52 | | | | | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | | | | | BETA: splitting (1262) gives:
% 131.23/18.52 | | | | | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | | | | | Case 1:
% 131.23/18.52 | | | | | | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | | | | | | (1263) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 131.23/18.52 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 131.23/18.52 | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.23/18.52 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.23/18.52 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 131.23/18.52 | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.23/18.52 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 131.23/18.52 | | | | | | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | | | | | | ALPHA: (1263) implies:
% 131.23/18.52 | | | | | | | | | | | | | | | | | | (1264) op(e1, e3) = e1
% 131.23/18.52 | | | | | | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (1235), (1264), (function-axioms) are
% 131.23/18.52 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #725.
% 131.23/18.52 | | | | | | | | | | | | | | | | | |
% 131.23/18.52 | | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.52 | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | (1265) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 =
% 131.23/18.53 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 131.23/18.53 | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2,
% 131.23/18.53 | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 131.23/18.53 | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 131.23/18.53 | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 131.23/18.53 | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 131.23/18.53 | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | ALPHA: (1265) implies:
% 131.23/18.53 | | | | | | | | | | | | | | | | | | (1266) op(e2, e2) = e1
% 131.23/18.53 | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1229), (1266), (function-axioms) are
% 131.23/18.53 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675.
% 131.23/18.53 | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | End of split
% 131.23/18.53 | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.53 | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | (1267) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 131.23/18.53 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 131.23/18.53 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 131.23/18.53 | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 131.23/18.53 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.23/18.53 | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 131.23/18.53 | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 131.23/18.53 | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 131.23/18.53 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.23/18.53 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 131.23/18.53 | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.23/18.53 | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 131.23/18.53 | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 131.23/18.53 | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.23/18.53 | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 131.23/18.53 | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 131.23/18.53 | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 131.23/18.53 | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 131.23/18.53 | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 131.23/18.53 | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 131.23/18.53 | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 131.23/18.53 | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 131.23/18.53 | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 131.23/18.53 | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 131.23/18.53 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 131.23/18.53 | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 131.23/18.53 | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 131.23/18.53 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 131.23/18.53 | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 131.23/18.53 | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 131.23/18.53 | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.23/18.53 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.23/18.53 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 131.23/18.53 | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 131.23/18.53 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.23/18.53 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 131.23/18.53 | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 131.23/18.53 | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 131.23/18.53 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 131.23/18.53 | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 131.23/18.53 | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 131.23/18.53 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 131.23/18.53 | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 131.23/18.53 | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 131.23/18.53 | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (39), (372), (1259), (1267),
% 131.23/18.53 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.23/18.53 | | | | | | | | | | | | | | | | | #596.
% 131.23/18.53 | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | End of split
% 131.23/18.53 | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | End of split
% 131.23/18.53 | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | End of split
% 131.23/18.53 | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | End of split
% 131.23/18.53 | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | End of split
% 131.23/18.53 | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | Case 2:
% 131.23/18.53 | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | (1268) all_34_2 = e3
% 131.23/18.53 | | | | | | | | | | | | (1269) ( ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 &
% 131.23/18.53 | | | | | | | | | | | | $i(all_34_0)) | ( ~ (all_34_1 = e1) & op(e3, e3)
% 131.23/18.53 | | | | | | | | | | | | = all_34_1 & $i(all_34_1))
% 131.23/18.53 | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | COMBINE_EQS: (307), (1268) imply:
% 131.23/18.53 | | | | | | | | | | | | (1270) all_4_2 = e3
% 131.23/18.53 | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | SIMP: (1270) implies:
% 131.23/18.53 | | | | | | | | | | | | (1271) all_4_2 = e3
% 131.23/18.53 | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | REDUCE: (349), (1271) imply:
% 131.23/18.53 | | | | | | | | | | | | (1272) ~ (all_52_3 = e3)
% 131.23/18.53 | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | REDUCE: (360), (1271) imply:
% 131.23/18.53 | | | | | | | | | | | | (1273) ~ (all_52_7 = e3)
% 131.23/18.53 | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | REDUCE: (367), (1271) imply:
% 131.23/18.53 | | | | | | | | | | | | (1274) ~ (all_52_11 = e3)
% 131.23/18.53 | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | REDUCE: (368), (1271) imply:
% 131.23/18.53 | | | | | | | | | | | | (1275) ~ (all_52_12 = e3)
% 131.23/18.53 | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | REDUCE: (36), (1271) imply:
% 131.23/18.53 | | | | | | | | | | | | (1276) op(e0, e0) = e3
% 131.23/18.53 | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | BETA: splitting (1269) gives:
% 131.23/18.53 | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | Case 1:
% 131.23/18.53 | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | (1277) ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 &
% 131.23/18.53 | | | | | | | | | | | | | $i(all_34_0)
% 131.23/18.53 | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | ALPHA: (1277) implies:
% 131.23/18.53 | | | | | | | | | | | | | (1278) ~ (all_34_0 = e2)
% 131.23/18.53 | | | | | | | | | | | | | (1279) op(e3, e0) = all_34_0
% 131.23/18.53 | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | BETA: splitting (94) gives:
% 131.23/18.53 | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | Case 1:
% 131.23/18.53 | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | (1280) ~ (all_42_2 = e0)
% 131.23/18.53 | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | REDUCE: (1224), (1280) imply:
% 131.23/18.53 | | | | | | | | | | | | | | (1281) $false
% 131.23/18.53 | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | CLOSE: (1281) is inconsistent.
% 131.23/18.53 | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | Case 2:
% 131.23/18.53 | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | (1282) ( ~ (all_42_0 = e1) & op(e0, e2) = all_42_0 &
% 131.23/18.53 | | | | | | | | | | | | | | $i(all_42_0)) | ( ~ (all_42_1 = e3) & op(e0, e0)
% 131.23/18.53 | | | | | | | | | | | | | | = all_42_1 & $i(all_42_1))
% 131.23/18.53 | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | BETA: splitting (1282) gives:
% 131.23/18.53 | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | Case 1:
% 131.23/18.53 | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | (1283) ~ (all_42_0 = e1) & op(e0, e2) = all_42_0 &
% 131.23/18.53 | | | | | | | | | | | | | | | $i(all_42_0)
% 131.23/18.53 | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | ALPHA: (1283) implies:
% 131.23/18.53 | | | | | | | | | | | | | | | (1284) ~ (all_42_0 = e1)
% 131.23/18.53 | | | | | | | | | | | | | | | (1285) op(e0, e2) = all_42_0
% 131.23/18.53 | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 131.23/18.53 | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | Case 1:
% 131.23/18.53 | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | (1286) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 131.23/18.53 | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 131.23/18.53 | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | BETA: splitting (1286) gives:
% 131.23/18.53 | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | Case 1:
% 131.23/18.53 | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | (1287) all_57_1 = e3 & op(e3, e2) = e3
% 131.23/18.53 | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | ALPHA: (1287) implies:
% 131.23/18.53 | | | | | | | | | | | | | | | | | (1288) op(e3, e2) = e3
% 131.23/18.53 | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 131.23/18.53 | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | Case 1:
% 131.23/18.53 | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | (1289) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 131.23/18.53 | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 131.23/18.53 | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | BETA: splitting (1289) gives:
% 131.23/18.53 | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | Case 1:
% 131.23/18.53 | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | (1290) all_57_12 = e3 & op(e0, e3) = e3
% 131.23/18.53 | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (1272), (1290), (function-axioms) are
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #628.
% 131.23/18.53 | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.53 | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | (1291) all_57_13 = e3 & op(e0, e2) = e3
% 131.23/18.53 | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (1273), (1291), (function-axioms) are
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #556.
% 131.23/18.53 | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | End of split
% 131.23/18.53 | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.53 | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | (1292) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 131.23/18.53 | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 131.23/18.53 | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | BETA: splitting (1292) gives:
% 131.23/18.53 | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | Case 1:
% 131.23/18.53 | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | (1293) all_57_14 = e3 & op(e0, e1) = e3
% 131.23/18.53 | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (1274), (1293), (function-axioms) are
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #652.
% 131.23/18.53 | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.53 | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | (1294) all_57_15 = e3 & op(e0, e0) = e3
% 131.23/18.53 | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7,
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | all_42_0, e2, e0, simplifying with (158), (1285)
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | gives:
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | (1295) all_52_7 = all_42_0
% 131.23/18.53 | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | all_34_0, e0, e3, simplifying with (168), (1279)
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | gives:
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | (1296) all_52_12 = all_34_0
% 131.23/18.53 | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e3,
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (170), (1288) gives:
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | (1297) all_52_4 = e3
% 131.23/18.53 | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (1295) imply:
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | (1298) all_54_13 = all_42_0
% 131.23/18.53 | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (1296) imply:
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | (1299) all_54_3 = all_34_0
% 131.23/18.53 | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | REDUCE: (134), (1297) imply:
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | (1300) ~ (all_52_8 = e3)
% 131.23/18.53 | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | REDUCE: (1273), (1295) imply:
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | (1301) ~ (all_42_0 = e3)
% 131.23/18.53 | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | REDUCE: (1226), (1295) imply:
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | (1302) ~ (all_42_0 = e0)
% 131.23/18.53 | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | REDUCE: (1275), (1296) imply:
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | (1303) ~ (all_34_0 = e3)
% 131.23/18.53 | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | REDUCE: (1237), (1296) imply:
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | (1304) ~ (all_34_0 = e1)
% 131.23/18.53 | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 131.23/18.53 | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | Case 1:
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | (1305) all_54_13 = e3
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1298), (1301), (1305) are inconsistent by
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | sub-proof #617.
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | (1306) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | (1307) all_54_3 = e3
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1299), (1307) imply:
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | (1308) all_34_0 = e3
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | SIMP: (1308) implies:
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | (1309) all_34_0 = e3
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1303), (1309) imply:
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | (1310) $false
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1310) is inconsistent.
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | (1311) ~ (all_54_3 = e3)
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | (1312) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1312) gives:
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | (1313) all_54_3 = e2
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1278), (1299), (1313) are inconsistent by
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | sub-proof #707.
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | (1314) all_54_3 = e1 | all_54_3 = e0
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1314) gives:
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | | (1315) all_54_3 = e1
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1299), (1304), (1315) are inconsistent by
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #706.
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | | (1316) all_54_3 = e0
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1299), (1316) imply:
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | | (1317) all_34_0 = e0
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1317) implies:
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | | (1318) all_34_0 = e0
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1279), (1318) imply:
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | | (1319) op(e3, e0) = e0
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | (1320) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1320) gives:
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | (1321) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (169), (1149), (1239), (1321),
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | #552.
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | (1322) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (1229), (1275), (1322),
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | #622.
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | (1323) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1323) gives:
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | (1324) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1229), (1319), (1324), (function-axioms) are
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #540.
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | (1325) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1325) gives:
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (1326) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1326) implies:
% 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (1327) ~ (all_56_15 = e2)
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (1328) op(e0, e2) = all_56_15
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1284), (1285), (1298), (1302), (1306), (1327),
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (1328), (function-axioms) are inconsistent by
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #539.
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (1329) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (39), (158), (372), (1151), (1226),
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (1276), (1319), (1329), (function-axioms) are
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #537.
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | End of split
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | End of split
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | End of split
% 131.54/18.55 | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | End of split
% 131.54/18.55 | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | End of split
% 131.54/18.55 | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | Case 2:
% 131.54/18.55 | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | (1330) all_57_3 = e3 & op(e2, e2) = e3
% 131.54/18.55 | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | ALPHA: (1330) implies:
% 131.54/18.55 | | | | | | | | | | | | | | | | | (1331) op(e2, e2) = e3
% 131.54/18.55 | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1229), (1331), (function-axioms) are
% 131.54/18.55 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641.
% 131.54/18.55 | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | End of split
% 131.54/18.55 | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | Case 2:
% 131.54/18.55 | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | (1332) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 131.54/18.55 | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 131.54/18.55 | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (1148), (1273), (1332),
% 131.54/18.55 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.54/18.55 | | | | | | | | | | | | | | | | #555.
% 131.54/18.55 | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | End of split
% 131.54/18.55 | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | Case 2:
% 131.54/18.55 | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | (1333) ~ (all_42_1 = e3) & op(e0, e0) = all_42_1 &
% 131.54/18.55 | | | | | | | | | | | | | | | $i(all_42_1)
% 131.54/18.55 | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | REF_CLOSE: (1276), (1333), (function-axioms) are inconsistent
% 131.54/18.55 | | | | | | | | | | | | | | | by sub-proof #602.
% 131.54/18.55 | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | End of split
% 131.54/18.55 | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | End of split
% 131.54/18.55 | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | Case 2:
% 131.54/18.55 | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | (1334) ~ (all_34_1 = e1) & op(e3, e3) = all_34_1 &
% 131.54/18.55 | | | | | | | | | | | | | $i(all_34_1)
% 131.54/18.55 | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | ALPHA: (1334) implies:
% 131.54/18.55 | | | | | | | | | | | | | (1335) ~ (all_34_1 = e1)
% 131.54/18.55 | | | | | | | | | | | | | (1336) op(e3, e3) = all_34_1
% 131.54/18.55 | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | REF_CLOSE: (1239), (1335), (1336), (function-axioms) are
% 131.54/18.55 | | | | | | | | | | | | | inconsistent by sub-proof #626.
% 131.54/18.55 | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | End of split
% 131.54/18.55 | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | End of split
% 131.54/18.55 | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | End of split
% 131.54/18.55 | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | End of split
% 131.54/18.55 | | | | | | | | |
% 131.54/18.55 | | | | | | | | End of split
% 131.54/18.55 | | | | | | | |
% 131.54/18.55 | | | | | | | Case 2:
% 131.54/18.55 | | | | | | | |
% 131.54/18.55 | | | | | | | | (1337) all_20_2 = e2
% 131.54/18.55 | | | | | | | |
% 131.54/18.55 | | | | | | | | COMBINE_EQS: (318), (1337) imply:
% 131.54/18.55 | | | | | | | | (1338) all_4_2 = e2
% 131.54/18.55 | | | | | | | |
% 131.54/18.55 | | | | | | | | SIMP: (1338) implies:
% 131.54/18.55 | | | | | | | | (1339) all_4_2 = e2
% 131.54/18.55 | | | | | | | |
% 131.54/18.55 | | | | | | | | REDUCE: (360), (1339) imply:
% 131.54/18.55 | | | | | | | | (1340) ~ (all_52_7 = e2)
% 131.54/18.55 | | | | | | | |
% 131.54/18.55 | | | | | | | | REDUCE: (367), (1339) imply:
% 131.54/18.55 | | | | | | | | (1341) ~ (all_52_11 = e2)
% 131.54/18.55 | | | | | | | |
% 131.54/18.55 | | | | | | | | REDUCE: (368), (1339) imply:
% 131.54/18.55 | | | | | | | | (1342) ~ (all_52_12 = e2)
% 131.54/18.55 | | | | | | | |
% 131.54/18.55 | | | | | | | | REDUCE: (369), (1339) imply:
% 131.54/18.55 | | | | | | | | (1343) ~ (all_52_13 = e2)
% 131.54/18.55 | | | | | | | |
% 131.54/18.55 | | | | | | | | REDUCE: (370), (1339) imply:
% 131.54/18.55 | | | | | | | | (1344) ~ (all_52_14 = e2)
% 131.54/18.55 | | | | | | | |
% 131.54/18.55 | | | | | | | | REDUCE: (36), (1339) imply:
% 131.54/18.55 | | | | | | | | (1345) op(e0, e0) = e2
% 131.54/18.55 | | | | | | | |
% 131.54/18.55 | | | | | | | | BETA: splitting (73) gives:
% 131.54/18.55 | | | | | | | |
% 131.54/18.55 | | | | | | | | Case 1:
% 131.54/18.55 | | | | | | | | |
% 131.54/18.55 | | | | | | | | | (1346) ~ (all_28_2 = e3)
% 131.54/18.55 | | | | | | | | |
% 131.54/18.55 | | | | | | | | | REDUCE: (316), (1346) imply:
% 131.54/18.55 | | | | | | | | | (1347) ~ (all_6_2 = e3)
% 131.54/18.55 | | | | | | | | |
% 131.54/18.55 | | | | | | | | | BETA: splitting (76) gives:
% 131.54/18.55 | | | | | | | | |
% 131.54/18.55 | | | | | | | | | Case 1:
% 131.54/18.55 | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | (1348) ~ (all_30_2 = e0)
% 131.54/18.55 | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | REDUCE: (309), (1348) imply:
% 131.54/18.55 | | | | | | | | | | (1349) ~ (all_8_2 = e0)
% 131.54/18.55 | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | BETA: splitting (199) gives:
% 131.54/18.55 | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | Case 1:
% 131.54/18.55 | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | (1350) all_54_5 = e3
% 131.54/18.55 | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | REF_CLOSE: (267), (376), (1350) are inconsistent by sub-proof
% 131.54/18.55 | | | | | | | | | | | #554.
% 131.54/18.55 | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | Case 2:
% 131.54/18.55 | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | (1351) ~ (all_54_5 = e3)
% 131.54/18.55 | | | | | | | | | | | (1352) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 131.54/18.55 | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | BETA: splitting (1352) gives:
% 131.54/18.55 | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | Case 1:
% 131.54/18.55 | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | (1353) all_54_5 = e2
% 131.54/18.55 | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | COMBINE_EQS: (267), (1353) imply:
% 131.54/18.55 | | | | | | | | | | | | (1354) all_8_2 = e2
% 131.54/18.55 | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | SIMP: (1354) implies:
% 131.54/18.55 | | | | | | | | | | | | (1355) all_8_2 = e2
% 131.54/18.55 | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | REDUCE: (347), (1355) imply:
% 131.54/18.55 | | | | | | | | | | | | (1356) ~ (all_52_1 = e2)
% 131.54/18.55 | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | REDUCE: (352), (1355) imply:
% 131.54/18.55 | | | | | | | | | | | | (1357) ~ (all_52_6 = e2)
% 131.54/18.55 | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | REDUCE: (356), (1355) imply:
% 131.54/18.55 | | | | | | | | | | | | (1358) ~ (all_52_9 = e2)
% 131.54/18.55 | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | REDUCE: (376), (1355) imply:
% 131.54/18.55 | | | | | | | | | | | | (1359) ~ (e3 = e2)
% 131.54/18.55 | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | REDUCE: (42), (1355) imply:
% 131.54/18.55 | | | | | | | | | | | | (1360) op(e2, e2) = e2
% 131.54/18.55 | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | BETA: splitting (221) gives:
% 131.54/18.55 | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | Case 1:
% 131.54/18.55 | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | (1361) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 131.54/18.55 | | | | | | | | | | | | | & op(e2, e1) = e2)
% 131.54/18.55 | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | BETA: splitting (1361) gives:
% 131.54/18.55 | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | Case 1:
% 131.54/18.55 | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | (1362) all_57_4 = e2 & op(e3, e1) = e2
% 131.54/18.55 | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | ALPHA: (1362) implies:
% 131.54/18.55 | | | | | | | | | | | | | | (1363) op(e3, e1) = e2
% 131.54/18.55 | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 131.54/18.55 | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | Case 1:
% 131.54/18.55 | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | (1364) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 131.54/18.55 | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 131.54/18.55 | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | REF_CLOSE: (45), (167), (378), (1356), (1364),
% 131.54/18.55 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.54/18.55 | | | | | | | | | | | | | | | #535.
% 131.54/18.55 | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | Case 2:
% 131.54/18.55 | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | (1365) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 131.54/18.55 | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 131.54/18.55 | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | BETA: splitting (1365) gives:
% 131.54/18.55 | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | Case 1:
% 131.54/18.55 | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | (1366) all_57_6 = e2 & op(e1, e3) = e2
% 131.54/18.55 | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | ALPHA: (1366) implies:
% 131.54/18.55 | | | | | | | | | | | | | | | | (1367) op(e1, e3) = e2
% 131.54/18.55 | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (39), (45), (91), (121), (123), (149),
% 131.54/18.55 | | | | | | | | | | | | | | | | (157), (163), (164), (165), (167), (169), (190),
% 131.54/18.55 | | | | | | | | | | | | | | | | (206), (246), (332), (344), (361), (364), (374),
% 131.54/18.55 | | | | | | | | | | | | | | | | (1343), (1345), (1347), (1360), (1363), (1367),
% 131.54/18.55 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.54/18.55 | | | | | | | | | | | | | | | | #522.
% 131.54/18.55 | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | Case 2:
% 131.54/18.55 | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | (1368) all_57_12 = e2 & op(e0, e3) = e2
% 131.54/18.55 | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | ALPHA: (1368) implies:
% 131.54/18.55 | | | | | | | | | | | | | | | | (1369) all_57_12 = e2
% 131.54/18.55 | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 131.54/18.55 | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | Case 1:
% 131.54/18.55 | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | (1370) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 131.54/18.55 | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 131.54/18.55 | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | BETA: splitting (1370) gives:
% 131.54/18.55 | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | Case 1:
% 131.54/18.55 | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | (1371) all_57_6 = e2 & op(e1, e3) = e2
% 131.54/18.55 | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | ALPHA: (1371) implies:
% 131.54/18.55 | | | | | | | | | | | | | | | | | | (1372) all_57_6 = e2
% 131.54/18.55 | | | | | | | | | | | | | | | | | | (1373) op(e1, e3) = e2
% 131.54/18.55 | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 131.54/18.55 | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | Case 1:
% 131.54/18.55 | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | (1374) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 131.54/18.55 | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | BETA: splitting (1374) gives:
% 131.54/18.55 | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | Case 1:
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | (1375) all_57_0 = e0 & op(e3, e3) = e0
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | ALPHA: (1375) implies:
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | (1376) op(e3, e3) = e0
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (374), (1376), (function-axioms) are
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #534.
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | Case 2:
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | (1377) all_57_2 = e0 & op(e2, e3) = e0
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | ALPHA: (1377) implies:
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | (1378) all_57_2 = e0
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | (1379) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1379) gives:
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | (1380) all_57_0 = e1 & op(e3, e3) = e1
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1380) implies:
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | (1381) op(e3, e3) = e1
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | (1382) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1382) gives:
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | (1383) all_57_0 = e3 & op(e3, e3) = e3
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1383) implies:
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | (1384) op(e3, e3) = e3
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1381), (1384), (function-axioms) are
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #775.
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | (1385) all_57_2 = e3 & op(e2, e3) = e3
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1385) implies:
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | (1386) all_57_2 = e3
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (231), (1369), (1372), (1381),
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | (1386), (function-axioms) are inconsistent by
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #519.
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | (1387) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1387) gives:
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | (1388) all_57_6 = e3 & op(e1, e3) = e3
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1388) implies:
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | (1389) all_57_6 = e3
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1372), (1389) are inconsistent by sub-proof
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | #592.
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | | | (1390) all_57_12 = e3 & op(e0, e3) = e3
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1390) implies:
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | | | (1391) all_57_12 = e3
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1369), (1391) are inconsistent by sub-proof
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | | | #518.
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | (1392) all_57_2 = e1 & op(e2, e3) = e1
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1392) implies:
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | (1393) all_57_2 = e1
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1378), (1393) are inconsistent by sub-proof
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | #646.
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | End of split
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | (1394) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1394) gives:
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | (1395) all_57_6 = e1 & op(e1, e3) = e1
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1395) implies:
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | (1396) op(e1, e3) = e1
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (1373), (1396), (function-axioms) are
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #517.
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | (1397) all_57_12 = e1 & op(e0, e3) = e1
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1369), (1397) are inconsistent by sub-proof
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | #516.
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | End of split
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | End of split
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | End of split
% 131.54/18.56 | | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | Case 2:
% 131.54/18.56 | | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | (1398) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 131.54/18.56 | | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | BETA: splitting (1398) gives:
% 131.54/18.56 | | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | Case 1:
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | (1399) all_57_6 = e0 & op(e1, e3) = e0
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1372), (1399) are inconsistent by sub-proof
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | #520.
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | Case 2:
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | (1400) all_57_12 = e0 & op(e0, e3) = e0
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1369), (1400) are inconsistent by sub-proof
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | | #578.
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | | End of split
% 131.54/18.56 | | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | End of split
% 131.54/18.56 | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | Case 2:
% 131.54/18.56 | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | (1401) all_57_7 = e2 & op(e1, e2) = e2
% 131.54/18.56 | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (1357), (1401), (function-axioms) are
% 131.54/18.56 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #515.
% 131.54/18.56 | | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | End of split
% 131.54/18.56 | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | Case 2:
% 131.54/18.56 | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | (1402) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 131.54/18.56 | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 131.54/18.56 | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (160), (372), (1344), (1402),
% 131.54/18.56 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.54/18.56 | | | | | | | | | | | | | | | | | #513.
% 131.54/18.56 | | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | End of split
% 131.54/18.56 | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | End of split
% 131.54/18.56 | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | End of split
% 131.54/18.56 | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | Case 2:
% 131.54/18.56 | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | (1403) all_57_5 = e2 & op(e2, e1) = e2
% 131.54/18.56 | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | ALPHA: (1403) implies:
% 131.54/18.56 | | | | | | | | | | | | | | (1404) op(e2, e1) = e2
% 131.54/18.56 | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | REF_CLOSE: (165), (1358), (1404), (function-axioms) are
% 131.54/18.56 | | | | | | | | | | | | | | inconsistent by sub-proof #770.
% 131.54/18.56 | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | End of split
% 131.54/18.56 | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | Case 2:
% 131.54/18.56 | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | (1405) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 131.54/18.56 | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 131.54/18.56 | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | REF_CLOSE: (39), (157), (372), (1341), (1405),
% 131.54/18.56 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.54/18.56 | | | | | | | | | | | | | #511.
% 131.54/18.56 | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | End of split
% 131.54/18.56 | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | Case 2:
% 131.54/18.56 | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | (1406) all_54_5 = e1 | all_54_5 = e0
% 131.54/18.56 | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | REF_CLOSE: (267), (373), (1349), (1406) are inconsistent by
% 131.54/18.56 | | | | | | | | | | | | sub-proof #624.
% 131.54/18.56 | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | End of split
% 131.54/18.56 | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | End of split
% 131.54/18.56 | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | Case 2:
% 131.54/18.56 | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | (1407) all_30_2 = e0
% 131.54/18.56 | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | COMBINE_EQS: (309), (1407) imply:
% 131.54/18.56 | | | | | | | | | | (1408) all_8_2 = e0
% 131.54/18.56 | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | SIMP: (1408) implies:
% 131.54/18.56 | | | | | | | | | | (1409) all_8_2 = e0
% 131.54/18.56 | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | REDUCE: (350), (1409) imply:
% 131.54/18.56 | | | | | | | | | | (1410) ~ (all_52_4 = e0)
% 131.54/18.56 | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | REDUCE: (354), (1409) imply:
% 131.54/18.56 | | | | | | | | | | (1411) ~ (all_52_7 = e0)
% 131.54/18.56 | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | REDUCE: (376), (1409) imply:
% 131.54/18.56 | | | | | | | | | | (1412) ~ (e3 = e0)
% 131.54/18.56 | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | REDUCE: (373), (1409) imply:
% 131.54/18.56 | | | | | | | | | | (1413) ~ (e1 = e0)
% 131.54/18.56 | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | REDUCE: (42), (1409) imply:
% 131.54/18.56 | | | | | | | | | | (1414) op(e2, e2) = e0
% 131.54/18.56 | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | BETA: splitting (79) gives:
% 131.54/18.56 | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | Case 1:
% 131.54/18.56 | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | (1415) ~ (all_32_2 = e1)
% 131.54/18.56 | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | REDUCE: (312), (1415) imply:
% 131.54/18.56 | | | | | | | | | | | (1416) ~ (all_10_2 = e1)
% 131.54/18.56 | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | BETA: splitting (204) gives:
% 131.54/18.56 | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | Case 1:
% 131.54/18.56 | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | (1417) all_54_0 = e3
% 131.54/18.56 | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | COMBINE_EQS: (278), (1417) imply:
% 131.54/18.56 | | | | | | | | | | | | (1418) all_10_2 = e3
% 131.54/18.56 | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | SIMP: (1418) implies:
% 131.54/18.56 | | | | | | | | | | | | (1419) all_10_2 = e3
% 131.54/18.56 | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | REDUCE: (346), (1419) imply:
% 131.54/18.56 | | | | | | | | | | | | (1420) ~ (all_52_12 = e3)
% 131.54/18.56 | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | REDUCE: (45), (1419) imply:
% 131.54/18.56 | | | | | | | | | | | | (1421) op(e3, e3) = e3
% 131.54/18.56 | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | BETA: splitting (206) gives:
% 131.54/18.56 | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | Case 1:
% 131.54/18.56 | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | (1422) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 131.54/18.56 | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.54/18.56 | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 131.54/18.56 | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 131.54/18.56 | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 131.54/18.56 | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 131.54/18.56 | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.54/18.56 | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 131.54/18.56 | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 131.54/18.56 | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 131.54/18.56 | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 131.54/18.56 | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 131.54/18.56 | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 131.54/18.56 | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 131.54/18.56 | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 131.54/18.56 | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 131.54/18.56 | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 131.54/18.56 | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 131.54/18.56 | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.54/18.56 | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 131.54/18.56 | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 131.54/18.56 | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 131.54/18.56 | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.54/18.56 | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.54/18.56 | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.54/18.56 | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 131.54/18.56 | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.54/18.56 | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 131.54/18.56 | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | BETA: splitting (1422) gives:
% 131.54/18.56 | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | Case 1:
% 131.54/18.56 | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | (1423) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 131.54/18.56 | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.54/18.56 | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 131.54/18.56 | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 131.54/18.56 | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 131.54/18.56 | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 131.54/18.56 | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.54/18.56 | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 131.54/18.56 | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 131.54/18.56 | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 131.54/18.56 | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 131.54/18.56 | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 131.54/18.56 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 131.54/18.56 | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 131.54/18.56 | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (1421), (1423), (function-axioms) are
% 131.54/18.56 | | | | | | | | | | | | | | inconsistent by sub-proof #623.
% 131.54/18.56 | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | Case 2:
% 131.54/18.56 | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | (1424) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 131.54/18.56 | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 131.54/18.56 | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 131.54/18.56 | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 131.54/18.56 | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.54/18.56 | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 131.54/18.56 | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 131.54/18.56 | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 131.54/18.56 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.54/18.56 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.54/18.56 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.54/18.56 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 131.54/18.56 | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.54/18.56 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 131.54/18.56 | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (1414), (1420), (1424),
% 131.54/18.56 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.54/18.56 | | | | | | | | | | | | | | #622.
% 131.54/18.56 | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | End of split
% 131.54/18.56 | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | Case 2:
% 131.54/18.56 | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | (1425) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 131.54/18.56 | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.54/18.56 | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.54/18.56 | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.54/18.56 | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 131.54/18.56 | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.54/18.56 | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 131.54/18.56 | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 131.54/18.56 | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 131.54/18.56 | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 131.54/18.56 | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 131.54/18.56 | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 131.54/18.56 | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 131.54/18.56 | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 131.54/18.56 | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 131.54/18.56 | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.54/18.56 | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 131.54/18.56 | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 131.54/18.56 | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 131.54/18.56 | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 131.54/18.56 | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 131.54/18.56 | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 131.54/18.56 | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 131.54/18.56 | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.54/18.56 | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 131.54/18.56 | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 131.54/18.56 | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 131.54/18.56 | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 131.54/18.56 | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 131.54/18.56 | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 131.54/18.56 | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 131.54/18.56 | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.54/18.56 | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 131.54/18.56 | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 131.54/18.56 | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 131.54/18.56 | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 131.54/18.56 | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 131.54/18.56 | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 131.54/18.56 | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.54/18.56 | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.54/18.56 | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 131.54/18.56 | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 131.54/18.56 | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 131.54/18.56 | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 131.54/18.56 | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 131.54/18.56 | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 131.54/18.56 | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 131.54/18.56 | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 131.54/18.56 | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 131.54/18.56 | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 131.54/18.56 | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 131.54/18.56 | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 131.54/18.56 | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 131.54/18.56 | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 131.54/18.56 | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 131.54/18.56 | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 131.54/18.56 | | | | | | | | | | | | | & $i(all_56_29))))
% 131.54/18.56 | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | BETA: splitting (1425) gives:
% 131.54/18.56 | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | Case 1:
% 131.54/18.56 | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | (1426) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 131.54/18.56 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.54/18.56 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.54/18.56 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.54/18.56 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 131.54/18.56 | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.54/18.56 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 131.54/18.56 | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 131.54/18.56 | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 131.54/18.56 | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 131.54/18.56 | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 131.54/18.56 | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 131.54/18.56 | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 131.54/18.56 | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 131.54/18.56 | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (1347), (1414), (1426),
% 131.54/18.56 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.54/18.56 | | | | | | | | | | | | | | #621.
% 131.54/18.56 | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | Case 2:
% 131.54/18.56 | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | (1427) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 131.54/18.56 | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 131.54/18.56 | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 131.54/18.56 | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 131.54/18.56 | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.54/18.56 | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 131.54/18.56 | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 131.54/18.56 | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 131.54/18.56 | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.54/18.56 | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 131.54/18.56 | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.54/18.56 | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 131.54/18.56 | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 131.54/18.56 | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.54/18.56 | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 131.54/18.56 | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 131.54/18.56 | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 131.54/18.56 | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 131.54/18.56 | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 131.54/18.56 | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 131.54/18.56 | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 131.54/18.56 | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 131.54/18.56 | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 131.54/18.56 | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 131.54/18.56 | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 131.54/18.56 | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 131.54/18.56 | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 131.54/18.56 | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 131.54/18.56 | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 131.54/18.56 | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 131.54/18.56 | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.54/18.56 | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.54/18.56 | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 131.54/18.56 | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 131.54/18.56 | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.54/18.56 | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 131.54/18.56 | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 131.54/18.56 | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 131.54/18.56 | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 131.54/18.56 | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 131.54/18.56 | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 131.54/18.56 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 131.54/18.56 | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 131.54/18.56 | | | | | | | | | | | | | | & $i(all_56_29))))
% 131.54/18.56 | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | BETA: splitting (1427) gives:
% 131.54/18.56 | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | Case 1:
% 131.54/18.56 | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | (1428) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 131.54/18.56 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 131.54/18.56 | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 131.54/18.56 | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 131.54/18.56 | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 131.54/18.56 | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 131.54/18.56 | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 131.54/18.56 | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | ALPHA: (1428) implies:
% 131.54/18.56 | | | | | | | | | | | | | | | (1429) op(e2, e0) = e2
% 131.54/18.56 | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | REF_CLOSE: (164), (1343), (1429), (function-axioms) are
% 131.54/18.56 | | | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 131.54/18.56 | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | Case 2:
% 131.54/18.56 | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | (1430) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 131.54/18.56 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.54/18.56 | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 131.54/18.56 | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.54/18.56 | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 131.54/18.56 | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 131.54/18.56 | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.54/18.56 | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 131.54/18.56 | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 131.54/18.56 | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 131.54/18.56 | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 131.54/18.56 | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 131.54/18.56 | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 131.54/18.56 | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 131.54/18.56 | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 131.54/18.56 | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 131.54/18.56 | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 131.54/18.56 | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 131.54/18.56 | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 131.54/18.56 | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 131.54/18.56 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 131.54/18.56 | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 131.54/18.56 | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 131.54/18.56 | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.54/18.56 | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.54/18.56 | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 131.54/18.56 | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 131.54/18.56 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.54/18.56 | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 131.54/18.56 | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 131.54/18.56 | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 131.54/18.56 | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 131.54/18.56 | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 131.54/18.56 | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 131.54/18.56 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 131.54/18.56 | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 131.54/18.56 | | | | | | | | | | | | | | | & $i(all_56_29))))
% 131.54/18.56 | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | BETA: splitting (1430) gives:
% 131.54/18.56 | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | Case 1:
% 131.54/18.56 | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | (1431) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 131.54/18.56 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 131.54/18.56 | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.54/18.56 | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 131.54/18.56 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 131.54/18.56 | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 131.54/18.56 | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 131.54/18.56 | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | ALPHA: (1431) implies:
% 131.54/18.56 | | | | | | | | | | | | | | | | (1432) op(e1, e1) = e2
% 131.54/18.56 | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (1432), (function-axioms) are
% 131.54/18.56 | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 131.54/18.56 | | | | | | | | | | | | | | | |
% 131.54/18.56 | | | | | | | | | | | | | | | Case 2:
% 131.54/18.56 | | | | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | | | | (1433) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 131.54/18.57 | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 131.54/18.57 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 131.54/18.57 | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 131.54/18.57 | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 131.54/18.57 | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 131.54/18.57 | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 131.54/18.57 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 131.54/18.57 | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 131.54/18.57 | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 131.54/18.57 | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.54/18.57 | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.54/18.57 | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 131.54/18.57 | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 131.54/18.57 | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 131.54/18.57 | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.54/18.57 | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.54/18.57 | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 131.54/18.57 | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 131.54/18.57 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.54/18.57 | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 131.54/18.57 | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 131.54/18.57 | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 131.54/18.57 | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 131.54/18.57 | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 131.54/18.57 | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 131.54/18.57 | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 131.54/18.57 | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 131.54/18.57 | | | | | | | | | | | | | | | | $i(all_56_29)))
% 131.54/18.57 | | | | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | | | | ALPHA: (1433) implies:
% 131.54/18.57 | | | | | | | | | | | | | | | | (1434) op(e0, e0) = all_56_31
% 131.54/18.57 | | | | | | | | | | | | | | | | (1435) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 131.54/18.57 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.54/18.57 | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.54/18.57 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.54/18.57 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 131.54/18.57 | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 131.54/18.57 | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 131.54/18.57 | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 131.54/18.57 | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 131.54/18.57 | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 131.54/18.57 | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 131.54/18.57 | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 131.54/18.57 | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 131.54/18.57 | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.54/18.57 | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.54/18.57 | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 131.54/18.57 | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 131.54/18.57 | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 131.54/18.57 | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 131.54/18.57 | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 131.54/18.57 | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 131.54/18.57 | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 131.54/18.57 | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 131.54/18.57 | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 131.54/18.57 | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 131.54/18.57 | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 131.54/18.57 | | | | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 131.54/18.57 | | | | | | | | | | | | | | | | all_56_31, e0, e0, simplifying with (1345), (1434)
% 131.54/18.57 | | | | | | | | | | | | | | | | gives:
% 131.54/18.57 | | | | | | | | | | | | | | | | (1436) all_56_31 = e2
% 131.54/18.57 | | | | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | | | | BETA: splitting (1435) gives:
% 131.54/18.57 | | | | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | | | | Case 1:
% 131.54/18.57 | | | | | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | | | | | (1437) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 131.54/18.57 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.54/18.57 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.54/18.57 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.54/18.57 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 131.54/18.57 | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 131.54/18.57 | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 131.54/18.57 | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 131.54/18.57 | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 131.54/18.57 | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 131.54/18.57 | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 131.54/18.57 | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 131.54/18.57 | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27))
% 131.54/18.57 | | | | | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (1411), (1421), (1437), (function-axioms)
% 131.54/18.57 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #544.
% 131.54/18.57 | | | | | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | | | | Case 2:
% 131.54/18.57 | | | | | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | | | | | (1438) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 131.54/18.57 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 131.54/18.57 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 131.54/18.57 | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 131.54/18.57 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.54/18.57 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 131.54/18.57 | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 131.54/18.57 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 131.54/18.57 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 131.54/18.57 | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 131.54/18.57 | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 131.54/18.57 | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 131.54/18.57 | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 131.54/18.57 | | | | | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (39), (91), (157), (190), (246), (332),
% 131.54/18.57 | | | | | | | | | | | | | | | | | (364), (1341), (1345), (1436), (1438),
% 131.54/18.57 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.54/18.57 | | | | | | | | | | | | | | | | | #524.
% 131.54/18.57 | | | | | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | | | | End of split
% 131.54/18.57 | | | | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | | | End of split
% 131.54/18.57 | | | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | | End of split
% 131.54/18.57 | | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | End of split
% 131.54/18.57 | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | End of split
% 131.54/18.57 | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | Case 2:
% 131.54/18.57 | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | (1439) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 131.54/18.57 | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | REF_CLOSE: (278), (374), (378), (1416), (1439) are
% 131.54/18.57 | | | | | | | | | | | | inconsistent by sub-proof #777.
% 131.54/18.57 | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | End of split
% 131.54/18.57 | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | Case 2:
% 131.54/18.57 | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | (1440) all_32_2 = e1
% 131.54/18.57 | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | COMBINE_EQS: (312), (1440) imply:
% 131.54/18.57 | | | | | | | | | | | (1441) all_10_2 = e1
% 131.54/18.57 | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | SIMP: (1441) implies:
% 131.54/18.57 | | | | | | | | | | | (1442) all_10_2 = e1
% 131.54/18.57 | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | COMBINE_EQS: (280), (1442) imply:
% 131.54/18.57 | | | | | | | | | | | (1443) all_50_2 = e1
% 131.54/18.57 | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | REDUCE: (336), (1442) imply:
% 131.54/18.57 | | | | | | | | | | | (1444) ~ (all_52_1 = e1)
% 131.54/18.57 | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | REDUCE: (338), (1442) imply:
% 131.54/18.57 | | | | | | | | | | | (1445) ~ (all_52_2 = e1)
% 131.54/18.57 | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | REDUCE: (342), (1442) imply:
% 131.54/18.57 | | | | | | | | | | | (1446) ~ (all_52_4 = e1)
% 131.54/18.57 | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | REDUCE: (378), (1442) imply:
% 131.54/18.57 | | | | | | | | | | | (1447) ~ (e2 = e1)
% 131.54/18.57 | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | REDUCE: (45), (1442) imply:
% 131.54/18.57 | | | | | | | | | | | (1448) op(e3, e3) = e1
% 131.54/18.57 | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | BETA: splitting (91) gives:
% 131.54/18.57 | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | Case 1:
% 131.54/18.57 | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | (1449) ~ (all_40_2 = e0)
% 131.54/18.57 | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | REDUCE: (332), (1449) imply:
% 131.54/18.57 | | | | | | | | | | | | (1450) ~ (all_6_2 = e0)
% 131.54/18.57 | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | BETA: splitting (194) gives:
% 131.54/18.57 | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | Case 1:
% 131.54/18.57 | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | (1451) all_54_10 = e3
% 131.54/18.57 | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | REF_CLOSE: (334), (1347), (1451) are inconsistent by
% 131.54/18.57 | | | | | | | | | | | | | sub-proof #742.
% 131.54/18.57 | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | Case 2:
% 131.54/18.57 | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | (1452) ~ (all_54_10 = e3)
% 131.54/18.57 | | | | | | | | | | | | | (1453) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 131.54/18.57 | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | BETA: splitting (1453) gives:
% 131.54/18.57 | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | Case 1:
% 131.54/18.57 | | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | | (1454) all_54_10 = e2
% 131.54/18.57 | | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | | REF_CLOSE: (334), (372), (1454) are inconsistent by sub-proof
% 131.54/18.57 | | | | | | | | | | | | | | #741.
% 131.54/18.57 | | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | Case 2:
% 131.54/18.57 | | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | | (1455) ~ (all_54_10 = e2)
% 131.54/18.57 | | | | | | | | | | | | | | (1456) all_54_10 = e1 | all_54_10 = e0
% 131.54/18.57 | | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | | BETA: splitting (1456) gives:
% 131.54/18.57 | | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | | Case 1:
% 131.54/18.57 | | | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | | | (1457) all_54_10 = e1
% 131.54/18.57 | | | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | | | COMBINE_EQS: (334), (1457) imply:
% 131.54/18.57 | | | | | | | | | | | | | | | (1458) all_6_2 = e1
% 131.54/18.57 | | | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | | | SIMP: (1458) implies:
% 131.54/18.57 | | | | | | | | | | | | | | | (1459) all_6_2 = e1
% 131.54/18.57 | | | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | | | REDUCE: (1347), (1459) imply:
% 131.54/18.57 | | | | | | | | | | | | | | | (1460) ~ (e3 = e1)
% 131.54/18.57 | | | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | | | REDUCE: (39), (1459) imply:
% 131.54/18.57 | | | | | | | | | | | | | | | (1461) op(e1, e1) = e1
% 131.54/18.57 | | | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 131.54/18.57 | | | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | | | Case 1:
% 131.54/18.57 | | | | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | | | | (1462) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 131.54/18.57 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.54/18.57 | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 131.54/18.57 | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 131.54/18.57 | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 131.54/18.57 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 131.54/18.57 | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.54/18.57 | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 131.54/18.57 | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 131.54/18.57 | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 131.54/18.57 | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 131.54/18.57 | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 131.54/18.57 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 131.54/18.57 | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 131.54/18.57 | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 131.54/18.57 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 131.54/18.57 | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 131.54/18.57 | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 131.54/18.57 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.54/18.57 | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 131.54/18.57 | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 131.54/18.57 | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 131.54/18.57 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.54/18.57 | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.54/18.57 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.54/18.57 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 131.54/18.57 | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.54/18.57 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 131.54/18.57 | | | | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | | | | BETA: splitting (1462) gives:
% 131.54/18.57 | | | | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | | | | Case 1:
% 131.54/18.57 | | | | | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | | | | | (1463) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 131.54/18.57 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.54/18.57 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 131.54/18.57 | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 131.54/18.57 | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 131.54/18.57 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 131.54/18.57 | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.54/18.57 | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 131.54/18.57 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 131.54/18.57 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 131.54/18.57 | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 131.54/18.57 | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 131.54/18.57 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 131.54/18.57 | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 131.54/18.57 | | | | | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1448), (1461), (1463), (function-axioms) are
% 131.54/18.57 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #509.
% 131.54/18.57 | | | | | | | | | | | | | | | | |
% 131.54/18.57 | | | | | | | | | | | | | | | | Case 2:
% 131.54/18.57 | | | | | | | | | | | | | | | | |
% 131.67/18.57 | | | | | | | | | | | | | | | | | (1464) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 131.67/18.57 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 131.67/18.57 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 131.67/18.57 | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 131.67/18.57 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.67/18.57 | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 131.67/18.57 | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 131.67/18.57 | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 131.67/18.57 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.67/18.57 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.67/18.57 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.67/18.57 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 131.67/18.57 | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.67/18.57 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 131.67/18.57 | | | | | | | | | | | | | | | | |
% 131.67/18.57 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (1414), (1448), (1464),
% 131.67/18.57 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.67/18.57 | | | | | | | | | | | | | | | | | #598.
% 131.67/18.57 | | | | | | | | | | | | | | | | |
% 131.67/18.57 | | | | | | | | | | | | | | | | End of split
% 131.67/18.57 | | | | | | | | | | | | | | | |
% 131.67/18.57 | | | | | | | | | | | | | | | Case 2:
% 131.67/18.57 | | | | | | | | | | | | | | | |
% 131.67/18.57 | | | | | | | | | | | | | | | | (1465) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 131.67/18.57 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.67/18.57 | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.67/18.57 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.67/18.57 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 131.67/18.57 | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.67/18.57 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 131.67/18.57 | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 131.67/18.57 | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 131.67/18.57 | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 131.67/18.57 | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 131.67/18.57 | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 131.67/18.57 | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 131.67/18.57 | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 131.67/18.57 | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 131.67/18.57 | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.67/18.57 | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 131.67/18.57 | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 131.67/18.57 | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 131.67/18.57 | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 131.67/18.57 | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 131.67/18.57 | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 131.67/18.57 | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 131.67/18.57 | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.67/18.57 | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 131.67/18.57 | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 131.67/18.57 | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 131.67/18.57 | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 131.67/18.57 | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 131.67/18.57 | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 131.67/18.57 | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 131.67/18.57 | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.67/18.57 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 131.67/18.57 | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 131.67/18.57 | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 131.67/18.57 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 131.67/18.57 | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 131.67/18.57 | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 131.67/18.57 | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.67/18.57 | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.67/18.57 | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 131.67/18.57 | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 131.67/18.57 | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 131.67/18.57 | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 131.67/18.57 | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 131.67/18.57 | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 131.67/18.57 | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 131.67/18.57 | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 131.67/18.57 | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 131.67/18.57 | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 131.67/18.57 | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 131.67/18.57 | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 131.67/18.57 | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 131.67/18.57 | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 131.67/18.57 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 131.67/18.57 | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 131.67/18.57 | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 131.67/18.57 | | | | | | | | | | | | | | | |
% 131.67/18.57 | | | | | | | | | | | | | | | | BETA: splitting (1465) gives:
% 131.67/18.57 | | | | | | | | | | | | | | | |
% 131.67/18.57 | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.57 | | | | | | | | | | | | | | | | |
% 131.67/18.57 | | | | | | | | | | | | | | | | | (1466) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 131.67/18.57 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.67/18.57 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.67/18.57 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.67/18.57 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 131.67/18.57 | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.67/18.57 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 131.67/18.57 | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 131.67/18.57 | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 131.67/18.57 | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 131.67/18.57 | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 131.67/18.57 | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 131.67/18.57 | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 131.67/18.57 | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 131.67/18.57 | | | | | | | | | | | | | | | | |
% 131.67/18.57 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (39), (1414), (1461), (1466),
% 131.67/18.57 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.67/18.57 | | | | | | | | | | | | | | | | | #508.
% 131.67/18.57 | | | | | | | | | | | | | | | | |
% 131.67/18.57 | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.57 | | | | | | | | | | | | | | | | |
% 131.67/18.57 | | | | | | | | | | | | | | | | | (1467) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 131.67/18.57 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 131.67/18.57 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 131.67/18.57 | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 131.67/18.57 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.67/18.57 | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 131.67/18.57 | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 131.67/18.57 | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 131.67/18.57 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.67/18.57 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 131.67/18.57 | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.67/18.57 | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 131.67/18.57 | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 131.67/18.57 | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.67/18.57 | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 131.67/18.57 | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 131.67/18.57 | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 131.67/18.57 | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 131.67/18.57 | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 131.67/18.57 | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 131.67/18.57 | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 131.67/18.57 | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 131.67/18.57 | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 131.67/18.57 | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 131.67/18.57 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 131.67/18.57 | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 131.67/18.57 | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 131.67/18.57 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 131.67/18.57 | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 131.67/18.57 | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 131.67/18.57 | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.67/18.57 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.67/18.57 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 131.67/18.57 | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 131.67/18.57 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.67/18.57 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 131.67/18.57 | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 131.67/18.57 | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 131.67/18.57 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 131.67/18.57 | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 131.67/18.57 | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 131.67/18.57 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 131.67/18.57 | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 131.67/18.57 | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 131.67/18.57 | | | | | | | | | | | | | | | | |
% 131.67/18.57 | | | | | | | | | | | | | | | | | BETA: splitting (1467) gives:
% 131.67/18.57 | | | | | | | | | | | | | | | | |
% 131.67/18.57 | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.57 | | | | | | | | | | | | | | | | | |
% 131.67/18.57 | | | | | | | | | | | | | | | | | | (1468) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 131.67/18.57 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 131.67/18.57 | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 131.67/18.57 | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 131.67/18.57 | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 131.67/18.57 | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 131.67/18.57 | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 131.67/18.57 | | | | | | | | | | | | | | | | | |
% 131.67/18.57 | | | | | | | | | | | | | | | | | | ALPHA: (1468) implies:
% 131.67/18.57 | | | | | | | | | | | | | | | | | | (1469) op(e2, e0) = e2
% 131.67/18.57 | | | | | | | | | | | | | | | | | |
% 131.67/18.57 | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (1343), (1469), (function-axioms) are
% 131.67/18.57 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 131.67/18.57 | | | | | | | | | | | | | | | | | |
% 131.67/18.57 | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.57 | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | (1470) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 131.67/18.58 | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 131.67/18.58 | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 131.67/18.58 | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 131.67/18.58 | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 131.67/18.58 | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 131.67/18.58 | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 131.67/18.58 | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 131.67/18.58 | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.67/18.58 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.67/18.58 | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 131.67/18.58 | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 131.67/18.58 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 131.67/18.58 | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 131.67/18.58 | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 131.67/18.58 | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 131.67/18.58 | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 131.67/18.58 | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | BETA: splitting (1470) gives:
% 131.67/18.58 | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | (1471) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 131.67/18.58 | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | ALPHA: (1471) implies:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | (1472) op(e1, e1) = e2
% 131.67/18.58 | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (1472), (function-axioms) are
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 131.67/18.58 | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | (1473) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 131.67/18.58 | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | ALPHA: (1473) implies:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | (1474) op(e0, e0) = all_56_31
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | (1475) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 131.67/18.58 | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | BETA: splitting (1475) gives:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | (1476) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27))
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (158), (1345), (1411), (1474), (1476),
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | #507.
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | (1477) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1477) gives:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | (1478) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7)
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23)
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1478) implies:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | (1479) op(e1, e1) = e0
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1461), (1479), (function-axioms) are
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #721.
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | (1480) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1480) implies:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | (1481) all_56_31 = e1
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1474), (1481) imply:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | (1482) op(e0, e0) = e1
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1345), (1482), (function-axioms) are
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #636.
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.58 | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.58 | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | End of split
% 131.67/18.58 | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | End of split
% 131.67/18.58 | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | End of split
% 131.67/18.58 | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | Case 2:
% 131.67/18.58 | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | (1483) all_54_10 = e0
% 131.67/18.58 | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | REF_CLOSE: (334), (1450), (1483) are inconsistent by
% 131.67/18.58 | | | | | | | | | | | | | | | sub-proof #506.
% 131.67/18.58 | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | End of split
% 131.67/18.58 | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | End of split
% 131.67/18.58 | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | End of split
% 131.67/18.58 | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | Case 2:
% 131.67/18.58 | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | (1484) all_40_2 = e0
% 131.67/18.58 | | | | | | | | | | | | (1485) ( ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 &
% 131.67/18.58 | | | | | | | | | | | | $i(all_40_0)) | ( ~ (all_40_1 = e2) & op(e0, e0)
% 131.67/18.58 | | | | | | | | | | | | = all_40_1 & $i(all_40_1))
% 131.67/18.58 | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | COMBINE_EQS: (332), (1484) imply:
% 131.67/18.58 | | | | | | | | | | | | (1486) all_6_2 = e0
% 131.67/18.58 | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | SIMP: (1486) implies:
% 131.67/18.58 | | | | | | | | | | | | (1487) all_6_2 = e0
% 131.67/18.58 | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | REDUCE: (348), (1487) imply:
% 131.67/18.58 | | | | | | | | | | | | (1488) ~ (all_52_2 = e0)
% 131.67/18.58 | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | REDUCE: (359), (1487) imply:
% 131.67/18.58 | | | | | | | | | | | | (1489) ~ (all_52_6 = e0)
% 131.67/18.58 | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | REDUCE: (362), (1487) imply:
% 131.67/18.58 | | | | | | | | | | | | (1490) ~ (all_52_9 = e0)
% 131.67/18.58 | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | REDUCE: (364), (1487) imply:
% 131.67/18.58 | | | | | | | | | | | | (1491) ~ (all_52_11 = e0)
% 131.67/18.58 | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | REDUCE: (372), (1487) imply:
% 131.67/18.58 | | | | | | | | | | | | (1492) ~ (e2 = e0)
% 131.67/18.58 | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | REDUCE: (39), (1487) imply:
% 131.67/18.58 | | | | | | | | | | | | (1493) op(e1, e1) = e0
% 131.67/18.58 | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | BETA: splitting (106) gives:
% 131.67/18.58 | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | Case 1:
% 131.67/18.58 | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | (1494) ~ (all_50_2 = e1)
% 131.67/18.58 | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | REDUCE: (1443), (1494) imply:
% 131.67/18.58 | | | | | | | | | | | | | (1495) $false
% 131.67/18.58 | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | CLOSE: (1495) is inconsistent.
% 131.67/18.58 | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | Case 2:
% 131.67/18.58 | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | (1496) ( ~ (all_50_0 = e2) & op(e1, e3) = all_50_0 &
% 131.67/18.58 | | | | | | | | | | | | | $i(all_50_0)) | ( ~ (all_50_1 = e0) & op(e1, e1)
% 131.67/18.58 | | | | | | | | | | | | | = all_50_1 & $i(all_50_1))
% 131.67/18.58 | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | BETA: splitting (231) gives:
% 131.67/18.58 | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | Case 1:
% 131.67/18.58 | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | (1497) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 131.67/18.58 | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 131.67/18.58 | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | BETA: splitting (1497) gives:
% 131.67/18.58 | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | Case 1:
% 131.67/18.58 | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | (1498) all_57_0 = e0 & op(e3, e3) = e0
% 131.67/18.58 | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | ALPHA: (1498) implies:
% 131.67/18.58 | | | | | | | | | | | | | | | (1499) op(e3, e3) = e0
% 131.67/18.58 | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | REF_CLOSE: (4), (1448), (1499), (function-axioms) are
% 131.67/18.58 | | | | | | | | | | | | | | | inconsistent by sub-proof #717.
% 131.67/18.58 | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | Case 2:
% 131.67/18.58 | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | (1500) all_57_2 = e0 & op(e2, e3) = e0
% 131.67/18.58 | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | ALPHA: (1500) implies:
% 131.67/18.58 | | | | | | | | | | | | | | | (1501) all_57_2 = e0
% 131.67/18.58 | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (162), (164),
% 131.67/18.58 | | | | | | | | | | | | | | | (170), (224), (225), (226), (227), (1343), (1410),
% 131.67/18.58 | | | | | | | | | | | | | | | (1411), (1414), (1489), (1501), (function-axioms)
% 131.67/18.58 | | | | | | | | | | | | | | | are inconsistent by sub-proof #498.
% 131.67/18.58 | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | End of split
% 131.67/18.58 | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | Case 2:
% 131.67/18.58 | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | (1502) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 131.67/18.58 | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 131.67/18.58 | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | BETA: splitting (1502) gives:
% 131.67/18.58 | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | Case 1:
% 131.67/18.58 | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | (1503) all_57_6 = e0 & op(e1, e3) = e0
% 131.67/18.58 | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | ALPHA: (1503) implies:
% 131.67/18.58 | | | | | | | | | | | | | | | (1504) all_57_6 = e0
% 131.67/18.58 | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 131.67/18.58 | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | Case 1:
% 131.67/18.58 | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | (1505) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 131.67/18.58 | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 131.67/18.58 | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | BETA: splitting (1505) gives:
% 131.67/18.58 | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.58 | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | (1506) all_57_0 = e2 & op(e3, e3) = e2
% 131.67/18.58 | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | ALPHA: (1506) implies:
% 131.67/18.58 | | | | | | | | | | | | | | | | | (1507) op(e3, e3) = e2
% 131.67/18.58 | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1448), (1507), (function-axioms) are
% 131.67/18.58 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743.
% 131.67/18.58 | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.58 | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | (1508) all_57_2 = e2 & op(e2, e3) = e2
% 131.67/18.58 | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | ALPHA: (1508) implies:
% 131.67/18.58 | | | | | | | | | | | | | | | | | (1509) all_57_2 = e2
% 131.67/18.58 | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | BETA: splitting (1485) gives:
% 131.67/18.58 | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.58 | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | (1510) ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | $i(all_40_0)
% 131.67/18.58 | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | ALPHA: (1510) implies:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | (1511) ~ (all_40_0 = e3)
% 131.67/18.58 | | | | | | | | | | | | | | | | | | (1512) op(e0, e1) = all_40_0
% 131.67/18.58 | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 131.67/18.58 | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | (1513) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 131.67/18.58 | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (1448), (1509), (1513),
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | #589.
% 131.67/18.58 | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | (1514) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 131.67/18.58 | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | BETA: splitting (1514) gives:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | (1515) all_57_6 = e3 & op(e1, e3) = e3
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | ALPHA: (1515) implies:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | (1516) all_57_6 = e3
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1504), (1516) are inconsistent by sub-proof
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | #588.
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | (1517) all_57_12 = e3 & op(e0, e3) = e3
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | ALPHA: (1517) implies:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | (1518) all_57_12 = e3
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | (1519) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1519) gives:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | (1520) all_57_6 = e2 & op(e1, e3) = e2
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1520) implies:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | (1521) all_57_6 = e2
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1504), (1521) imply:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | (1522) e2 = e0
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1522) implies:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | (1523) e2 = e0
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1509), (1523) imply:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | (1524) all_57_2 = e0
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (162), (164),
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | (170), (224), (225), (226), (227), (1343), (1410),
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | (1411), (1414), (1489), (1524), (function-axioms)
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #498.
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | (1525) all_57_7 = e2 & op(e1, e2) = e2
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1525) implies:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | (1526) all_57_7 = e2
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (163), (167),
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | (169), (170), (214), (216), (218), (222), (224),
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | (228), (230), (231), (232), (233), (236), (237),
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | (238), (361), (1345), (1410), (1414), (1444),
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | (1445), (1446), (1448), (1493), (1504), (1509),
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | (1511), (1512), (1518), (1526), (function-axioms)
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #485.
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | (1527) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (160), (372), (1344), (1527),
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | #513.
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.58 | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.58 | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.58 | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | (1528) ~ (all_40_1 = e2) & op(e0, e0) = all_40_1 &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | $i(all_40_1)
% 131.67/18.58 | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | REF_CLOSE: (1345), (1528), (function-axioms) are inconsistent
% 131.67/18.58 | | | | | | | | | | | | | | | | | | by sub-proof #528.
% 131.67/18.58 | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | End of split
% 131.67/18.58 | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | End of split
% 131.67/18.58 | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | Case 2:
% 131.67/18.58 | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | (1529) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 131.67/18.58 | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 131.67/18.58 | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | BETA: splitting (1529) gives:
% 131.67/18.58 | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.58 | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | (1530) all_57_6 = e2 & op(e1, e3) = e2
% 131.67/18.58 | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | ALPHA: (1530) implies:
% 131.67/18.58 | | | | | | | | | | | | | | | | | (1531) all_57_6 = e2
% 131.67/18.58 | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1504), (1531) are inconsistent by sub-proof
% 131.67/18.58 | | | | | | | | | | | | | | | | | #586.
% 131.67/18.58 | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.58 | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | (1532) all_57_12 = e2 & op(e0, e3) = e2
% 131.67/18.58 | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | ALPHA: (1532) implies:
% 131.67/18.58 | | | | | | | | | | | | | | | | | (1533) all_57_12 = e2
% 131.67/18.58 | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | BETA: splitting (1485) gives:
% 131.67/18.58 | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.58 | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | (1534) ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 &
% 131.67/18.58 | | | | | | | | | | | | | | | | | | $i(all_40_0)
% 131.67/18.58 | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | ALPHA: (1534) implies:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | (1535) ~ (all_40_0 = e3)
% 131.67/18.58 | | | | | | | | | | | | | | | | | | (1536) op(e0, e1) = all_40_0
% 131.67/18.58 | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 131.67/18.58 | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | (1537) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 131.67/18.58 | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | BETA: splitting (1537) gives:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | (1538) all_57_0 = e3 & op(e3, e3) = e3
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | ALPHA: (1538) implies:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | (1539) op(e3, e3) = e3
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1448), (1539), (function-axioms) are
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #775.
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | (1540) all_57_2 = e3 & op(e2, e3) = e3
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | ALPHA: (1540) implies:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | (1541) all_57_2 = e3
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | (1542) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1542) gives:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | (1543) all_57_6 = e2 & op(e1, e3) = e2
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1543) implies:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | (1544) all_57_6 = e2
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (231), (1448), (1533), (1541),
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | (1544), (function-axioms) are inconsistent by
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | sub-proof #519.
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | (1545) all_57_7 = e2 & op(e1, e2) = e2
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1545) implies:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | (1546) all_57_7 = e2
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | (1547) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1547) gives:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1548) all_57_12 = e3 & op(e0, e3) = e3
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1548) implies:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1549) all_57_12 = e3
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1533), (1549) imply:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1550) e3 = e2
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1550) implies:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1551) e3 = e2
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1541), (1551) imply:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1552) all_57_2 = e2
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (163), (167),
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (169), (170), (214), (216), (218), (222), (224),
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (228), (230), (231), (232), (233), (236), (237),
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (238), (361), (1345), (1410), (1414), (1444),
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1445), (1446), (1448), (1493), (1504), (1535),
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1536), (1546), (1549), (1552), (function-axioms)
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #485.
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1553) all_57_13 = e3 & op(e0, e2) = e3
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1553) implies:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1554) all_57_13 = e3
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (208), (209), (1345),
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1533), (1554), (function-axioms) are inconsistent
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #482.
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | (1555) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1555) gives:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1556) all_57_14 = e3 & op(e0, e1) = e3
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1556) implies:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1557) op(e0, e1) = e3
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1535), (1536), (1557), (function-axioms) are
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #529.
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1558) all_57_15 = e3 & op(e0, e0) = e3
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1558) implies:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1559) op(e0, e0) = e3
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1345), (1559), (function-axioms) are
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #634.
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | (1560) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (160), (372), (1344), (1560),
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | #513.
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.59 | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | (1561) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 131.67/18.59 | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | BETA: splitting (1561) gives:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | (1562) all_57_6 = e3 & op(e1, e3) = e3
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | ALPHA: (1562) implies:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | (1563) all_57_6 = e3
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1504), (1563) are inconsistent by sub-proof
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | #588.
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | (1564) all_57_12 = e3 & op(e0, e3) = e3
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | ALPHA: (1564) implies:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | (1565) all_57_12 = e3
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1533), (1565) are inconsistent by sub-proof
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | #518.
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.59 | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.59 | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.59 | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | (1566) ~ (all_40_1 = e2) & op(e0, e0) = all_40_1 &
% 131.67/18.59 | | | | | | | | | | | | | | | | | | $i(all_40_1)
% 131.67/18.59 | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | REF_CLOSE: (1345), (1566), (function-axioms) are inconsistent
% 131.67/18.59 | | | | | | | | | | | | | | | | | | by sub-proof #528.
% 131.67/18.59 | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | End of split
% 131.67/18.59 | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | End of split
% 131.67/18.59 | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | End of split
% 131.67/18.59 | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | Case 2:
% 131.67/18.59 | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | (1567) all_57_12 = e0 & op(e0, e3) = e0
% 131.67/18.59 | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | ALPHA: (1567) implies:
% 131.67/18.59 | | | | | | | | | | | | | | | (1568) all_57_12 = e0
% 131.67/18.59 | | | | | | | | | | | | | | | (1569) op(e0, e3) = e0
% 131.67/18.59 | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 131.67/18.59 | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | Case 1:
% 131.67/18.59 | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | (1570) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 131.67/18.59 | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 131.67/18.59 | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (170), (1410), (1448), (1570),
% 131.67/18.59 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.67/18.59 | | | | | | | | | | | | | | | | #692.
% 131.67/18.59 | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | Case 2:
% 131.67/18.59 | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | (1571) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 131.67/18.59 | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 131.67/18.59 | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | BETA: splitting (1571) gives:
% 131.67/18.59 | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.59 | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | (1572) all_57_4 = e0 & op(e3, e1) = e0
% 131.67/18.59 | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | ALPHA: (1572) implies:
% 131.67/18.59 | | | | | | | | | | | | | | | | | (1573) op(e3, e1) = e0
% 131.67/18.59 | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (169), (361), (1493), (1573),
% 131.67/18.59 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.67/18.59 | | | | | | | | | | | | | | | | | #619.
% 131.67/18.59 | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.59 | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | (1574) all_57_9 = e0 & op(e3, e0) = e0
% 131.67/18.59 | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | ALPHA: (1574) implies:
% 131.67/18.59 | | | | | | | | | | | | | | | | | (1575) op(e3, e0) = e0
% 131.67/18.59 | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | BETA: splitting (1485) gives:
% 131.67/18.59 | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.59 | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | (1576) ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 &
% 131.67/18.59 | | | | | | | | | | | | | | | | | | $i(all_40_0)
% 131.67/18.59 | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | ALPHA: (1576) implies:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | (1577) ~ (all_40_0 = e3)
% 131.67/18.59 | | | | | | | | | | | | | | | | | | (1578) op(e0, e1) = all_40_0
% 131.67/18.59 | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | BETA: splitting (1496) gives:
% 131.67/18.59 | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | (1579) ~ (all_50_0 = e2) & op(e1, e3) = all_50_0 &
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | $i(all_50_0)
% 131.67/18.59 | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | ALPHA: (1579) implies:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | (1580) ~ (all_50_0 = e2)
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | (1581) op(e1, e3) = all_50_0
% 131.67/18.59 | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | all_40_0, e1, e0, simplifying with (157), (1578)
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | gives:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | (1582) all_52_11 = all_40_0
% 131.67/18.59 | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e0,
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (159), (1569) gives:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | (1583) all_52_3 = e0
% 131.67/18.59 | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2,
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | all_50_0, e3, e1, simplifying with (163), (1581)
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | gives:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | (1584) all_52_2 = all_50_0
% 131.67/18.59 | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | e0, e0, e3, simplifying with (168), (1575) gives:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | (1585) all_52_12 = e0
% 131.67/18.59 | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (1582) imply:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | (1586) all_54_14 = all_40_0
% 131.67/18.59 | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (1584) imply:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | (1587) all_54_8 = all_50_0
% 131.67/18.59 | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | REDUCE: (149), (1584) imply:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | (1588) ~ (all_52_1 = all_50_0)
% 131.67/18.59 | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | REDUCE: (140), (1583) imply:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | (1589) ~ (all_52_7 = e0)
% 131.67/18.59 | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | REDUCE: (125), (1582) imply:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | (1590) ~ (all_52_7 = all_40_0)
% 131.67/18.59 | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | REDUCE: (121), (1582) imply:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | (1591) ~ (all_52_8 = all_40_0)
% 131.67/18.59 | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | REDUCE: (118), (1582) imply:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | (1592) ~ (all_52_9 = all_40_0)
% 131.67/18.59 | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | REDUCE: (1341), (1582) imply:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | (1593) ~ (all_40_0 = e2)
% 131.67/18.59 | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | REDUCE: (1491), (1582) imply:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | (1594) ~ (all_40_0 = e0)
% 131.67/18.59 | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | (1595) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1595) gives:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | (1596) all_57_0 = e2 & op(e3, e3) = e2
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1596) implies:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | (1597) op(e3, e3) = e2
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1448), (1597), (function-axioms) are
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743.
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | (1598) all_57_2 = e2 & op(e2, e3) = e2
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1598) implies:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | (1599) op(e2, e3) = e2
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | (1600) all_54_14 = e3
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1586), (1600) imply:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | (1601) all_40_0 = e3
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1601) implies:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | (1602) all_40_0 = e3
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1577), (1602) imply:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | (1603) $false
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1603) is inconsistent.
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | (1604) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1604) gives:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | (1605) all_54_14 = e2
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1586), (1605) imply:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | (1606) all_40_0 = e2
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1606) implies:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | (1607) all_40_0 = e2
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1593), (1607) imply:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | (1608) $false
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1608) is inconsistent.
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | (1609) all_54_14 = e1 | all_54_14 = e0
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1609) gives:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1610) all_54_14 = e1
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1586), (1610) imply:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1611) all_40_0 = e1
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1611) implies:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1612) all_40_0 = e1
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1590), (1612) imply:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1613) ~ (all_52_7 = e1)
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1591), (1612) imply:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1614) ~ (all_52_8 = e1)
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1592), (1612) imply:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1615) ~ (all_52_9 = e1)
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | (1616) all_54_13 = e3
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (1616) imply:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | (1617) all_52_7 = e3
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1617) implies:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | (1618) all_52_7 = e3
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (1618) imply:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | (1619) ~ (all_52_4 = e3)
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (1620) all_54_8 = e3
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1587), (1620) imply:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (1621) all_50_0 = e3
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1621) implies:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (1622) all_50_0 = e3
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1588), (1622) imply:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (1623) ~ (all_52_1 = e3)
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1624) all_54_4 = e3
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (1623), (1624) are inconsistent by
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #481.
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1625) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1626) all_54_1 = e3
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (271), (1619), (1626) are inconsistent by
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #740.
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1627) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1625) gives:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1628) all_54_4 = e2
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (1628) imply:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1629) all_52_1 = e2
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (1629) imply:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1630) ~ (all_52_9 = e2)
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1630) implies:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1631) ~ (all_52_9 = e2)
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1627) gives:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1632) all_54_1 = e2
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (1632) imply:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1633) all_52_4 = e2
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1633) implies:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1634) all_52_4 = e2
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (1634) imply:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1635) ~ (all_52_8 = e2)
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1635) implies:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1636) ~ (all_52_8 = e2)
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1637) all_54_2 = e3
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (1637) imply:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1638) all_52_8 = e3
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1638) implies:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1639) all_52_8 = e3
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (1639) imply:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1640) ~ (all_52_9 = e3)
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1640) implies:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1641) ~ (all_52_9 = e3)
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1642) all_54_6 = e3
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (1642) imply:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1643) all_52_9 = e3
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1641), (1643) imply:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1644) $false
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1644) is inconsistent.
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1645) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (1490), (1615), (1631), (1645) are
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #478.
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1646) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (194), (270), (334), (361), (372), (1347),
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1493), (1614), (1636), (1646), (function-axioms)
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #476.
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1647) all_54_1 = e1 | all_54_1 = e0
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1647) gives:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1648) all_54_1 = e1
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (271), (1446), (1648) are inconsistent by
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #731.
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1649) all_54_1 = e0
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (271), (1410), (1649) are inconsistent by
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #702.
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1650) ~ (all_54_4 = e2)
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (268), (1650) imply:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1651) ~ (all_52_1 = e2)
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (1599), (1651), (function-axioms) are
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #779.
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (1652) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (1445), (1488), (1580), (1587), (1652) are
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #473.
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | (1653) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1653) gives:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (1654) all_54_13 = e2
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (1340), (1654) are inconsistent by
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #472.
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (1655) all_54_13 = e1 | all_54_13 = e0
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (1411), (1613), (1655) are inconsistent by
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #470.
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1656) all_54_14 = e0
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1586), (1656) imply:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1657) all_40_0 = e0
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1657) implies:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1658) all_40_0 = e0
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1594), (1658) imply:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1659) $false
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1659) is inconsistent.
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | (1660) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1660) gives:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | (1661) all_57_6 = e2 & op(e1, e3) = e2
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1661) implies:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | (1662) op(e1, e3) = e2
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1580), (1581), (1662), (function-axioms) are
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #735.
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | (1663) all_57_12 = e2 & op(e0, e3) = e2
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1663) implies:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | (1664) all_57_12 = e2
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1568), (1664) are inconsistent by sub-proof
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | #682.
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.59 | | | | | | | | | | | | | | | | | | |
% 131.67/18.59 | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.59 | | | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | (1665) ~ (all_50_1 = e0) & op(e1, e1) = all_50_1 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | $i(all_50_1)
% 131.67/18.60 | | | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1493), (1665), (function-axioms) are inconsistent
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | by sub-proof #719.
% 131.67/18.60 | | | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.60 | | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.60 | | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | | (1666) ~ (all_40_1 = e2) & op(e0, e0) = all_40_1 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | $i(all_40_1)
% 131.67/18.60 | | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | | REF_CLOSE: (1345), (1666), (function-axioms) are inconsistent
% 131.67/18.60 | | | | | | | | | | | | | | | | | | by sub-proof #528.
% 131.67/18.60 | | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | End of split
% 131.67/18.60 | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | End of split
% 131.67/18.60 | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | End of split
% 131.67/18.60 | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | End of split
% 131.67/18.60 | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | End of split
% 131.67/18.60 | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | End of split
% 131.67/18.60 | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | End of split
% 131.67/18.60 | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | End of split
% 131.67/18.60 | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | End of split
% 131.67/18.60 | | | | | | | | |
% 131.67/18.60 | | | | | | | | Case 2:
% 131.67/18.60 | | | | | | | | |
% 131.67/18.60 | | | | | | | | | (1667) all_28_2 = e3
% 131.67/18.60 | | | | | | | | |
% 131.67/18.60 | | | | | | | | | COMBINE_EQS: (316), (1667) imply:
% 131.67/18.60 | | | | | | | | | (1668) all_6_2 = e3
% 131.67/18.60 | | | | | | | | |
% 131.67/18.60 | | | | | | | | | SIMP: (1668) implies:
% 131.67/18.60 | | | | | | | | | (1669) all_6_2 = e3
% 131.67/18.60 | | | | | | | | |
% 131.67/18.60 | | | | | | | | | REDUCE: (359), (1669) imply:
% 131.67/18.60 | | | | | | | | | (1670) ~ (all_52_6 = e3)
% 131.67/18.60 | | | | | | | | |
% 131.67/18.60 | | | | | | | | | REDUCE: (361), (1669) imply:
% 131.67/18.60 | | | | | | | | | (1671) ~ (all_52_8 = e3)
% 131.67/18.60 | | | | | | | | |
% 131.67/18.60 | | | | | | | | | REDUCE: (362), (1669) imply:
% 131.67/18.60 | | | | | | | | | (1672) ~ (all_52_9 = e3)
% 131.67/18.60 | | | | | | | | |
% 131.67/18.60 | | | | | | | | | REDUCE: (364), (1669) imply:
% 131.67/18.60 | | | | | | | | | (1673) ~ (all_52_11 = e3)
% 131.67/18.60 | | | | | | | | |
% 131.67/18.60 | | | | | | | | | REDUCE: (39), (1669) imply:
% 131.67/18.60 | | | | | | | | | (1674) op(e1, e1) = e3
% 131.67/18.60 | | | | | | | | |
% 131.67/18.60 | | | | | | | | | BETA: splitting (76) gives:
% 131.67/18.60 | | | | | | | | |
% 131.67/18.60 | | | | | | | | | Case 1:
% 131.67/18.60 | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | (1675) ~ (all_30_2 = e0)
% 131.67/18.60 | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | REDUCE: (309), (1675) imply:
% 131.67/18.60 | | | | | | | | | | (1676) ~ (all_8_2 = e0)
% 131.67/18.60 | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | BETA: splitting (199) gives:
% 131.67/18.60 | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | Case 1:
% 131.67/18.60 | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | (1677) all_54_5 = e3
% 131.67/18.60 | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | COMBINE_EQS: (267), (1677) imply:
% 131.67/18.60 | | | | | | | | | | | (1678) all_8_2 = e3
% 131.67/18.60 | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | REDUCE: (376), (1678) imply:
% 131.67/18.60 | | | | | | | | | | | (1679) $false
% 131.67/18.60 | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | CLOSE: (1679) is inconsistent.
% 131.67/18.60 | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | Case 2:
% 131.67/18.60 | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | (1680) ~ (all_54_5 = e3)
% 131.67/18.60 | | | | | | | | | | | (1681) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 131.67/18.60 | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | BETA: splitting (1681) gives:
% 131.67/18.60 | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | Case 1:
% 131.67/18.60 | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | (1682) all_54_5 = e2
% 131.67/18.60 | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | COMBINE_EQS: (267), (1682) imply:
% 131.67/18.60 | | | | | | | | | | | | (1683) all_8_2 = e2
% 131.67/18.60 | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | REDUCE: (347), (1683) imply:
% 131.67/18.60 | | | | | | | | | | | | (1684) ~ (all_52_1 = e2)
% 131.67/18.60 | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | REDUCE: (356), (1683) imply:
% 131.67/18.60 | | | | | | | | | | | | (1685) ~ (all_52_9 = e2)
% 131.67/18.60 | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | REDUCE: (376), (1683) imply:
% 131.67/18.60 | | | | | | | | | | | | (1686) ~ (e3 = e2)
% 131.67/18.60 | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | BETA: splitting (225) gives:
% 131.67/18.60 | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | Case 1:
% 131.67/18.60 | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | (1687) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 131.67/18.60 | | | | | | | | | | | | | & op(e2, e2) = e2)
% 131.67/18.60 | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | BETA: splitting (1687) gives:
% 131.67/18.60 | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | Case 1:
% 131.67/18.60 | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | (1688) all_57_2 = e2 & op(e2, e3) = e2
% 131.67/18.60 | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | ALPHA: (1688) implies:
% 131.67/18.60 | | | | | | | | | | | | | | (1689) op(e2, e3) = e2
% 131.67/18.60 | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | REF_CLOSE: (167), (1684), (1689), (function-axioms) are
% 131.67/18.60 | | | | | | | | | | | | | | inconsistent by sub-proof #779.
% 131.67/18.60 | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | Case 2:
% 131.67/18.60 | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | (1690) all_57_3 = e2 & op(e2, e2) = e2
% 131.67/18.60 | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | ALPHA: (1690) implies:
% 131.67/18.60 | | | | | | | | | | | | | | (1691) all_57_3 = e2
% 131.67/18.60 | | | | | | | | | | | | | | (1692) op(e2, e2) = e2
% 131.67/18.60 | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 131.67/18.60 | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | Case 1:
% 131.67/18.60 | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | (1693) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 131.67/18.60 | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 131.67/18.60 | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | REF_CLOSE: (45), (167), (378), (1684), (1693),
% 131.67/18.60 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.67/18.60 | | | | | | | | | | | | | | | #535.
% 131.67/18.60 | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | Case 2:
% 131.67/18.60 | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | (1694) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 131.67/18.60 | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 131.67/18.60 | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | BETA: splitting (1694) gives:
% 131.67/18.60 | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | Case 1:
% 131.67/18.60 | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | (1695) all_57_6 = e2 & op(e1, e3) = e2
% 131.67/18.60 | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | ALPHA: (1695) implies:
% 131.67/18.60 | | | | | | | | | | | | | | | | (1696) op(e1, e3) = e2
% 131.67/18.60 | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 131.67/18.60 | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.60 | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | (1697) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 131.67/18.60 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.67/18.60 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 131.67/18.60 | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 131.67/18.60 | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.67/18.60 | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 131.67/18.60 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 131.67/18.60 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 131.67/18.60 | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 131.67/18.60 | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 131.67/18.60 | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 131.67/18.60 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 131.67/18.60 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 131.67/18.60 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 131.67/18.60 | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 131.67/18.60 | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 131.67/18.60 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.67/18.60 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.67/18.60 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 131.67/18.60 | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | BETA: splitting (1697) gives:
% 131.67/18.60 | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.60 | | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | | (1698) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 131.67/18.60 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.67/18.60 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 131.67/18.60 | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.67/18.60 | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 131.67/18.60 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 131.67/18.60 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 131.67/18.60 | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 131.67/18.60 | | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (169), (378), (1671), (1698),
% 131.67/18.60 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.67/18.60 | | | | | | | | | | | | | | | | | | #469.
% 131.67/18.60 | | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.60 | | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | | (1699) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 131.67/18.60 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 131.67/18.60 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 131.67/18.60 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 131.67/18.60 | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 131.67/18.60 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.67/18.60 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 131.67/18.60 | | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (167), (374), (1684), (1699),
% 131.67/18.60 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.67/18.60 | | | | | | | | | | | | | | | | | | #533.
% 131.67/18.60 | | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | End of split
% 131.67/18.60 | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.60 | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | (1700) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 131.67/18.60 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.67/18.60 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.67/18.60 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 131.67/18.60 | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 131.67/18.60 | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 131.67/18.60 | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 131.67/18.60 | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 131.67/18.60 | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 131.67/18.60 | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 131.67/18.60 | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 131.67/18.60 | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 131.67/18.60 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.67/18.60 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 131.67/18.60 | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 131.67/18.60 | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 131.67/18.60 | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 131.67/18.60 | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 131.67/18.60 | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 131.67/18.60 | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 131.67/18.60 | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 131.67/18.60 | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 131.67/18.60 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 131.67/18.60 | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 131.67/18.60 | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 131.67/18.60 | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 131.67/18.60 | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 131.67/18.60 | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 131.67/18.60 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 131.67/18.60 | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 131.67/18.60 | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 131.67/18.60 | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.67/18.60 | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 131.67/18.60 | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 131.67/18.60 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 131.67/18.60 | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 131.67/18.60 | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 131.67/18.60 | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 131.67/18.60 | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 131.67/18.60 | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 131.67/18.60 | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 131.67/18.60 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 131.67/18.60 | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 131.67/18.60 | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 131.67/18.60 | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 131.67/18.60 | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | BETA: splitting (1700) gives:
% 131.67/18.60 | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.60 | | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | | (1701) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 131.67/18.60 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.67/18.60 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 131.67/18.60 | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 131.67/18.60 | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 131.67/18.60 | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 131.67/18.60 | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 131.67/18.60 | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 131.67/18.60 | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 131.67/18.60 | | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (165), (1685), (1696), (1701),
% 131.67/18.60 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.67/18.60 | | | | | | | | | | | | | | | | | | #468.
% 131.67/18.60 | | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.60 | | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | | (1702) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 131.67/18.60 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 131.67/18.60 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 131.67/18.60 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 131.67/18.60 | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 131.67/18.60 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.67/18.60 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 131.67/18.60 | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.67/18.60 | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 131.67/18.60 | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.67/18.60 | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 131.67/18.60 | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 131.67/18.60 | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 131.67/18.60 | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 131.67/18.60 | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 131.67/18.60 | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 131.67/18.60 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 131.67/18.60 | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 131.67/18.60 | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 131.67/18.60 | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.67/18.60 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.67/18.60 | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 131.67/18.60 | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 131.67/18.60 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 131.67/18.60 | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 131.67/18.60 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 131.67/18.60 | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 131.67/18.60 | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 131.67/18.60 | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 131.67/18.60 | | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | | BETA: splitting (1702) gives:
% 131.67/18.60 | | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.60 | | | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | (1703) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 131.67/18.60 | | | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | ALPHA: (1703) implies:
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | (1704) op(e2, e0) = e2
% 131.67/18.60 | | | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (1343), (1704), (function-axioms) are
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 131.67/18.60 | | | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.60 | | | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | (1705) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 131.67/18.60 | | | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | BETA: splitting (1705) gives:
% 131.67/18.60 | | | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | | (1706) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | | ALPHA: (1706) implies:
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | | (1707) op(e1, e1) = e2
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (1707), (function-axioms) are
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.60 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | (1708) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | ALPHA: (1708) implies:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | (1709) op(e0, e0) = all_56_31
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | (1710) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | (1711) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1711) gives:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | (1712) all_57_4 = e2 & op(e3, e1) = e2
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1712) implies:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | (1713) op(e3, e1) = e2
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | all_56_31, e0, e0, simplifying with (1345), (1709)
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | gives:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | (1714) all_56_31 = e2
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e2,
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (169), (1713) gives:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | (1715) all_52_8 = e2
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1710) gives:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | (1716) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27))
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1692), (1714), (1716), (function-axioms) are
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #530.
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | (1717) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (1674), (1714), (1717),
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | #467.
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | (1718) all_57_5 = e2 & op(e2, e1) = e2
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1718) implies:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | (1719) op(e2, e1) = e2
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (1685), (1719), (function-axioms) are
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #770.
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | (1720) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1720) gives:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | (1721) all_57_8 = e2 & op(e1, e1) = e2
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1721) implies:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | (1722) op(e1, e1) = e2
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (1722), (function-axioms) are
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | (1723) all_57_14 = e2 & op(e0, e1) = e2
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1723) implies:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | (1724) all_57_14 = e2
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | (1725) op(e0, e1) = e2
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | (1726) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1726) gives:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | (1727) all_57_0 = e2 & op(e3, e3) = e2
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1727) implies:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | (1728) op(e3, e3) = e2
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (378), (1728), (function-axioms) are
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #536.
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | (1729) all_57_1 = e2 & op(e3, e2) = e2
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1729) implies:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | (1730) all_57_1 = e2
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (227), (228),
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | (230), (1670), (1691), (1730), (function-axioms)
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #463.
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | (1731) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1731) gives:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | (1732) all_57_4 = e2 & op(e3, e1) = e2
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1732) implies:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | (1733) all_57_4 = e2
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | (1734) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1734) gives:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | (1735) all_57_4 = e1 & op(e3, e1) = e1
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1733), (1735) are inconsistent by sub-proof
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | #462.
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | (1736) all_57_5 = e1 & op(e2, e1) = e1
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1736) implies:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | (1737) all_57_5 = e1
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1738) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1738) gives:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1739) all_57_4 = e0 & op(e3, e1) = e0
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1733), (1739) are inconsistent by sub-proof
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #647.
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1740) all_57_5 = e0 & op(e2, e1) = e0
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1737), (1740) are inconsistent by sub-proof
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #461.
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1741) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1741) gives:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1742) all_57_8 = e0 & op(e1, e1) = e0
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1742) implies:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1743) op(e1, e1) = e0
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1674), (1743), (function-axioms) are
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753.
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1744) all_57_14 = e0 & op(e0, e1) = e0
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1744) implies:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1745) op(e0, e1) = e0
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1725), (1745), (function-axioms) are
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #660.
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | (1746) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1746) gives:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | (1747) all_57_8 = e1 & op(e1, e1) = e1
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1747) implies:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | (1748) op(e1, e1) = e1
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (1674), (1748), (function-axioms) are
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #662.
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | (1749) all_57_14 = e1 & op(e0, e1) = e1
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1749) implies:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | (1750) all_57_14 = e1
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1724), (1750) imply:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | (1751) e2 = e1
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (1751) imply:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | (1752) $false
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1752) is inconsistent.
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | (1753) all_57_9 = e2 & op(e3, e0) = e2
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (1342), (1753), (function-axioms) are
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #460.
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.61 | | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.61 | | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | | End of split
% 131.67/18.61 | | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | End of split
% 131.67/18.61 | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | Case 2:
% 131.67/18.61 | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | (1754) all_57_12 = e2 & op(e0, e3) = e2
% 131.67/18.61 | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | ALPHA: (1754) implies:
% 131.67/18.61 | | | | | | | | | | | | | | | | (1755) all_57_12 = e2
% 131.67/18.61 | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (208), (209),
% 131.67/18.61 | | | | | | | | | | | | | | | | (211), (1345), (1673), (1755), (function-axioms)
% 131.67/18.61 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #458.
% 131.67/18.61 | | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | | End of split
% 131.67/18.61 | | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | | End of split
% 131.67/18.61 | | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | End of split
% 131.67/18.61 | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | Case 2:
% 131.67/18.61 | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | (1756) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 131.67/18.61 | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 131.67/18.61 | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | | REF_CLOSE: (164), (165), (1343), (1685), (1756),
% 131.67/18.61 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.67/18.61 | | | | | | | | | | | | | #625.
% 131.67/18.61 | | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | End of split
% 131.67/18.61 | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | Case 2:
% 131.67/18.61 | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | (1757) all_54_5 = e1 | all_54_5 = e0
% 131.67/18.61 | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | REF_CLOSE: (267), (373), (1676), (1757) are inconsistent by
% 131.67/18.61 | | | | | | | | | | | | sub-proof #624.
% 131.67/18.61 | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | End of split
% 131.67/18.61 | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | End of split
% 131.67/18.61 | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | Case 2:
% 131.67/18.61 | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | (1758) all_30_2 = e0
% 131.67/18.61 | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | COMBINE_EQS: (309), (1758) imply:
% 131.67/18.61 | | | | | | | | | | (1759) all_8_2 = e0
% 131.67/18.61 | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | SIMP: (1759) implies:
% 131.67/18.61 | | | | | | | | | | (1760) all_8_2 = e0
% 131.67/18.61 | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | REDUCE: (350), (1760) imply:
% 131.67/18.61 | | | | | | | | | | (1761) ~ (all_52_4 = e0)
% 131.67/18.61 | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | REDUCE: (352), (1760) imply:
% 131.67/18.61 | | | | | | | | | | (1762) ~ (all_52_6 = e0)
% 131.67/18.61 | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | REDUCE: (354), (1760) imply:
% 131.67/18.61 | | | | | | | | | | (1763) ~ (all_52_7 = e0)
% 131.67/18.61 | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | REDUCE: (356), (1760) imply:
% 131.67/18.61 | | | | | | | | | | (1764) ~ (all_52_9 = e0)
% 131.67/18.61 | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | REDUCE: (376), (1760) imply:
% 131.67/18.61 | | | | | | | | | | (1765) ~ (e3 = e0)
% 131.67/18.61 | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | REDUCE: (373), (1760) imply:
% 131.67/18.61 | | | | | | | | | | (1766) ~ (e1 = e0)
% 131.67/18.61 | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | REDUCE: (42), (1760) imply:
% 131.67/18.61 | | | | | | | | | | (1767) op(e2, e2) = e0
% 131.67/18.61 | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | BETA: splitting (206) gives:
% 131.67/18.61 | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | Case 1:
% 131.67/18.61 | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | (1768) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 131.67/18.61 | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.67/18.61 | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 131.67/18.61 | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 131.67/18.61 | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 131.67/18.61 | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 131.67/18.61 | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.67/18.61 | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 131.67/18.61 | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 131.67/18.61 | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 131.67/18.61 | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 131.67/18.61 | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 131.67/18.61 | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 131.67/18.61 | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 131.67/18.61 | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 131.67/18.61 | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 131.67/18.61 | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 131.67/18.61 | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 131.67/18.61 | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.67/18.61 | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 131.67/18.61 | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 131.67/18.61 | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 131.67/18.61 | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.67/18.61 | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.67/18.61 | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.67/18.61 | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 131.67/18.61 | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.67/18.61 | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 131.67/18.61 | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | BETA: splitting (1768) gives:
% 131.67/18.61 | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | Case 1:
% 131.67/18.61 | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | (1769) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 131.67/18.61 | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.67/18.61 | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 131.67/18.61 | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 131.67/18.61 | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 131.67/18.61 | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 131.67/18.61 | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.67/18.61 | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 131.67/18.61 | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 131.67/18.61 | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 131.67/18.61 | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 131.67/18.61 | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 131.67/18.61 | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 131.67/18.61 | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 131.67/18.61 | | | | | | | | | | | |
% 131.67/18.61 | | | | | | | | | | | | REF_CLOSE: (45), (169), (378), (1671), (1769),
% 131.67/18.62 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.67/18.62 | | | | | | | | | | | | #469.
% 131.67/18.62 | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | Case 2:
% 131.67/18.62 | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | (1770) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 131.67/18.62 | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 131.67/18.62 | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 131.67/18.62 | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 131.67/18.62 | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.67/18.62 | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 131.67/18.62 | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 131.67/18.62 | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 131.67/18.62 | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.67/18.62 | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.67/18.62 | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.67/18.62 | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 131.67/18.62 | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.67/18.62 | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 131.67/18.62 | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | REF_CLOSE: (7), (45), (374), (1767), (1770),
% 131.67/18.62 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.67/18.62 | | | | | | | | | | | | #457.
% 131.67/18.62 | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | End of split
% 131.67/18.62 | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | Case 2:
% 131.67/18.62 | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | (1771) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 131.67/18.62 | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.67/18.62 | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.67/18.62 | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.67/18.62 | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 131.67/18.62 | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.67/18.62 | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 131.67/18.62 | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 131.67/18.62 | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 131.67/18.62 | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 131.67/18.62 | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 131.67/18.62 | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 131.67/18.62 | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 131.67/18.62 | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 131.67/18.62 | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 131.67/18.62 | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.67/18.62 | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 131.67/18.62 | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 131.67/18.62 | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 131.67/18.62 | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 131.67/18.62 | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 131.67/18.62 | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 131.67/18.62 | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 131.67/18.62 | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.67/18.62 | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 131.67/18.62 | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 131.67/18.62 | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 131.67/18.62 | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 131.67/18.62 | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 131.67/18.62 | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 131.67/18.62 | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 131.67/18.62 | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.67/18.62 | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 131.67/18.62 | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 131.67/18.62 | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 131.67/18.62 | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 131.67/18.62 | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 131.67/18.62 | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 131.67/18.62 | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.67/18.62 | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.67/18.62 | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 131.67/18.62 | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 131.67/18.62 | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 131.67/18.62 | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 131.67/18.62 | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 131.67/18.62 | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 131.67/18.62 | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 131.67/18.62 | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 131.67/18.62 | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 131.67/18.62 | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 131.67/18.62 | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 131.67/18.62 | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 131.67/18.62 | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 131.67/18.62 | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 131.67/18.62 | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 131.67/18.62 | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 131.67/18.62 | | | | | | | | | | | & $i(all_56_29))))
% 131.67/18.62 | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | BETA: splitting (1771) gives:
% 131.67/18.62 | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | Case 1:
% 131.67/18.62 | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | (1772) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 131.67/18.62 | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.67/18.62 | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.67/18.62 | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.67/18.62 | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 131.67/18.62 | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.67/18.62 | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 131.67/18.62 | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 131.67/18.62 | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 131.67/18.62 | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 131.67/18.62 | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 131.67/18.62 | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 131.67/18.62 | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 131.67/18.62 | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 131.67/18.62 | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | BETA: splitting (1772) gives:
% 131.67/18.62 | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | Case 1:
% 131.67/18.62 | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | (1773) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 131.67/18.62 | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 131.67/18.62 | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.67/18.62 | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.67/18.62 | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 131.67/18.62 | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.67/18.62 | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 131.67/18.62 | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | ALPHA: (1773) implies:
% 131.67/18.62 | | | | | | | | | | | | | (1774) op(e1, e3) = e1
% 131.67/18.62 | | | | | | | | | | | | | (1775) op(e3, e0) = all_56_25
% 131.67/18.62 | | | | | | | | | | | | | (1776) op(e3, e3) = all_56_1
% 131.67/18.62 | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | BETA: splitting (223) gives:
% 131.67/18.62 | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | Case 1:
% 131.67/18.62 | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | (1777) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 131.67/18.62 | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 131.67/18.62 | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | BETA: splitting (1777) gives:
% 131.67/18.62 | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | Case 1:
% 131.67/18.62 | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | (1778) all_57_2 = e0 & op(e2, e3) = e0
% 131.67/18.62 | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | ALPHA: (1778) implies:
% 131.67/18.62 | | | | | | | | | | | | | | | (1779) all_57_2 = e0
% 131.67/18.62 | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 131.67/18.62 | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | Case 1:
% 131.67/18.62 | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | | (1780) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 131.67/18.62 | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 131.67/18.62 | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | | BETA: splitting (1780) gives:
% 131.67/18.62 | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.62 | | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | | | (1781) all_57_1 = e0 & op(e3, e2) = e0
% 131.67/18.62 | | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (1761), (1781), (function-axioms) are
% 131.67/18.62 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #693.
% 131.67/18.62 | | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.62 | | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | | | (1782) all_57_3 = e0 & op(e2, e2) = e0
% 131.67/18.62 | | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | | | ALPHA: (1782) implies:
% 131.67/18.62 | | | | | | | | | | | | | | | | | (1783) all_57_3 = e0
% 131.67/18.62 | | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 131.67/18.62 | | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.62 | | | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | | | | (1784) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 131.67/18.62 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 131.67/18.62 | | | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1779), (1783), (1784) are inconsistent by
% 131.67/18.62 | | | | | | | | | | | | | | | | | | sub-proof #678.
% 131.67/18.62 | | | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.62 | | | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | | | | (1785) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 131.67/18.62 | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 131.67/18.62 | | | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | | | | BETA: splitting (1785) gives:
% 131.67/18.62 | | | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | | | | Case 1:
% 131.67/18.62 | | | | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | | | | | (1786) all_57_5 = e2 & op(e2, e1) = e2
% 131.67/18.62 | | | | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | | | | | ALPHA: (1786) implies:
% 131.67/18.62 | | | | | | | | | | | | | | | | | | | (1787) all_57_5 = e2
% 131.67/18.62 | | | | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (165), (224), (226), (1672),
% 131.67/18.62 | | | | | | | | | | | | | | | | | | | (1767), (1779), (1787), (function-axioms) are
% 131.67/18.62 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #456.
% 131.67/18.62 | | | | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | | | | Case 2:
% 131.67/18.62 | | | | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | | | | | (1788) all_57_10 = e2 & op(e2, e0) = e2
% 131.67/18.62 | | | | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | | | | | ALPHA: (1788) implies:
% 131.67/18.62 | | | | | | | | | | | | | | | | | | | (1789) op(e2, e0) = e2
% 131.67/18.62 | | | | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (1343), (1789), (function-axioms) are
% 131.67/18.62 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 131.67/18.62 | | | | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | | | | End of split
% 131.67/18.62 | | | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | | | End of split
% 131.67/18.62 | | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | | End of split
% 131.67/18.62 | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | Case 2:
% 131.67/18.62 | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | | (1790) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 131.67/18.62 | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 131.67/18.62 | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (1762), (1763), (1790),
% 131.67/18.62 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.67/18.62 | | | | | | | | | | | | | | | | #504.
% 131.67/18.62 | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | End of split
% 131.67/18.62 | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | Case 2:
% 131.67/18.62 | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | (1791) all_57_3 = e0 & op(e2, e2) = e0
% 131.67/18.62 | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1,
% 131.67/18.62 | | | | | | | | | | | | | | | e3, e1, simplifying with (163), (1774) gives:
% 131.67/18.62 | | | | | | | | | | | | | | | (1792) all_52_2 = e1
% 131.67/18.62 | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 131.67/18.62 | | | | | | | | | | | | | | | all_56_25, e0, e3, simplifying with (168), (1775)
% 131.67/18.62 | | | | | | | | | | | | | | | gives:
% 131.67/18.62 | | | | | | | | | | | | | | | (1793) all_56_25 = all_52_12
% 131.67/18.62 | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2,
% 131.67/18.62 | | | | | | | | | | | | | | | all_56_1, e3, e3, simplifying with (45), (1776)
% 131.67/18.62 | | | | | | | | | | | | | | | gives:
% 131.67/18.62 | | | | | | | | | | | | | | | (1794) all_56_1 = all_10_2
% 131.67/18.62 | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | REDUCE: (338), (1792) imply:
% 131.67/18.62 | | | | | | | | | | | | | | | (1795) ~ (all_10_2 = e1)
% 131.67/18.62 | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | SIMP: (1795) implies:
% 131.67/18.62 | | | | | | | | | | | | | | | (1796) ~ (all_10_2 = e1)
% 131.67/18.62 | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (39), (45), (158), (164), (165), (167),
% 131.67/18.62 | | | | | | | | | | | | | | | (168), (204), (206), (226), (278), (336), (346),
% 131.67/18.62 | | | | | | | | | | | | | | | (371), (372), (374), (378), (1672), (1674),
% 131.67/18.62 | | | | | | | | | | | | | | | (1763), (1767), (1796), (function-axioms) are
% 131.67/18.62 | | | | | | | | | | | | | | | inconsistent by sub-proof #541.
% 131.67/18.62 | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | End of split
% 131.67/18.62 | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | Case 2:
% 131.67/18.62 | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | (1797) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 131.67/18.62 | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 131.67/18.62 | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | BETA: splitting (1797) gives:
% 131.67/18.62 | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | Case 1:
% 131.67/18.62 | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | (1798) all_57_5 = e0 & op(e2, e1) = e0
% 131.67/18.62 | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | REF_CLOSE: (165), (1764), (1798), (function-axioms) are
% 131.67/18.62 | | | | | | | | | | | | | | | inconsistent by sub-proof #455.
% 131.67/18.62 | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | Case 2:
% 131.67/18.62 | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | (1799) all_57_10 = e0 & op(e2, e0) = e0
% 131.67/18.62 | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | ALPHA: (1799) implies:
% 131.67/18.62 | | | | | | | | | | | | | | | (1800) all_57_10 = e0
% 131.67/18.62 | | | | | | | | | | | | | | | (1801) op(e2, e0) = e0
% 131.67/18.62 | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 131.67/18.62 | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | Case 1:
% 131.67/18.62 | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | | (1802) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 131.67/18.62 | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 131.67/18.62 | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (224), (225),
% 131.67/18.62 | | | | | | | | | | | | | | | | (226), (1761), (1800), (1801), (1802),
% 131.67/18.62 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.67/18.62 | | | | | | | | | | | | | | | | #445.
% 131.67/18.62 | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | Case 2:
% 131.67/18.62 | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | | (1803) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 131.67/18.62 | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 131.67/18.62 | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (1762), (1763), (1803),
% 131.67/18.62 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.67/18.62 | | | | | | | | | | | | | | | | #504.
% 131.67/18.62 | | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | | End of split
% 131.67/18.62 | | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | | End of split
% 131.67/18.62 | | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | End of split
% 131.67/18.62 | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | Case 2:
% 131.67/18.62 | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | (1804) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 =
% 131.67/18.62 | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 131.67/18.62 | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2,
% 131.67/18.62 | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 131.67/18.62 | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 131.67/18.62 | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 131.67/18.62 | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 131.67/18.62 | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | ALPHA: (1804) implies:
% 131.67/18.62 | | | | | | | | | | | | | (1805) op(e2, e2) = e1
% 131.67/18.62 | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | REF_CLOSE: (4), (1767), (1805), (function-axioms) are
% 131.67/18.62 | | | | | | | | | | | | | inconsistent by sub-proof #675.
% 131.67/18.62 | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | End of split
% 131.67/18.62 | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | Case 2:
% 131.67/18.62 | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | (1806) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 131.67/18.62 | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 131.67/18.62 | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 131.67/18.62 | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 131.67/18.62 | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.67/18.62 | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 131.67/18.62 | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 131.67/18.62 | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 131.67/18.62 | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.67/18.62 | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 131.67/18.62 | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.67/18.62 | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 131.67/18.62 | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 131.67/18.62 | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.67/18.62 | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 131.67/18.62 | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 131.67/18.62 | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 131.67/18.62 | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 131.67/18.62 | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 131.67/18.62 | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 131.67/18.62 | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 131.67/18.62 | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 131.67/18.62 | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 131.67/18.62 | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 131.67/18.62 | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 131.67/18.62 | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 131.67/18.62 | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 131.67/18.62 | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 131.67/18.62 | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 131.67/18.62 | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 131.67/18.62 | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.67/18.62 | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.67/18.62 | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 131.67/18.62 | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 131.67/18.62 | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.67/18.62 | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 131.67/18.62 | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 131.67/18.62 | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 131.67/18.62 | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 131.67/18.62 | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 131.67/18.62 | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 131.67/18.62 | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 131.67/18.62 | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 131.67/18.62 | | | | | | | | | | | | & $i(all_56_29))))
% 131.67/18.62 | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | BETA: splitting (1806) gives:
% 131.67/18.62 | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | Case 1:
% 131.67/18.62 | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | (1807) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 131.67/18.62 | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 131.67/18.62 | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 131.67/18.62 | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 131.67/18.62 | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 131.67/18.62 | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 131.67/18.62 | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 131.67/18.62 | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | ALPHA: (1807) implies:
% 131.67/18.62 | | | | | | | | | | | | | (1808) op(e2, e0) = e2
% 131.67/18.62 | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | REF_CLOSE: (164), (1343), (1808), (function-axioms) are
% 131.67/18.62 | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 131.67/18.62 | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | Case 2:
% 131.67/18.62 | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | (1809) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 131.67/18.62 | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.67/18.62 | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 131.67/18.62 | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.67/18.62 | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 131.67/18.62 | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 131.67/18.62 | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.67/18.62 | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 131.67/18.62 | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 131.67/18.62 | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 131.67/18.62 | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 131.67/18.62 | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 131.67/18.62 | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 131.67/18.62 | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 131.67/18.62 | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 131.67/18.62 | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 131.67/18.62 | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 131.67/18.62 | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 131.67/18.62 | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 131.67/18.62 | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 131.67/18.62 | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 131.67/18.62 | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 131.67/18.62 | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 131.67/18.62 | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.67/18.62 | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.67/18.62 | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 131.67/18.62 | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 131.67/18.62 | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.67/18.62 | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 131.67/18.62 | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 131.67/18.62 | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 131.67/18.62 | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 131.67/18.62 | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 131.67/18.62 | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 131.67/18.62 | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 131.67/18.62 | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 131.67/18.62 | | | | | | | | | | | | | & $i(all_56_29))))
% 131.67/18.62 | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | BETA: splitting (1809) gives:
% 131.67/18.62 | | | | | | | | | | | | |
% 131.67/18.62 | | | | | | | | | | | | | Case 1:
% 131.67/18.62 | | | | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | | | | | (1810) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 131.67/18.63 | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 131.67/18.63 | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.67/18.63 | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 131.67/18.63 | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 131.67/18.63 | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 131.67/18.63 | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 131.67/18.63 | | | | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | | | | | ALPHA: (1810) implies:
% 131.67/18.63 | | | | | | | | | | | | | | (1811) op(e1, e1) = e2
% 131.67/18.63 | | | | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (1811), (function-axioms) are
% 131.67/18.63 | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 131.67/18.63 | | | | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | | | | Case 2:
% 131.67/18.63 | | | | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | | | | | (1812) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 131.67/18.63 | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 131.67/18.63 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 131.67/18.63 | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 131.67/18.63 | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 131.67/18.63 | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 131.67/18.63 | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 131.67/18.63 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 131.67/18.63 | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 131.67/18.63 | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 131.67/18.63 | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.67/18.63 | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.67/18.63 | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 131.67/18.63 | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 131.67/18.63 | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 131.67/18.63 | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.67/18.63 | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.67/18.63 | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 131.67/18.63 | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 131.67/18.63 | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.67/18.63 | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 131.67/18.63 | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 131.67/18.63 | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 131.67/18.63 | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 131.67/18.63 | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 131.67/18.63 | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 131.67/18.63 | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 131.67/18.63 | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 131.67/18.63 | | | | | | | | | | | | | | $i(all_56_29)))
% 131.67/18.63 | | | | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | | | | | ALPHA: (1812) implies:
% 131.67/18.63 | | | | | | | | | | | | | | (1813) op(e0, e0) = all_56_31
% 131.67/18.63 | | | | | | | | | | | | | | (1814) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 131.67/18.63 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.67/18.63 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.67/18.63 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.67/18.63 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 131.67/18.63 | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 131.67/18.63 | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 131.67/18.63 | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 131.67/18.63 | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 131.67/18.63 | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 131.67/18.63 | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 131.67/18.63 | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 131.67/18.63 | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 131.67/18.63 | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.67/18.63 | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.67/18.63 | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 131.67/18.63 | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 131.67/18.63 | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 131.67/18.63 | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 131.67/18.63 | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 131.67/18.63 | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 131.67/18.63 | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 131.67/18.63 | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 131.67/18.63 | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 131.67/18.63 | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 131.67/18.63 | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 131.67/18.63 | | | | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 131.67/18.63 | | | | | | | | | | | | | | all_56_31, e0, e0, simplifying with (1345), (1813)
% 131.67/18.63 | | | | | | | | | | | | | | gives:
% 131.67/18.63 | | | | | | | | | | | | | | (1815) all_56_31 = e2
% 131.67/18.63 | | | | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | | | | | BETA: splitting (1814) gives:
% 131.67/18.63 | | | | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | | | | | Case 1:
% 131.67/18.63 | | | | | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | | | | | | (1816) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 131.67/18.63 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.67/18.63 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.67/18.63 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.67/18.63 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 131.67/18.63 | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 131.67/18.63 | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 131.67/18.63 | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 131.67/18.63 | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 131.67/18.63 | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 131.67/18.63 | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 131.67/18.63 | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 131.67/18.63 | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27))
% 131.67/18.63 | | | | | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | | | | | | BETA: splitting (1816) gives:
% 131.67/18.63 | | | | | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | | | | | | Case 1:
% 131.67/18.63 | | | | | | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | | | | | | | (1817) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 131.67/18.63 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 131.67/18.63 | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.67/18.63 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.67/18.63 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 131.67/18.63 | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 131.67/18.63 | | | | | | | | | | | | | | | | $i(all_56_25)
% 131.67/18.63 | | | | | | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | | | | | | | ALPHA: (1817) implies:
% 131.67/18.63 | | | | | | | | | | | | | | | | (1818) all_56_31 = e3
% 131.67/18.63 | | | | | | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1815), (1818) are inconsistent by sub-proof
% 131.67/18.63 | | | | | | | | | | | | | | | | #532.
% 131.67/18.63 | | | | | | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | | | | | | Case 2:
% 131.67/18.63 | | | | | | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | | | | | | | (1819) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 131.67/18.63 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 131.67/18.63 | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.67/18.63 | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 131.67/18.63 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 131.67/18.63 | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 131.67/18.63 | | | | | | | | | | | | | | | | $i(all_56_27)
% 131.67/18.63 | | | | | | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | | | | | | | ALPHA: (1819) implies:
% 131.67/18.63 | | | | | | | | | | | | | | | | (1820) op(e0, e2) = e0
% 131.67/18.63 | | | | | | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | | | | | | | REF_CLOSE: (158), (1763), (1820), (function-axioms) are
% 131.67/18.63 | | | | | | | | | | | | | | | | inconsistent by sub-proof #545.
% 131.67/18.63 | | | | | | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | | | | | | End of split
% 131.67/18.63 | | | | | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | | | | | Case 2:
% 131.67/18.63 | | | | | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | | | | | | (1821) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 131.67/18.63 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 131.67/18.63 | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 131.67/18.63 | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 131.67/18.63 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.67/18.63 | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 131.67/18.63 | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 131.67/18.63 | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 131.67/18.63 | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 131.67/18.63 | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 131.67/18.63 | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 131.67/18.63 | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 131.67/18.63 | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 131.67/18.63 | | | | | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (1674), (1815), (1821),
% 131.67/18.63 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.67/18.63 | | | | | | | | | | | | | | | #467.
% 131.67/18.63 | | | | | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | | | | | End of split
% 131.67/18.63 | | | | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | | | | End of split
% 131.67/18.63 | | | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | | | End of split
% 131.67/18.63 | | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | | End of split
% 131.67/18.63 | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | End of split
% 131.67/18.63 | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | End of split
% 131.67/18.63 | | | | | | | | |
% 131.67/18.63 | | | | | | | | End of split
% 131.67/18.63 | | | | | | | |
% 131.67/18.63 | | | | | | | End of split
% 131.67/18.63 | | | | | | |
% 131.67/18.63 | | | | | | Case 2:
% 131.67/18.63 | | | | | | |
% 131.67/18.63 | | | | | | | (1822) all_16_2 = e2
% 131.67/18.63 | | | | | | | (1823) ( ~ (all_16_0 = e1) & op(e2, e3) = all_16_0 &
% 131.67/18.63 | | | | | | | $i(all_16_0)) | ( ~ (all_16_1 = e0) & op(e2, e2) =
% 131.67/18.63 | | | | | | | all_16_1 & $i(all_16_1))
% 131.67/18.63 | | | | | | |
% 131.67/18.63 | | | | | | | COMBINE_EQS: (327), (1822) imply:
% 131.67/18.63 | | | | | | | (1824) all_10_2 = e2
% 131.67/18.63 | | | | | | |
% 131.67/18.63 | | | | | | | REDUCE: (336), (1824) imply:
% 131.67/18.63 | | | | | | | (1825) ~ (all_52_1 = e2)
% 131.67/18.63 | | | | | | |
% 131.67/18.63 | | | | | | | REDUCE: (338), (1824) imply:
% 131.67/18.63 | | | | | | | (1826) ~ (all_52_2 = e2)
% 131.67/18.63 | | | | | | |
% 131.67/18.63 | | | | | | | REDUCE: (340), (1824) imply:
% 131.67/18.63 | | | | | | | (1827) ~ (all_52_3 = e2)
% 131.67/18.63 | | | | | | |
% 131.67/18.63 | | | | | | | REDUCE: (342), (1824) imply:
% 131.67/18.63 | | | | | | | (1828) ~ (all_52_4 = e2)
% 131.67/18.63 | | | | | | |
% 131.67/18.63 | | | | | | | REDUCE: (344), (1824) imply:
% 131.67/18.63 | | | | | | | (1829) ~ (all_52_8 = e2)
% 131.67/18.63 | | | | | | |
% 131.67/18.63 | | | | | | | REDUCE: (346), (1824) imply:
% 131.67/18.63 | | | | | | | (1830) ~ (all_52_12 = e2)
% 131.67/18.63 | | | | | | |
% 131.67/18.63 | | | | | | | BETA: splitting (236) gives:
% 131.67/18.63 | | | | | | |
% 131.67/18.63 | | | | | | | Case 1:
% 131.67/18.63 | | | | | | | |
% 131.67/18.63 | | | | | | | | (1831) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 &
% 131.67/18.63 | | | | | | | | op(e3, e2) = e2)
% 131.67/18.63 | | | | | | | |
% 131.67/18.63 | | | | | | | | BETA: splitting (1831) gives:
% 131.67/18.63 | | | | | | | |
% 131.67/18.63 | | | | | | | | Case 1:
% 131.67/18.63 | | | | | | | | |
% 131.67/18.63 | | | | | | | | | (1832) all_57_0 = e2 & op(e3, e3) = e2
% 131.67/18.63 | | | | | | | | |
% 131.67/18.63 | | | | | | | | | ALPHA: (1832) implies:
% 131.67/18.63 | | | | | | | | | (1833) all_57_0 = e2
% 131.67/18.63 | | | | | | | | | (1834) op(e3, e3) = e2
% 131.67/18.63 | | | | | | | | |
% 131.67/18.63 | | | | | | | | | BETA: splitting (61) gives:
% 131.67/18.63 | | | | | | | | |
% 131.67/18.63 | | | | | | | | | Case 1:
% 131.67/18.63 | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | (1835) ~ (all_20_2 = e2)
% 131.67/18.63 | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | REDUCE: (318), (1835) imply:
% 131.67/18.63 | | | | | | | | | | (1836) ~ (all_4_2 = e2)
% 131.67/18.63 | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | BETA: splitting (73) gives:
% 131.67/18.63 | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | Case 1:
% 131.67/18.63 | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | | (1837) ~ (all_28_2 = e3)
% 131.67/18.63 | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | | REDUCE: (316), (1837) imply:
% 131.67/18.63 | | | | | | | | | | | (1838) ~ (all_6_2 = e3)
% 131.67/18.63 | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | | BETA: splitting (76) gives:
% 131.67/18.63 | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | | Case 1:
% 131.67/18.63 | | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | | | (1839) ~ (all_30_2 = e0)
% 131.67/18.63 | | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | | | REDUCE: (309), (1839) imply:
% 131.67/18.63 | | | | | | | | | | | | (1840) ~ (all_8_2 = e0)
% 131.67/18.63 | | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | | | BETA: splitting (199) gives:
% 131.67/18.63 | | | | | | | | | | | |
% 131.67/18.63 | | | | | | | | | | | | Case 1:
% 131.67/18.63 | | | | | | | | | | | | |
% 131.93/18.63 | | | | | | | | | | | | | (1841) all_54_5 = e3
% 131.93/18.63 | | | | | | | | | | | | |
% 131.93/18.63 | | | | | | | | | | | | | COMBINE_EQS: (267), (1841) imply:
% 131.93/18.63 | | | | | | | | | | | | | (1842) all_8_2 = e3
% 131.93/18.63 | | | | | | | | | | | | |
% 131.93/18.63 | | | | | | | | | | | | | REDUCE: (376), (1842) imply:
% 131.93/18.63 | | | | | | | | | | | | | (1843) $false
% 131.93/18.63 | | | | | | | | | | | | |
% 131.93/18.63 | | | | | | | | | | | | | CLOSE: (1843) is inconsistent.
% 131.93/18.63 | | | | | | | | | | | | |
% 131.93/18.63 | | | | | | | | | | | | Case 2:
% 131.93/18.63 | | | | | | | | | | | | |
% 131.93/18.63 | | | | | | | | | | | | | (1844) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 131.93/18.63 | | | | | | | | | | | | |
% 131.93/18.63 | | | | | | | | | | | | | BETA: splitting (1844) gives:
% 131.93/18.63 | | | | | | | | | | | | |
% 131.93/18.63 | | | | | | | | | | | | | Case 1:
% 131.93/18.63 | | | | | | | | | | | | | |
% 131.93/18.63 | | | | | | | | | | | | | | (1845) all_54_5 = e2
% 131.93/18.63 | | | | | | | | | | | | | |
% 131.93/18.63 | | | | | | | | | | | | | | COMBINE_EQS: (267), (1845) imply:
% 131.93/18.63 | | | | | | | | | | | | | | (1846) all_8_2 = e2
% 131.93/18.63 | | | | | | | | | | | | | |
% 131.93/18.63 | | | | | | | | | | | | | | REDUCE: (356), (1846) imply:
% 131.93/18.63 | | | | | | | | | | | | | | (1847) ~ (all_52_9 = e2)
% 131.93/18.63 | | | | | | | | | | | | | |
% 131.93/18.63 | | | | | | | | | | | | | | REDUCE: (358), (1846) imply:
% 131.93/18.63 | | | | | | | | | | | | | | (1848) ~ (all_52_13 = e2)
% 131.93/18.63 | | | | | | | | | | | | | |
% 131.93/18.63 | | | | | | | | | | | | | | REDUCE: (42), (1846) imply:
% 131.93/18.63 | | | | | | | | | | | | | | (1849) op(e2, e2) = e2
% 131.93/18.63 | | | | | | | | | | | | | |
% 131.93/18.63 | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 131.93/18.63 | | | | | | | | | | | | | |
% 131.93/18.63 | | | | | | | | | | | | | | Case 1:
% 131.93/18.63 | | | | | | | | | | | | | | |
% 131.93/18.63 | | | | | | | | | | | | | | | (1850) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 131.93/18.63 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.93/18.63 | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 131.93/18.63 | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 131.93/18.63 | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 131.93/18.63 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 131.93/18.63 | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.93/18.63 | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 131.93/18.63 | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 131.93/18.63 | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 131.93/18.63 | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 131.93/18.63 | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 131.93/18.63 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 131.93/18.63 | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 131.93/18.63 | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 131.93/18.63 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 131.93/18.63 | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 131.93/18.63 | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 131.93/18.63 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.93/18.63 | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 131.93/18.63 | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 131.93/18.63 | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 131.93/18.63 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.93/18.63 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.93/18.63 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.93/18.63 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 131.93/18.63 | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.93/18.63 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 131.93/18.63 | | | | | | | | | | | | | | |
% 131.93/18.63 | | | | | | | | | | | | | | | BETA: splitting (1850) gives:
% 131.93/18.63 | | | | | | | | | | | | | | |
% 131.93/18.63 | | | | | | | | | | | | | | | Case 1:
% 131.93/18.63 | | | | | | | | | | | | | | | |
% 131.93/18.63 | | | | | | | | | | | | | | | | (1851) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 131.93/18.63 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.93/18.63 | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 131.93/18.63 | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 131.93/18.63 | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 131.93/18.63 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 131.93/18.63 | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.93/18.63 | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 131.93/18.63 | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 131.93/18.63 | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 131.93/18.63 | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 131.93/18.63 | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 131.93/18.63 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 131.93/18.63 | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 131.93/18.63 | | | | | | | | | | | | | | | |
% 131.93/18.63 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1834), (1849), (1851), (function-axioms) are
% 131.93/18.63 | | | | | | | | | | | | | | | | inconsistent by sub-proof #444.
% 131.93/18.63 | | | | | | | | | | | | | | | |
% 131.93/18.63 | | | | | | | | | | | | | | | Case 2:
% 131.93/18.63 | | | | | | | | | | | | | | | |
% 131.93/18.63 | | | | | | | | | | | | | | | | (1852) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 131.93/18.63 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 131.93/18.63 | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 131.93/18.63 | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 131.93/18.63 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.93/18.63 | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 131.93/18.63 | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 131.93/18.63 | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 131.93/18.63 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.93/18.63 | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.93/18.63 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.93/18.63 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 131.93/18.63 | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.93/18.63 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 131.93/18.63 | | | | | | | | | | | | | | | |
% 131.93/18.63 | | | | | | | | | | | | | | | | REF_CLOSE: (5), (167), (1825), (1834), (1852),
% 131.93/18.63 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.93/18.63 | | | | | | | | | | | | | | | | #443.
% 131.93/18.63 | | | | | | | | | | | | | | | |
% 131.93/18.63 | | | | | | | | | | | | | | | End of split
% 131.93/18.63 | | | | | | | | | | | | | | |
% 131.93/18.63 | | | | | | | | | | | | | | Case 2:
% 131.93/18.63 | | | | | | | | | | | | | | |
% 131.93/18.63 | | | | | | | | | | | | | | | (1853) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 131.93/18.63 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.93/18.63 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.93/18.63 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.93/18.63 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 131.93/18.63 | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.93/18.63 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 131.93/18.63 | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 131.93/18.63 | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 131.93/18.63 | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 131.93/18.63 | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 131.93/18.63 | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 131.93/18.63 | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 131.93/18.63 | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 131.93/18.63 | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 131.93/18.63 | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.93/18.63 | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 131.93/18.63 | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 131.93/18.63 | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 131.93/18.63 | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 131.93/18.63 | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 131.93/18.63 | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 131.93/18.63 | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 131.93/18.63 | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.93/18.63 | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 131.93/18.63 | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 131.93/18.63 | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 131.93/18.63 | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 131.93/18.63 | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 131.93/18.63 | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 131.93/18.63 | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 131.93/18.63 | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.93/18.63 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 131.93/18.63 | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 131.93/18.63 | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 131.93/18.63 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 131.93/18.63 | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 131.93/18.63 | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 131.93/18.63 | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.93/18.63 | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.93/18.63 | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 131.93/18.63 | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 131.93/18.63 | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 131.93/18.63 | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 131.93/18.63 | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 131.93/18.63 | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 131.93/18.63 | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 131.93/18.63 | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 131.93/18.63 | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 131.93/18.63 | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 131.93/18.63 | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 131.93/18.63 | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 131.93/18.63 | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 131.93/18.63 | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 131.93/18.63 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 131.93/18.63 | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 131.93/18.63 | | | | | | | | | | | | | | | & $i(all_56_29))))
% 131.93/18.63 | | | | | | | | | | | | | | |
% 131.93/18.63 | | | | | | | | | | | | | | | BETA: splitting (1853) gives:
% 131.93/18.63 | | | | | | | | | | | | | | |
% 131.93/18.63 | | | | | | | | | | | | | | | Case 1:
% 131.93/18.63 | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | (1854) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 131.93/18.64 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.93/18.64 | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.93/18.64 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.93/18.64 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 131.93/18.64 | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 131.93/18.64 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 131.93/18.64 | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 131.93/18.64 | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 131.93/18.64 | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 131.93/18.64 | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 131.93/18.64 | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 131.93/18.64 | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 131.93/18.64 | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 131.93/18.64 | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | REF_CLOSE: (39), (165), (1838), (1847), (1854),
% 131.93/18.64 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.93/18.64 | | | | | | | | | | | | | | | | #769.
% 131.93/18.64 | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | Case 2:
% 131.93/18.64 | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | (1855) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 131.93/18.64 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 131.93/18.64 | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 131.93/18.64 | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 131.93/18.64 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.93/18.64 | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 131.93/18.64 | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 131.93/18.64 | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 131.93/18.64 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.93/18.64 | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 131.93/18.64 | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.93/18.64 | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 131.93/18.64 | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 131.93/18.64 | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.93/18.64 | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 131.93/18.64 | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 131.93/18.64 | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 131.93/18.64 | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 131.93/18.64 | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 131.93/18.64 | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 131.93/18.64 | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 131.93/18.64 | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 131.93/18.64 | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 131.93/18.64 | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 131.93/18.64 | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 131.93/18.64 | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 131.93/18.64 | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 131.93/18.64 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 131.93/18.64 | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 131.93/18.64 | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 131.93/18.64 | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.93/18.64 | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.93/18.64 | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 131.93/18.64 | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 131.93/18.64 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.93/18.64 | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 131.93/18.64 | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 131.93/18.64 | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 131.93/18.64 | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 131.93/18.64 | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 131.93/18.64 | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 131.93/18.64 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 131.93/18.64 | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 131.93/18.64 | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 131.93/18.64 | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | BETA: splitting (1855) gives:
% 131.93/18.64 | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | Case 1:
% 131.93/18.64 | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | (1856) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 131.93/18.64 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 131.93/18.64 | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 131.93/18.64 | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 131.93/18.64 | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 131.93/18.64 | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 131.93/18.64 | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 131.93/18.64 | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | ALPHA: (1856) implies:
% 131.93/18.64 | | | | | | | | | | | | | | | | | (1857) op(e2, e0) = e2
% 131.93/18.64 | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (1848), (1857), (function-axioms) are
% 131.93/18.64 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 131.93/18.64 | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | Case 2:
% 131.93/18.64 | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | (1858) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 131.93/18.64 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 131.93/18.64 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 131.93/18.64 | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.93/18.64 | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 131.93/18.64 | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 131.93/18.64 | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 131.93/18.64 | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 131.93/18.64 | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 131.93/18.64 | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 131.93/18.64 | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 131.93/18.64 | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 131.93/18.64 | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 131.93/18.64 | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 131.93/18.64 | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 131.93/18.64 | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 131.93/18.64 | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 131.93/18.64 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 131.93/18.64 | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 131.93/18.64 | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 131.93/18.64 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 131.93/18.64 | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 131.93/18.64 | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 131.93/18.64 | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.93/18.64 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.93/18.64 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 131.93/18.64 | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 131.93/18.64 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.93/18.64 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 131.93/18.64 | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 131.93/18.64 | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 131.93/18.64 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 131.93/18.64 | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 131.93/18.64 | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 131.93/18.64 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 131.93/18.64 | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 131.93/18.64 | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 131.93/18.64 | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | BETA: splitting (1858) gives:
% 131.93/18.64 | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | Case 1:
% 131.93/18.64 | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | (1859) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 131.93/18.64 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 131.93/18.64 | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.93/18.64 | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 131.93/18.64 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 131.93/18.64 | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 131.93/18.64 | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 131.93/18.64 | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | ALPHA: (1859) implies:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | (1860) op(e1, e1) = e2
% 131.93/18.64 | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (1860), (function-axioms) are
% 131.93/18.64 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 131.93/18.64 | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | Case 2:
% 131.93/18.64 | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | (1861) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 131.93/18.64 | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 131.93/18.64 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 131.93/18.64 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 131.93/18.64 | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 131.93/18.64 | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 131.93/18.64 | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 131.93/18.64 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 131.93/18.64 | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 131.93/18.64 | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 131.93/18.64 | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.93/18.64 | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 131.93/18.64 | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 131.93/18.64 | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 131.93/18.64 | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 131.93/18.64 | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.93/18.64 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.93/18.64 | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 131.93/18.64 | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 131.93/18.64 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.93/18.64 | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 131.93/18.64 | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 131.93/18.64 | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 131.93/18.64 | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 131.93/18.64 | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 131.93/18.64 | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 131.93/18.64 | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 131.93/18.64 | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 131.93/18.64 | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | ALPHA: (1861) implies:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | (1862) op(e0, e0) = all_56_31
% 131.93/18.64 | | | | | | | | | | | | | | | | | | (1863) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 131.93/18.64 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.93/18.64 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.93/18.64 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.93/18.64 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 131.93/18.64 | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 131.93/18.64 | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 131.93/18.64 | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 131.93/18.64 | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 131.93/18.64 | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 131.93/18.64 | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 131.93/18.64 | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 131.93/18.64 | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 131.93/18.64 | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 131.93/18.64 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 131.93/18.64 | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 131.93/18.64 | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 131.93/18.64 | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 131.93/18.64 | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 131.93/18.64 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 131.93/18.64 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 131.93/18.64 | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 131.93/18.64 | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 131.93/18.64 | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 131.93/18.64 | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 131.93/18.64 | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 131.93/18.64 | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | Case 1:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | (1864) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 131.93/18.64 | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (1829), (1847), (1864),
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | #441.
% 131.93/18.64 | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | Case 2:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | (1865) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 131.93/18.64 | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | BETA: splitting (1865) gives:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | Case 1:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | (1866) all_57_8 = e2 & op(e1, e1) = e2
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | ALPHA: (1866) implies:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | (1867) op(e1, e1) = e2
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (1867), (function-axioms) are
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | Case 2:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | (1868) all_57_14 = e2 & op(e0, e1) = e2
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | ALPHA: (1868) implies:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | (1869) all_57_14 = e2
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | (1870) op(e0, e1) = e2
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | (1871) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (1830), (1848), (1871),
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | #440.
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | (1872) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1872) gives:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | (1873) all_57_11 = e2 & op(e1, e0) = e2
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1873) implies:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | (1874) all_57_11 = e2
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | (1875) op(e1, e0) = e2
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | (1876) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1876) gives:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | (1877) all_57_2 = e2 & op(e2, e3) = e2
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1877) implies:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | (1878) op(e2, e3) = e2
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (1825), (1878), (function-axioms) are
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #779.
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | (1879) all_57_3 = e2 & op(e2, e2) = e2
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1879) implies:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | (1880) all_57_3 = e2
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | all_56_31, e0, e0, simplifying with (36), (1862)
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | (1881) all_56_31 = all_4_2
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | e2, e1, e0, simplifying with (157), (1870) gives:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | (1882) all_52_11 = e2
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, e1, simplifying with (160), (1875) gives:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | (1883) all_52_14 = e2
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (1883) imply:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | (1884) ~ (all_6_2 = e2)
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (370), (1883) imply:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | (1885) ~ (all_4_2 = e2)
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1863) gives:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | (1886) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27))
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1886) gives:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (1887) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1887) implies:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (1888) all_56_31 = e3
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (1889) op(e0, e3) = e0
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (1890) op(e3, e3) = all_56_1
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1881), (1888) imply:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (1891) all_4_2 = e3
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1891) implies:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (1892) all_4_2 = e3
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (1892) imply:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (1893) all_44_2 = e3
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (1892) imply:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (1894) ~ (all_52_7 = e3)
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (1892) imply:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (1895) ~ (all_52_13 = e3)
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (1892) imply:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (1896) op(e0, e0) = e3
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1897) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1897) gives:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1898) all_57_9 = e3 & op(e3, e0) = e3
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1898) implies:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1899) all_57_9 = e3
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (208), (212), (1862),
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1863), (1874), (1875), (1896), (1899),
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #439.
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1900) all_57_10 = e3 & op(e2, e0) = e3
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (1895), (1900), (function-axioms) are
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749.
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1901) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1901) gives:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1902) all_57_11 = e3 & op(e1, e0) = e3
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1874), (1902) are inconsistent by sub-proof
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #723.
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1903) all_57_15 = e3 & op(e0, e0) = e3
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1903) implies:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1904) all_57_15 = e3
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1905) ~ (all_44_2 = e3)
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1893), (1905) imply:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1906) $false
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1906) is inconsistent.
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1907) ( ~ (all_44_0 = e1) & op(e3, e0) = all_44_0 &
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_44_0)) | ( ~ (all_44_1 = e2) & op(e3, e3)
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_44_1 & $i(all_44_1))
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1908) ~ (all_46_2 = e0)
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (295), (1908) imply:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1909) ~ (all_6_2 = e0)
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1910) all_54_10 = e3
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (1838), (1910) are inconsistent by
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #742.
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1911) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1911) gives:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1912) all_54_10 = e2
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (372), (1912) are inconsistent by sub-proof
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #741.
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1913) ~ (all_54_10 = e2)
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1914) all_54_10 = e1 | all_54_10 = e0
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1914) gives:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1915) all_54_10 = e1
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (1915) imply:
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1916) all_6_2 = e1
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1916) implies:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1917) all_6_2 = e1
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (295), (1917) imply:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1918) all_46_2 = e1
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (348), (1917) imply:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1919) ~ (all_52_2 = e1)
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (1917) imply:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1920) ~ (e2 = e1)
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (1917) imply:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1921) op(e1, e1) = e1
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e0,
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (159), (1889) gives:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1922) all_52_3 = e0
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_56_1,
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (1834), (1890) gives:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1923) all_56_1 = e2
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (1922) imply:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1924) ~ (all_52_2 = e0)
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1827), (1922) imply:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1925) ~ (e2 = e0)
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1926) all_54_8 = e3
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (1926) imply:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1927) all_52_2 = e3
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1927) implies:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1928) all_52_2 = e3
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (1928) imply:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1929) ~ (all_52_6 = e3)
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1929) implies:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1930) ~ (all_52_6 = e3)
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1931) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1931) gives:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1932) all_57_1 = e3 & op(e3, e2) = e3
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1932) implies:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1933) all_57_1 = e3
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1907) gives:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1934) ~ (all_44_0 = e1) & op(e3, e0) = all_44_0 &
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_44_0)
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1934) implies:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1935) ~ (all_44_0 = e1)
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1936) op(e3, e0) = all_44_0
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1937) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1937) gives:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1938) all_57_0 = e1 & op(e3, e3) = e1
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1938) implies:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1939) op(e3, e3) = e1
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1834), (1939), (function-axioms) are
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743.
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1940) all_57_1 = e1 & op(e3, e2) = e1
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1940) implies:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1941) all_57_1 = e1
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1933), (1941) imply:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1942) e3 = e1
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (1942) imply:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1943) $false
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1943) is inconsistent.
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1944) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1944) gives:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1945) all_57_4 = e1 & op(e3, e1) = e1
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1945) implies:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1946) all_57_4 = e1
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1947) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1947) gives:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1948) all_57_4 = e0 & op(e3, e1) = e0
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1948) implies:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1949) all_57_4 = e0
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1946), (1949) imply:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1950) e1 = e0
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1950) implies:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1951) e1 = e0
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1918), (1951) imply:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1952) all_46_2 = e0
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (100), (1870), (1896), (1952), (function-axioms)
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #570.
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1953) all_57_5 = e0 & op(e2, e1) = e0
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1953) implies:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1954) all_57_5 = e0
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1955) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1955) gives:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1956) all_57_4 = e3 & op(e3, e1) = e3
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1946), (1956) are inconsistent by sub-proof
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #438.
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1957) all_57_5 = e3 & op(e2, e1) = e3
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1957) implies:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1958) all_57_5 = e3
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1954), (1958) imply:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1959) e3 = e0
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1959) implies:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1960) e3 = e0
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (1960) imply:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1961) $false
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1961) is inconsistent.
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1962) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1962) gives:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1963) all_57_8 = e3 & op(e1, e1) = e3
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1963) implies:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1964) op(e1, e1) = e3
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (1921), (1964), (function-axioms) are
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #662.
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1965) all_57_14 = e3 & op(e0, e1) = e3
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1965) implies:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1966) all_57_14 = e3
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1869), (1966) imply:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1967) e3 = e2
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1904), (1967) imply:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1968) all_57_15 = e2
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (208), (209),
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (1869), (1894), (1968), (function-axioms)
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #433.
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1969) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1969) gives:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1970) all_57_8 = e0 & op(e1, e1) = e0
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1970) implies:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1971) op(e1, e1) = e0
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1921), (1971), (function-axioms) are
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #721.
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1972) all_57_14 = e0 & op(e0, e1) = e0
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1972) implies:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1973) op(e0, e1) = e0
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1870), (1973), (function-axioms) are
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #660.
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1974) all_57_9 = e1 & op(e3, e0) = e1
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1974) implies:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1975) op(e3, e0) = e1
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1935), (1936), (1975), (function-axioms) are
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #432.
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1976) ~ (all_44_1 = e2) & op(e3, e3) = all_44_1 &
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_44_1)
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1834), (1976), (function-axioms) are inconsistent
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #431.
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1977) all_57_3 = e3 & op(e2, e2) = e3
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1977) implies:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1978) all_57_3 = e3
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1880), (1978) imply:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1979) e3 = e2
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1979) implies:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1980) e3 = e2
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1904), (1980) imply:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1981) all_57_15 = e2
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (208), (209),
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (1869), (1894), (1981), (function-axioms)
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #433.
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1982) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (1894), (1930), (1982),
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #555.
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1983) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (1826), (1919), (1924), (1983) are
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #429.
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1984) all_54_10 = e0
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (100), (295), (334), (1870), (1896), (1984),
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #569.
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1985) ( ~ (all_46_0 = e2) & op(e0, e1) = all_46_0 &
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_46_0)) | ( ~ (all_46_1 = e3) & op(e0, e0)
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_46_1 & $i(all_46_1))
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1870), (1896), (1985), (function-axioms) are
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #757.
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | (1986) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27)
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1986) implies:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | (1987) ~ (all_56_11 = e2)
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | (1988) op(e2, e2) = all_56_11
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1849), (1987), (1988), (function-axioms) are
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #531.
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | (1989) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (1870), (1875), (1989),
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | #428.
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | (1990) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (165), (1847), (1848), (1990),
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | #625.
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | End of split
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | (1991) all_57_15 = e2 & op(e0, e0) = e2
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1991) implies:
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | (1992) op(e0, e0) = e2
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (1836), (1862), (1992), (function-axioms)
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #427.
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | End of split
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | | End of split
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | | End of split
% 131.93/18.65 | | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | | End of split
% 131.93/18.65 | | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | | End of split
% 131.93/18.65 | | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | | End of split
% 131.93/18.65 | | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | | End of split
% 131.93/18.65 | | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | End of split
% 131.93/18.65 | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | Case 2:
% 131.93/18.65 | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | (1993) all_54_5 = e1 | all_54_5 = e0
% 131.93/18.65 | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | REF_CLOSE: (267), (373), (1840), (1993) are inconsistent by
% 131.93/18.65 | | | | | | | | | | | | | | sub-proof #624.
% 131.93/18.65 | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | End of split
% 131.93/18.65 | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | End of split
% 131.93/18.65 | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | Case 2:
% 131.93/18.65 | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | (1994) all_30_2 = e0
% 131.93/18.65 | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | COMBINE_EQS: (309), (1994) imply:
% 131.93/18.65 | | | | | | | | | | | | (1995) all_8_2 = e0
% 131.93/18.65 | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | COMBINE_EQS: (301), (1995) imply:
% 131.93/18.65 | | | | | | | | | | | | (1996) all_42_2 = e0
% 131.93/18.65 | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | REDUCE: (347), (1995) imply:
% 131.93/18.65 | | | | | | | | | | | | (1997) ~ (all_52_1 = e0)
% 131.93/18.65 | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | REDUCE: (350), (1995) imply:
% 131.93/18.65 | | | | | | | | | | | | (1998) ~ (all_52_4 = e0)
% 131.93/18.65 | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | REDUCE: (352), (1995) imply:
% 131.93/18.65 | | | | | | | | | | | | (1999) ~ (all_52_6 = e0)
% 131.93/18.65 | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | REDUCE: (354), (1995) imply:
% 131.93/18.65 | | | | | | | | | | | | (2000) ~ (all_52_7 = e0)
% 131.93/18.65 | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | REDUCE: (373), (1995) imply:
% 131.93/18.65 | | | | | | | | | | | | (2001) ~ (e1 = e0)
% 131.93/18.65 | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | REDUCE: (42), (1995) imply:
% 131.93/18.65 | | | | | | | | | | | | (2002) op(e2, e2) = e0
% 131.93/18.65 | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | BETA: splitting (1823) gives:
% 131.93/18.65 | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | Case 1:
% 131.93/18.65 | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | (2003) ~ (all_16_0 = e1) & op(e2, e3) = all_16_0 &
% 131.93/18.65 | | | | | | | | | | | | | $i(all_16_0)
% 131.93/18.65 | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | ALPHA: (2003) implies:
% 131.93/18.65 | | | | | | | | | | | | | (2004) ~ (all_16_0 = e1)
% 131.93/18.65 | | | | | | | | | | | | | (2005) op(e2, e3) = all_16_0
% 131.93/18.65 | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | BETA: splitting (227) gives:
% 131.93/18.65 | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | Case 1:
% 131.93/18.65 | | | | | | | | | | | | | |
% 131.93/18.65 | | | | | | | | | | | | | | (2006) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 131.93/18.65 | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 131.93/18.65 | | | | | | | | | | | | | |
% 131.93/18.66 | | | | | | | | | | | | | | BETA: splitting (2006) gives:
% 131.93/18.66 | | | | | | | | | | | | | |
% 131.93/18.66 | | | | | | | | | | | | | | Case 1:
% 131.93/18.66 | | | | | | | | | | | | | | |
% 131.93/18.66 | | | | | | | | | | | | | | | (2007) all_57_1 = e0 & op(e3, e2) = e0
% 131.93/18.66 | | | | | | | | | | | | | | |
% 131.93/18.66 | | | | | | | | | | | | | | | REF_CLOSE: (170), (1998), (2007), (function-axioms) are
% 131.93/18.66 | | | | | | | | | | | | | | | inconsistent by sub-proof #693.
% 131.93/18.66 | | | | | | | | | | | | | | |
% 131.93/18.66 | | | | | | | | | | | | | | Case 2:
% 131.93/18.66 | | | | | | | | | | | | | | |
% 131.93/18.66 | | | | | | | | | | | | | | | (2008) all_57_3 = e0 & op(e2, e2) = e0
% 131.93/18.66 | | | | | | | | | | | | | | |
% 131.93/18.66 | | | | | | | | | | | | | | | ALPHA: (2008) implies:
% 131.93/18.66 | | | | | | | | | | | | | | | (2009) all_57_3 = e0
% 131.93/18.66 | | | | | | | | | | | | | | |
% 131.93/18.66 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 131.93/18.66 | | | | | | | | | | | | | | | all_16_0, e3, e2, simplifying with (167), (2005)
% 131.93/18.66 | | | | | | | | | | | | | | | gives:
% 131.93/18.66 | | | | | | | | | | | | | | | (2010) all_52_1 = all_16_0
% 131.93/18.66 | | | | | | | | | | | | | | |
% 131.93/18.66 | | | | | | | | | | | | | | | COMBINE_EQS: (268), (2010) imply:
% 131.93/18.66 | | | | | | | | | | | | | | | (2011) all_54_4 = all_16_0
% 131.93/18.66 | | | | | | | | | | | | | | |
% 131.93/18.66 | | | | | | | | | | | | | | | REDUCE: (149), (2010) imply:
% 131.93/18.66 | | | | | | | | | | | | | | | (2012) ~ (all_52_2 = all_16_0)
% 131.93/18.66 | | | | | | | | | | | | | | |
% 131.93/18.66 | | | | | | | | | | | | | | | SIMP: (2012) implies:
% 131.93/18.66 | | | | | | | | | | | | | | | (2013) ~ (all_52_2 = all_16_0)
% 131.93/18.66 | | | | | | | | | | | | | | |
% 131.93/18.66 | | | | | | | | | | | | | | | REDUCE: (148), (2010) imply:
% 131.93/18.66 | | | | | | | | | | | | | | | (2014) ~ (all_52_3 = all_16_0)
% 131.93/18.66 | | | | | | | | | | | | | | |
% 131.93/18.66 | | | | | | | | | | | | | | | SIMP: (2014) implies:
% 131.93/18.66 | | | | | | | | | | | | | | | (2015) ~ (all_52_3 = all_16_0)
% 131.93/18.66 | | | | | | | | | | | | | | |
% 131.93/18.66 | | | | | | | | | | | | | | | REDUCE: (146), (2010) imply:
% 131.93/18.66 | | | | | | | | | | | | | | | (2016) ~ (all_52_9 = all_16_0)
% 131.93/18.66 | | | | | | | | | | | | | | |
% 131.93/18.66 | | | | | | | | | | | | | | | SIMP: (2016) implies:
% 131.93/18.66 | | | | | | | | | | | | | | | (2017) ~ (all_52_9 = all_16_0)
% 131.93/18.66 | | | | | | | | | | | | | | |
% 131.93/18.66 | | | | | | | | | | | | | | | REDUCE: (145), (2010) imply:
% 131.93/18.66 | | | | | | | | | | | | | | | (2018) ~ (all_52_13 = all_16_0)
% 131.93/18.66 | | | | | | | | | | | | | | |
% 131.93/18.66 | | | | | | | | | | | | | | | SIMP: (2018) implies:
% 131.93/18.66 | | | | | | | | | | | | | | | (2019) ~ (all_52_13 = all_16_0)
% 131.93/18.66 | | | | | | | | | | | | | | |
% 131.93/18.66 | | | | | | | | | | | | | | | REDUCE: (1825), (2010) imply:
% 131.93/18.66 | | | | | | | | | | | | | | | (2020) ~ (all_16_0 = e2)
% 131.93/18.66 | | | | | | | | | | | | | | |
% 131.93/18.66 | | | | | | | | | | | | | | | REDUCE: (1997), (2010) imply:
% 131.93/18.66 | | | | | | | | | | | | | | | (2021) ~ (all_16_0 = e0)
% 131.93/18.66 | | | | | | | | | | | | | | |
% 131.93/18.66 | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 131.93/18.66 | | | | | | | | | | | | | | |
% 131.93/18.66 | | | | | | | | | | | | | | | Case 1:
% 131.93/18.66 | | | | | | | | | | | | | | | |
% 131.93/18.66 | | | | | | | | | | | | | | | | (2022) all_54_4 = e3
% 131.93/18.66 | | | | | | | | | | | | | | | |
% 131.93/18.66 | | | | | | | | | | | | | | | | COMBINE_EQS: (2011), (2022) imply:
% 131.93/18.66 | | | | | | | | | | | | | | | | (2023) all_16_0 = e3
% 131.93/18.66 | | | | | | | | | | | | | | | |
% 131.93/18.66 | | | | | | | | | | | | | | | | REDUCE: (2013), (2023) imply:
% 131.93/18.66 | | | | | | | | | | | | | | | | (2024) ~ (all_52_2 = e3)
% 131.93/18.66 | | | | | | | | | | | | | | | |
% 131.93/18.66 | | | | | | | | | | | | | | | | REDUCE: (2015), (2023) imply:
% 131.93/18.66 | | | | | | | | | | | | | | | | (2025) ~ (all_52_3 = e3)
% 131.93/18.66 | | | | | | | | | | | | | | | |
% 131.93/18.66 | | | | | | | | | | | | | | | | REDUCE: (2017), (2023) imply:
% 131.93/18.66 | | | | | | | | | | | | | | | | (2026) ~ (all_52_9 = e3)
% 131.93/18.66 | | | | | | | | | | | | | | | |
% 131.93/18.66 | | | | | | | | | | | | | | | | REDUCE: (2019), (2023) imply:
% 131.93/18.66 | | | | | | | | | | | | | | | | (2027) ~ (all_52_13 = e3)
% 131.93/18.66 | | | | | | | | | | | | | | | |
% 131.93/18.66 | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 131.93/18.66 | | | | | | | | | | | | | | | |
% 131.93/18.66 | | | | | | | | | | | | | | | | Case 1:
% 131.93/18.66 | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | (2028) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 132.03/18.66 | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 132.03/18.66 | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | BETA: splitting (2028) gives:
% 132.03/18.66 | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.66 | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | (2029) all_57_2 = e3 & op(e2, e3) = e3
% 132.03/18.66 | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | ALPHA: (2029) implies:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | (2030) all_57_2 = e3
% 132.03/18.66 | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 132.03/18.66 | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | (2031) ~ (all_34_2 = e3)
% 132.03/18.66 | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | REDUCE: (307), (2031) imply:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | (2032) ~ (all_4_2 = e3)
% 132.03/18.66 | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | (2033) all_54_15 = e3
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (2032), (2033) are inconsistent by
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | sub-proof #601.
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | (2034) ~ (all_54_15 = e3)
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | (2035) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2035) gives:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | (2036) all_54_15 = e2
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (1836), (2036) are inconsistent by
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | sub-proof #748.
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | (2037) ~ (all_54_15 = e2)
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | (2038) all_54_15 = e1 | all_54_15 = e0
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2038) gives:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | (2039) all_54_15 = e1
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (371), (2039) are inconsistent by sub-proof
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | #747.
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | (2040) all_54_15 = e0
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (2040) imply:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | (2041) all_4_2 = e0
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | SIMP: (2041) implies:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | (2042) all_4_2 = e0
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (349), (2042) imply:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | (2043) ~ (all_52_3 = e0)
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (2042) imply:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | (2044) ~ (all_52_12 = e0)
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2032), (2042) imply:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | (2045) ~ (e3 = e0)
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1836), (2042) imply:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | (2046) ~ (e2 = e0)
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (2042) imply:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | (2047) op(e0, e0) = e0
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | (2048) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (1834), (2030), (2048),
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | #426.
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | (2049) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2049) gives:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | (2050) all_57_6 = e0 & op(e1, e3) = e0
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2050) implies:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | (2051) all_57_6 = e0
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | (2052) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2052) gives:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | (2053) all_57_0 = e1 & op(e3, e3) = e1
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2053) implies:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | (2054) op(e3, e3) = e1
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (39), (168), (169), (170),
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | (206), (232), (372), (1838), (1998), (2002),
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | (2044), (2047), (2054), (function-axioms) are
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #595.
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | (2055) all_57_2 = e1 & op(e2, e3) = e1
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2004), (2005), (2055), (function-axioms) are
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #425.
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | (2056) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2056) gives:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | (2057) all_57_6 = e1 & op(e1, e3) = e1
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (144), (163), (192), (248), (1827), (2025),
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | (2043), (2057), (function-axioms) are inconsistent
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #422.
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | (2058) all_57_12 = e1 & op(e0, e3) = e1
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2058) implies:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | (2059) all_57_12 = e1
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2060) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2060) gives:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2061) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2061) gives:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2062) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2062) implies:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2063) op(e3, e2) = e3
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2064) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (170), (1834), (1998), (2064),
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #421.
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2065) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2065) gives:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2066) all_57_4 = e0 & op(e3, e1) = e0
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2066) implies:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2067) all_57_4 = e0
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2068) op(e3, e1) = e0
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2069) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (165), (169), (2026), (2068), (2069),
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #420.
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2070) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2070) gives:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2071) all_57_8 = e3 & op(e1, e1) = e3
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2071) implies:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2072) op(e1, e1) = e3
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (1838), (2072), (function-axioms) are
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #771.
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2073) all_57_14 = e3 & op(e0, e1) = e3
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2073) implies:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2074) all_57_14 = e3
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2075) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2075) gives:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2076) all_57_4 = e2 & op(e3, e1) = e2
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (1829), (2076), (function-axioms) are
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #442.
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2077) all_57_5 = e2 & op(e2, e1) = e2
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2077) implies:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2078) all_57_5 = e2
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2079) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2079) gives:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2080) all_57_4 = e1 & op(e3, e1) = e1
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2067), (2080) are inconsistent by sub-proof
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #419.
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2081) all_57_5 = e1 & op(e2, e1) = e1
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2081) implies:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2082) all_57_5 = e1
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2078), (2082) are inconsistent by sub-proof
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #418.
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2083) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2083) gives:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2084) all_57_8 = e1 & op(e1, e1) = e1
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2084) implies:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2085) op(e1, e1) = e1
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2086) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2086) gives:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2087) all_57_12 = e2 & op(e0, e3) = e2
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2087) implies:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2088) all_57_12 = e2
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (233), (1833), (2030), (2051),
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2088) are inconsistent by sub-proof #416.
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2089) all_57_13 = e2 & op(e0, e2) = e2
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2089) implies:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2090) all_57_13 = e2
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2091) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2002), (2004), (2005), (2091),
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #415.
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2092) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2092) gives:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2093) all_57_5 = e1 & op(e2, e1) = e1
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2093) implies:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2094) all_57_5 = e1
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2078), (2094) are inconsistent by sub-proof
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #418.
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2095) all_57_10 = e1 & op(e2, e0) = e1
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2095) implies:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2096) all_57_10 = e1
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2097) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2097) gives:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2098) all_57_9 = e2 & op(e3, e0) = e2
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (1830), (2098), (function-axioms) are
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #460.
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2099) all_57_10 = e2 & op(e2, e0) = e2
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2099) implies:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2100) all_57_10 = e2
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2096), (2100) are inconsistent by sub-proof
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #414.
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2101) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2101) gives:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2102) all_57_11 = e2 & op(e1, e0) = e2
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2102) implies:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2103) all_57_11 = e2
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2104) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2104) gives:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2105) all_57_6 = e3 & op(e1, e3) = e3
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (2024), (2105), (function-axioms) are
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #761.
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2106) all_57_7 = e3 & op(e1, e2) = e3
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2106) implies:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2107) all_57_7 = e3
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2108) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2108) gives:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2109) all_57_1 = e1 & op(e3, e2) = e1
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2109) implies:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2110) op(e3, e2) = e1
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2063), (2110), (function-axioms) are
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #413.
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2111) all_57_3 = e1 & op(e2, e2) = e1
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2111) implies:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2112) op(e2, e2) = e1
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2002), (2112), (function-axioms) are
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675.
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2113) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2113) gives:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2114) all_57_7 = e1 & op(e1, e2) = e1
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2114) implies:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2115) all_57_7 = e1
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2107), (2115) imply:
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2116) e3 = e1
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2116) implies:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2117) e3 = e1
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2074), (2117) imply:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2118) all_57_14 = e1
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (39), (221), (222),
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (1838), (2067), (2118), (function-axioms)
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #558.
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2119) all_57_13 = e1 & op(e0, e2) = e1
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2119) implies:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2120) all_57_13 = e1
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2090), (2120) are inconsistent by sub-proof
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #567.
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2121) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2121) gives:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2122) all_57_8 = e3 & op(e1, e1) = e3
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2122) implies:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2123) op(e1, e1) = e3
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (2085), (2123), (function-axioms) are
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #662.
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2124) all_57_11 = e3 & op(e1, e0) = e3
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2124) implies:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2125) all_57_11 = e3
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2103), (2125) imply:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2126) e3 = e2
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2126) implies:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2127) e3 = e2
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2074), (2127) imply:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2128) all_57_14 = e2
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (208), (209), (211),
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2090), (2128) are inconsistent by sub-proof #401.
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2129) all_57_15 = e2 & op(e0, e0) = e2
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2129) implies:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2130) all_57_15 = e2
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (208), (2059), (2074), (2090),
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2130) are inconsistent by sub-proof #398.
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2131) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2131) gives:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2132) all_57_14 = e2 & op(e0, e1) = e2
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2132) implies:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2133) all_57_14 = e2
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2074), (2133) are inconsistent by sub-proof
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #407.
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2134) all_57_15 = e2 & op(e0, e0) = e2
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2134) implies:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2135) op(e0, e0) = e2
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2047), (2135), (function-axioms) are
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #714.
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2136) all_57_14 = e1 & op(e0, e1) = e1
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2136) implies:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2137) all_57_14 = e1
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (39), (221), (222),
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (1838), (2067), (2137), (function-axioms)
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #558.
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2138) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2138) gives:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2139) all_57_8 = e2 & op(e1, e1) = e2
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2139) implies:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2140) op(e1, e1) = e2
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (2140), (function-axioms) are
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2141) all_57_14 = e2 & op(e0, e1) = e2
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2074), (2141) are inconsistent by sub-proof
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #397.
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2142) all_57_9 = e0 & op(e3, e0) = e0
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (2044), (2142), (function-axioms) are
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #618.
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2143) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2143) implies:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2144) op(e3, e3) = e1
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (235), (237),
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2059), (2144), (function-axioms) are inconsistent
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #583.
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2145) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2145) gives:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2146) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3,
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2146) implies:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2147) op(e3, e3) = e0
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1834), (2147), (function-axioms) are
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495.
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2148) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2,
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2148) implies:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2149) op(e2, e2) = e3
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2002), (2149), (function-axioms) are
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641.
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2150) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2150) gives:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2151) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (1838), (2002), (2151),
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #621.
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2152) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (39), (372), (2047), (2152),
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #596.
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | (2153) all_57_12 = e0 & op(e0, e3) = e0
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2153) implies:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | (2154) all_57_12 = e0
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | (2155) op(e0, e3) = e0
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | (2156) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2156) gives:
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (2157) all_57_0 = e1 & op(e3, e3) = e1
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2157) implies:
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (2158) op(e3, e3) = e1
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2159) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2159) gives:
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2160) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2160) gives:
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2161) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1834), (2158), (function-axioms) are
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743.
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2162) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2162) implies:
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2163) op(e3, e1) = e3
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (168), (169), (170), (232), (1998),
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2044), (2158), (2163), (function-axioms) are
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #599.
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2164) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2164) gives:
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2165) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3,
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2165) implies:
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2166) op(e0, e3) = all_56_7
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (2043), (2155), (2166), (function-axioms)
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #620.
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2167) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2,
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2167) implies:
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2168) op(e2, e2) = e3
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2002), (2168), (function-axioms) are
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641.
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2169) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2169) gives:
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2170) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (1838), (2002), (2170),
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #621.
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2171) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2171) gives:
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2172) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2172) implies:
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2173) op(e0, e3) = all_56_7
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (2043), (2155), (2173), (function-axioms)
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #620.
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2174) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (39), (372), (2047), (2174),
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #709.
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | (2175) all_57_2 = e1 & op(e2, e3) = e1
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2004), (2005), (2175), (function-axioms) are
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #425.
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | (2176) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2176) gives:
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | (2177) all_57_6 = e1 & op(e1, e3) = e1
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (144), (163), (192), (248), (1827), (2025),
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | (2043), (2177), (function-axioms) are inconsistent
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #422.
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | (2178) all_57_12 = e1 & op(e0, e3) = e1
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2178) implies:
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | (2179) all_57_12 = e1
% 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2154), (2179) are inconsistent by sub-proof
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | #581.
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.71 | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | (2180) all_34_2 = e3
% 132.03/18.71 | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (2180) imply:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | (2181) all_4_2 = e3
% 132.03/18.71 | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | SIMP: (2181) implies:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | (2182) all_4_2 = e3
% 132.03/18.71 | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (2182) imply:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | (2183) all_44_2 = e3
% 132.03/18.71 | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | REDUCE: (367), (2182) imply:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | (2184) ~ (all_52_11 = e3)
% 132.03/18.71 | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | REDUCE: (368), (2182) imply:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | (2185) ~ (all_52_12 = e3)
% 132.03/18.71 | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | REDUCE: (370), (2182) imply:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | (2186) ~ (all_52_14 = e3)
% 132.03/18.71 | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | REDUCE: (36), (2182) imply:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | (2187) op(e0, e0) = e3
% 132.03/18.71 | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | (2188) ~ (all_42_2 = e0)
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | REDUCE: (1996), (2188) imply:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | (2189) $false
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | CLOSE: (2189) is inconsistent.
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | (2190) ( ~ (all_42_0 = e1) & op(e0, e2) = all_42_0 &
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | $i(all_42_0)) | ( ~ (all_42_1 = e3) & op(e0, e0)
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | = all_42_1 & $i(all_42_1))
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | (2191) ~ (all_44_2 = e3)
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | REDUCE: (2183), (2191) imply:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | (2192) $false
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | CLOSE: (2192) is inconsistent.
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | (2193) ( ~ (all_44_0 = e1) & op(e3, e0) = all_44_0 &
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | $i(all_44_0)) | ( ~ (all_44_1 = e2) & op(e3, e3)
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | = all_44_1 & $i(all_44_1))
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | (2194) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2194) gives:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | (2195) all_57_4 = e3 & op(e3, e1) = e3
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2195) implies:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | (2196) all_57_4 = e3
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | (2197) op(e3, e1) = e3
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | (2198) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2198) gives:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | (2199) all_57_6 = e3 & op(e1, e3) = e3
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (2024), (2199), (function-axioms) are
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #761.
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | (2200) all_57_7 = e3 & op(e1, e2) = e3
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2200) implies:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | (2201) all_57_7 = e3
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (2202) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (170), (1834), (1998), (2202),
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | #421.
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (2203) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2203) gives:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2204) all_57_4 = e0 & op(e3, e1) = e0
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2204) implies:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2205) op(e3, e1) = e0
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (169), (2197), (2205), (function-axioms) are
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #600.
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2206) all_57_9 = e0 & op(e3, e0) = e0
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2206) implies:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2207) all_57_9 = e0
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2208) op(e3, e0) = e0
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2209) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2209) gives:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2210) all_57_0 = e1 & op(e3, e3) = e1
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2210) implies:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2211) op(e3, e3) = e1
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1834), (2211), (function-axioms) are
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743.
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2212) all_57_1 = e1 & op(e3, e2) = e1
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2212) implies:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2213) all_57_1 = e1
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2214) op(e3, e2) = e1
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2215) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2215) gives:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2216) all_57_6 = e2 & op(e1, e3) = e2
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2216) implies:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2217) all_57_6 = e2
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2218) op(e1, e3) = e2
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2219) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (158), (162), (170), (227), (1828), (1998),
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1999), (2000), (2219), (function-axioms) are
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #395.
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2220) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2220) gives:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2221) all_57_7 = e2 & op(e1, e2) = e2
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2221) implies:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2222) all_57_7 = e2
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2201), (2222) imply:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2223) e3 = e2
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2030), (2223) imply:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2224) all_57_2 = e2
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (233), (237), (1834), (2217),
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2224), (function-axioms) are inconsistent by
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #393.
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2225) all_57_13 = e2 & op(e0, e2) = e2
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2225) implies:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2226) all_57_13 = e2
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2227) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2227) gives:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2228) all_57_12 = e3 & op(e0, e3) = e3
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (231), (233), (1834),
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2217), (2228), (function-axioms) are inconsistent
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #391.
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2229) all_57_13 = e3 & op(e0, e2) = e3
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (228), (229), (2009),
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2201), (2229) are inconsistent by sub-proof #388.
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2230) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2230) gives:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2231) all_57_14 = e3 & op(e0, e1) = e3
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (2184), (2231), (function-axioms) are
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #652.
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2232) all_57_15 = e3 & op(e0, e0) = e3
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2232) implies:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2233) all_57_15 = e3
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2234) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2234) gives:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2235) all_57_0 = e1 & op(e3, e3) = e1
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2235) implies:
% 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2236) op(e3, e3) = e1
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1834), (2236), (function-axioms) are
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743.
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2237) all_57_2 = e1 & op(e2, e3) = e1
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2004), (2005), (2237), (function-axioms) are
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #425.
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2238) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2238) gives:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2239) all_57_6 = e1 & op(e1, e3) = e1
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2239) implies:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2240) op(e1, e3) = e1
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (2218), (2240), (function-axioms) are
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #517.
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2241) all_57_12 = e1 & op(e0, e3) = e1
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2241) implies:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2242) all_57_12 = e1
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2243) all_57_15 = e0 & op(e0, e0) = e0
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2243) implies:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2244) op(e0, e0) = e0
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (160), (164), (214), (2027), (2186), (2207),
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2244), (function-axioms) are inconsistent by
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #386.
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2245) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2245) implies:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2246) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2247) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2247) gives:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2248) all_57_4 = e2 & op(e3, e1) = e2
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2248) implies:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2249) op(e3, e1) = e2
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, e3, e1,
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, simplifying with (2197), (2249) gives:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2250) e3 = e2
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (2250) imply:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2251) $false
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2251) is inconsistent.
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2252) all_57_5 = e2 & op(e2, e1) = e2
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2252) implies:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2253) all_57_5 = e2
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2254) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2254) gives:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2255) all_57_0 = e0 & op(e3, e3) = e0
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2255) implies:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2256) op(e3, e3) = e0
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1834), (2256), (function-axioms) are
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495.
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2257) all_57_2 = e0 & op(e2, e3) = e0
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2257) implies:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2258) all_57_2 = e0
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (165), (224), (226), (2002),
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2026), (2253), (2258), (function-axioms) are
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #456.
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2259) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2259) gives:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2260) all_57_6 = e0 & op(e1, e3) = e0
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2260) implies:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2261) all_57_6 = e0
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2217), (2261) are inconsistent by sub-proof
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #586.
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2262) all_57_12 = e0 & op(e0, e3) = e0
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2262) implies:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2263) all_57_12 = e0
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2242), (2263) are inconsistent by sub-proof
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #581.
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2264) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2264) gives:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2265) all_57_8 = e2 & op(e1, e1) = e2
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2265) implies:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2266) op(e1, e1) = e2
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (2266), (function-axioms) are
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2267) all_57_14 = e2 & op(e0, e1) = e2
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2267) implies:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2268) all_57_14 = e2
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (209), (2226), (2233), (2246),
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2268) are inconsistent by sub-proof #403.
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2269) all_57_7 = e2 & op(e1, e2) = e2
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2201), (2269) are inconsistent by sub-proof
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #385.
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2270) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2270) gives:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2271) all_57_8 = e2 & op(e1, e1) = e2
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2271) implies:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2272) op(e1, e1) = e2
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (2272), (function-axioms) are
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2273) all_57_11 = e2 & op(e1, e0) = e2
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2273) implies:
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2274) op(e1, e0) = e2
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2275) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2275) gives:
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2276) all_57_9 = e1 & op(e3, e0) = e1
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2276) implies:
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2277) all_57_9 = e1
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2278) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2278) gives:
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2279) all_57_0 = e0 & op(e3, e3) = e0
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2279) implies:
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2280) op(e3, e3) = e0
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1834), (2280), (function-axioms) are
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495.
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2281) all_57_1 = e0 & op(e3, e2) = e0
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2281) implies:
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2282) all_57_1 = e0
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2213), (2282) imply:
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2283) e1 = e0
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (2283) imply:
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2284) $false
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2284) is inconsistent.
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2203) gives:
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2285) all_57_4 = e0 & op(e3, e1) = e0
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2196), (2285) are inconsistent by sub-proof
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #384.
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2207), (2277) are inconsistent by sub-proof
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #383.
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2286) all_57_10 = e1 & op(e2, e0) = e1
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2286) implies:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2287) op(e2, e0) = e1
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2190) gives:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2288) ~ (all_42_0 = e1) & op(e0, e2) = all_42_0 &
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_42_0)
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2288) implies:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2289) ~ (all_42_0 = e1)
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2290) op(e0, e2) = all_42_0
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2291) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (158), (162), (170), (227), (1828), (1998),
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1999), (2000), (2291), (function-axioms) are
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #395.
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2292) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2292) gives:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2293) all_57_7 = e2 & op(e1, e2) = e2
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2201), (2293) are inconsistent by sub-proof
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #385.
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2294) all_57_13 = e2 & op(e0, e2) = e2
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2294) implies:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2295) op(e0, e2) = e2
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2193) gives:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2296) ~ (all_44_0 = e1) & op(e3, e0) = all_44_0 &
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_44_0)
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2296) implies:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2297) ~ (all_44_0 = e1)
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2298) op(e3, e0) = all_44_0
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e2,
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (158), (2295) gives:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2299) all_52_7 = e2
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7,
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_42_0, e2, e0, simplifying with (158), (2290)
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2300) all_52_7 = all_42_0
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, e1, simplifying with (160), (2274) gives:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2301) all_52_14 = e2
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e0, e2, simplifying with (164), (2287) gives:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2302) all_52_13 = e1
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e0, e3, simplifying with (168), (2208) gives:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2303) all_52_12 = e0
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_44_0, e0, e3, simplifying with (168), (2298)
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2304) all_52_12 = all_44_0
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e1,
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (170), (2214) gives:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2305) all_52_4 = e1
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2299), (2300) imply:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2306) all_42_0 = e2
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2306) implies:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2307) all_42_0 = e2
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2303), (2304) imply:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2308) all_44_0 = e0
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2185), (2303) imply:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2309) ~ (e3 = e0)
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2027), (2302) imply:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2310) ~ (e3 = e1)
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (2301) imply:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2311) ~ (all_6_2 = e2)
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2312) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2312) gives:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2313) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2313) gives:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2314) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2314) implies:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2315) op(e3, e2) = e3
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2214), (2315), (function-axioms) are
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #413.
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2316) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2316) implies:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2317) op(e3, e3) = e1
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1834), (2317), (function-axioms) are
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743.
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2318) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (2002), (2185), (2318),
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #622.
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2319) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2319) gives:
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2320) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2002), (2208), (2320), (function-axioms) are
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #540.
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2321) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2321) gives:
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2322) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2322) implies:
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2323) ~ (all_56_15 = e2)
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2324) op(e0, e2) = all_56_15
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2295), (2323), (2324), (function-axioms) are
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #609.
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2325) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2325) gives:
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2326) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2326) implies:
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2327) op(e1, e1) = e2
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (2327), (function-axioms) are
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2328) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2328) implies:
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2329) op(e0, e0) = all_56_31
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2330) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2330) gives:
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2331) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27))
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (2000), (2208), (2331), (function-axioms)
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #538.
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2332) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2332) gives:
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2333) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7)
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23)
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2333) implies:
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2334) op(e1, e0) = e1
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2274), (2334), (function-axioms) are
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #720.
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2335) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2335) implies:
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2336) all_56_31 = e1
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2329), (2336) imply:
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2337) op(e0, e0) = e1
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2187), (2337), (function-axioms) are
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #606.
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2338) ~ (all_44_1 = e2) & op(e3, e3) = all_44_1 &
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_44_1)
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1834), (2338), (function-axioms) are inconsistent
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #431.
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2339) ~ (all_42_1 = e3) & op(e0, e0) = all_42_1 &
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_42_1)
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2187), (2339), (function-axioms) are inconsistent
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #602.
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2340) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (2187), (2274), (2340),
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #557.
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2341) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2341) gives:
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2342) all_57_4 = e1 & op(e3, e1) = e1
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2196), (2342) are inconsistent by sub-proof
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #382.
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2343) all_57_9 = e1 & op(e3, e0) = e1
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2343) implies:
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2344) all_57_9 = e1
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2207), (2344) are inconsistent by sub-proof
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #383.
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | (2345) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (160), (1838), (2186), (2345),
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | #653.
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | (2346) all_57_5 = e3 & op(e2, e1) = e3
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (2026), (2346), (function-axioms) are
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547.
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | (2347) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (157), (1838), (2184), (2347),
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | #651.
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | End of split
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | | End of split
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | | End of split
% 132.31/18.75 | | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | End of split
% 132.31/18.75 | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | Case 2:
% 132.31/18.75 | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | (2348) all_57_3 = e3 & op(e2, e2) = e3
% 132.31/18.75 | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | ALPHA: (2348) implies:
% 132.31/18.75 | | | | | | | | | | | | | | | | | | (2349) op(e2, e2) = e3
% 132.31/18.75 | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2002), (2349), (function-axioms) are
% 132.31/18.75 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641.
% 132.31/18.75 | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | End of split
% 132.31/18.75 | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | Case 2:
% 132.31/18.75 | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | (2350) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 132.31/18.75 | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 132.31/18.75 | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | BETA: splitting (2350) gives:
% 132.31/18.75 | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | Case 1:
% 132.31/18.75 | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | (2351) all_57_5 = e3 & op(e2, e1) = e3
% 132.31/18.75 | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (2026), (2351), (function-axioms) are
% 132.31/18.75 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547.
% 132.31/18.75 | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | Case 2:
% 132.31/18.75 | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | (2352) all_57_10 = e3 & op(e2, e0) = e3
% 132.31/18.75 | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2027), (2352), (function-axioms) are
% 132.31/18.75 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749.
% 132.31/18.75 | | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | | End of split
% 132.31/18.75 | | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | End of split
% 132.31/18.75 | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | Case 2:
% 132.31/18.75 | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | (2353) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 132.31/18.75 | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | | REF_CLOSE: (2004), (2011), (2020), (2021), (2353) are
% 132.31/18.75 | | | | | | | | | | | | | | | | inconsistent by sub-proof #381.
% 132.31/18.75 | | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | End of split
% 132.31/18.75 | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | End of split
% 132.31/18.75 | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | Case 2:
% 132.31/18.75 | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | (2354) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 132.31/18.75 | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 132.31/18.75 | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (1999), (2000), (2354),
% 132.31/18.75 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.31/18.75 | | | | | | | | | | | | | | #504.
% 132.31/18.75 | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | End of split
% 132.31/18.75 | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | Case 2:
% 132.31/18.75 | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | (2355) ~ (all_16_1 = e0) & op(e2, e2) = all_16_1 &
% 132.31/18.75 | | | | | | | | | | | | | $i(all_16_1)
% 132.31/18.75 | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | REF_CLOSE: (2002), (2355), (function-axioms) are inconsistent
% 132.31/18.75 | | | | | | | | | | | | | by sub-proof #380.
% 132.31/18.75 | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | End of split
% 132.31/18.75 | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | End of split
% 132.31/18.75 | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | Case 2:
% 132.31/18.75 | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | (2356) all_28_2 = e3
% 132.31/18.75 | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | COMBINE_EQS: (316), (2356) imply:
% 132.31/18.75 | | | | | | | | | | | (2357) all_6_2 = e3
% 132.31/18.75 | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | COMBINE_EQS: (302), (2357) imply:
% 132.31/18.75 | | | | | | | | | | | (2358) all_36_2 = e3
% 132.31/18.75 | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | REDUCE: (359), (2357) imply:
% 132.31/18.75 | | | | | | | | | | | (2359) ~ (all_52_6 = e3)
% 132.31/18.75 | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | REDUCE: (361), (2357) imply:
% 132.31/18.75 | | | | | | | | | | | (2360) ~ (all_52_8 = e3)
% 132.31/18.75 | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | REDUCE: (362), (2357) imply:
% 132.31/18.75 | | | | | | | | | | | (2361) ~ (all_52_9 = e3)
% 132.31/18.75 | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | REDUCE: (364), (2357) imply:
% 132.31/18.75 | | | | | | | | | | | (2362) ~ (all_52_11 = e3)
% 132.31/18.75 | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | REDUCE: (366), (2357) imply:
% 132.31/18.75 | | | | | | | | | | | (2363) ~ (all_52_14 = e3)
% 132.31/18.75 | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | BETA: splitting (85) gives:
% 132.31/18.75 | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | Case 1:
% 132.31/18.75 | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | (2364) ~ (all_36_2 = e3)
% 132.31/18.75 | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | REDUCE: (2358), (2364) imply:
% 132.31/18.75 | | | | | | | | | | | | (2365) $false
% 132.31/18.75 | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | CLOSE: (2365) is inconsistent.
% 132.31/18.75 | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | Case 2:
% 132.31/18.75 | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | (2366) ( ~ (all_36_0 = e0) & op(e3, e1) = all_36_0 &
% 132.31/18.75 | | | | | | | | | | | | $i(all_36_0)) | ( ~ (all_36_1 = e2) & op(e3, e3)
% 132.31/18.75 | | | | | | | | | | | | = all_36_1 & $i(all_36_1))
% 132.31/18.75 | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | BETA: splitting (2366) gives:
% 132.31/18.75 | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | Case 1:
% 132.31/18.75 | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | (2367) ~ (all_36_0 = e0) & op(e3, e1) = all_36_0 &
% 132.31/18.75 | | | | | | | | | | | | | $i(all_36_0)
% 132.31/18.75 | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | ALPHA: (2367) implies:
% 132.31/18.75 | | | | | | | | | | | | | (2368) ~ (all_36_0 = e0)
% 132.31/18.75 | | | | | | | | | | | | | (2369) op(e3, e1) = all_36_0
% 132.31/18.75 | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | BETA: splitting (222) gives:
% 132.31/18.75 | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | Case 1:
% 132.31/18.75 | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | (2370) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 132.31/18.75 | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 132.31/18.75 | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | BETA: splitting (2370) gives:
% 132.31/18.75 | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | Case 1:
% 132.31/18.75 | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | (2371) all_57_4 = e3 & op(e3, e1) = e3
% 132.31/18.75 | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | REF_CLOSE: (169), (2360), (2369), (2371), (function-axioms)
% 132.31/18.75 | | | | | | | | | | | | | | | are inconsistent by sub-proof #379.
% 132.31/18.75 | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | Case 2:
% 132.31/18.75 | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | (2372) all_57_5 = e3 & op(e2, e1) = e3
% 132.31/18.75 | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | REF_CLOSE: (165), (2361), (2372), (function-axioms) are
% 132.31/18.75 | | | | | | | | | | | | | | | inconsistent by sub-proof #547.
% 132.31/18.75 | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | End of split
% 132.31/18.75 | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | Case 2:
% 132.31/18.75 | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | (2373) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 132.31/18.75 | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 132.31/18.75 | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | BETA: splitting (2373) gives:
% 132.31/18.75 | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | Case 1:
% 132.31/18.75 | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | (2374) all_57_8 = e3 & op(e1, e1) = e3
% 132.31/18.75 | | | | | | | | | | | | | | |
% 132.31/18.75 | | | | | | | | | | | | | | | ALPHA: (2374) implies:
% 132.31/18.75 | | | | | | | | | | | | | | | (2375) all_57_8 = e3
% 132.31/18.75 | | | | | | | | | | | | | | | (2376) op(e1, e1) = e3
% 132.31/18.75 | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8,
% 132.31/18.76 | | | | | | | | | | | | | | | all_36_0, e1, e3, simplifying with (169), (2369)
% 132.31/18.76 | | | | | | | | | | | | | | | gives:
% 132.31/18.76 | | | | | | | | | | | | | | | (2377) all_52_8 = all_36_0
% 132.31/18.76 | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | COMBINE_EQS: (270), (2377) imply:
% 132.31/18.76 | | | | | | | | | | | | | | | (2378) all_54_2 = all_36_0
% 132.31/18.76 | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | REDUCE: (134), (2377) imply:
% 132.31/18.76 | | | | | | | | | | | | | | | (2379) ~ (all_52_4 = all_36_0)
% 132.31/18.76 | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | REDUCE: (123), (2377) imply:
% 132.31/18.76 | | | | | | | | | | | | | | | (2380) ~ (all_52_9 = all_36_0)
% 132.31/18.76 | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | SIMP: (2380) implies:
% 132.31/18.76 | | | | | | | | | | | | | | | (2381) ~ (all_52_9 = all_36_0)
% 132.31/18.76 | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | REDUCE: (121), (2377) imply:
% 132.31/18.76 | | | | | | | | | | | | | | | (2382) ~ (all_52_11 = all_36_0)
% 132.31/18.76 | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | SIMP: (2382) implies:
% 132.31/18.76 | | | | | | | | | | | | | | | (2383) ~ (all_52_11 = all_36_0)
% 132.31/18.76 | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | REDUCE: (2360), (2377) imply:
% 132.31/18.76 | | | | | | | | | | | | | | | (2384) ~ (all_36_0 = e3)
% 132.31/18.76 | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | REDUCE: (1829), (2377) imply:
% 132.31/18.76 | | | | | | | | | | | | | | | (2385) ~ (all_36_0 = e2)
% 132.31/18.76 | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 132.31/18.76 | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | Case 1:
% 132.31/18.76 | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | (2386) all_54_2 = e3
% 132.31/18.76 | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | COMBINE_EQS: (2378), (2386) imply:
% 132.31/18.76 | | | | | | | | | | | | | | | | (2387) all_36_0 = e3
% 132.31/18.76 | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | REDUCE: (2384), (2387) imply:
% 132.31/18.76 | | | | | | | | | | | | | | | | (2388) $false
% 132.31/18.76 | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | CLOSE: (2388) is inconsistent.
% 132.31/18.76 | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | Case 2:
% 132.31/18.76 | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | (2389) ~ (all_54_2 = e3)
% 132.31/18.76 | | | | | | | | | | | | | | | | (2390) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 132.31/18.76 | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | BETA: splitting (2390) gives:
% 132.31/18.76 | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | Case 1:
% 132.31/18.76 | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | (2391) all_54_2 = e2
% 132.31/18.76 | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | COMBINE_EQS: (2378), (2391) imply:
% 132.31/18.76 | | | | | | | | | | | | | | | | | (2392) all_36_0 = e2
% 132.31/18.76 | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | REDUCE: (2385), (2392) imply:
% 132.31/18.76 | | | | | | | | | | | | | | | | | (2393) $false
% 132.31/18.76 | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | CLOSE: (2393) is inconsistent.
% 132.31/18.76 | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | Case 2:
% 132.31/18.76 | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | (2394) ~ (all_54_2 = e2)
% 132.31/18.76 | | | | | | | | | | | | | | | | | (2395) all_54_2 = e1 | all_54_2 = e0
% 132.31/18.76 | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | BETA: splitting (2395) gives:
% 132.31/18.76 | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | Case 1:
% 132.31/18.76 | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | (2396) all_54_2 = e1
% 132.31/18.76 | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2378), (2396) imply:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | (2397) all_36_0 = e1
% 132.31/18.76 | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | REDUCE: (2379), (2397) imply:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | (2398) ~ (all_52_4 = e1)
% 132.31/18.76 | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | REDUCE: (2381), (2397) imply:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | (2399) ~ (all_52_9 = e1)
% 132.31/18.76 | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | REDUCE: (2383), (2397) imply:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | (2400) ~ (all_52_11 = e1)
% 132.31/18.76 | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | REDUCE: (2384), (2397) imply:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | (2401) ~ (e3 = e1)
% 132.31/18.76 | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | REDUCE: (2385), (2397) imply:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | (2402) ~ (e2 = e1)
% 132.31/18.76 | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | REDUCE: (2369), (2397) imply:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | (2403) op(e3, e1) = e1
% 132.31/18.76 | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 132.31/18.76 | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | Case 1:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | (2404) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 132.31/18.76 | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (170), (1834), (2398), (2404),
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | #378.
% 132.31/18.76 | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | Case 2:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | (2405) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 132.31/18.76 | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | BETA: splitting (2405) gives:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | Case 1:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | (2406) all_57_4 = e1 & op(e3, e1) = e1
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | ALPHA: (2406) implies:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | (2407) all_57_4 = e1
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | (2408) ~ (all_30_2 = e0)
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | REDUCE: (309), (2408) imply:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | (2409) ~ (all_8_2 = e0)
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | (2410) all_54_5 = e3
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (376), (2410) are inconsistent by sub-proof
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | #554.
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | (2411) ~ (all_54_5 = e3)
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | (2412) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2412) gives:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | (2413) all_54_5 = e2
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (2413) imply:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | (2414) all_8_2 = e2
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2414) implies:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | (2415) all_8_2 = e2
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (352), (2415) imply:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | (2416) ~ (all_52_6 = e2)
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (356), (2415) imply:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | (2417) ~ (all_52_9 = e2)
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (358), (2415) imply:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | (2418) ~ (all_52_13 = e2)
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (376), (2415) imply:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | (2419) ~ (e3 = e2)
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (2415) imply:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | (2420) op(e2, e2) = e2
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | (2421) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2421) gives:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | (2422) all_57_6 = e2 & op(e1, e3) = e2
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2422) implies:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | (2423) all_57_6 = e2
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | (2424) op(e1, e3) = e2
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (2425) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (1830), (2418), (2425),
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | #440.
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (2426) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2426) gives:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2427) all_57_11 = e2 & op(e1, e0) = e2
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2427) implies:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2428) all_57_11 = e2
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2429) op(e1, e0) = e2
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2430) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (1829), (2417), (2430),
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #441.
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2431) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2431) gives:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2432) all_57_8 = e2 & op(e1, e1) = e2
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2432) implies:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2433) all_57_8 = e2
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (215), (216),
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218), (2359), (2428), (2433), (function-axioms)
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #571.
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2434) all_57_14 = e2 & op(e0, e1) = e2
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2434) implies:
% 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2435) all_57_14 = e2
% 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2436) op(e0, e1) = e2
% 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2437) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2437) gives:
% 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2438) all_57_9 = e1 & op(e3, e0) = e1
% 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2438) implies:
% 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2439) all_57_9 = e1
% 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2440) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2440) gives:
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2441) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1834), (2420), (2441), (function-axioms) are
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #444.
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2442) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (167), (1825), (1834), (2442),
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #443.
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2443) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2443) gives:
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2444) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (165), (2417), (2424), (2444),
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #468.
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2445) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2445) gives:
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2446) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2446) implies:
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2447) op(e2, e0) = e2
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2418), (2447), (function-axioms) are
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2448) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2448) gives:
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2449) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2449) implies:
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2450) op(e1, e1) = e2
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (2450), (function-axioms) are
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2451) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2451) implies:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2452) op(e0, e0) = all_56_31
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2453) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2454) all_57_15 = e0 & op(e0, e0) = e0
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2454) implies:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2455) op(e0, e0) = e0
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (2452), (2453), (2455),
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #710.
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2456) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2456) implies:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2457) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2458) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2458) gives:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2459) all_57_0 = e0 & op(e3, e3) = e0
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2459) implies:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2460) op(e3, e3) = e0
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1834), (2460), (function-axioms) are
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495.
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2461) all_57_1 = e0 & op(e3, e2) = e0
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2461) implies:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2462) all_57_1 = e0
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2463) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2463) gives:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2464) all_57_2 = e2 & op(e2, e3) = e2
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2464) implies:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2465) all_57_2 = e2
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (233), (237), (1834), (2423),
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2465), (function-axioms) are inconsistent by
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #393.
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2466) all_57_3 = e2 & op(e2, e2) = e2
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2466) implies:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2467) all_57_3 = e2
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2457) gives:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2468) all_57_9 = e0 & op(e3, e0) = e0
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2468) implies:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2469) all_57_9 = e0
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2439), (2469) are inconsistent by sub-proof
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #383.
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2470) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2470) gives:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2471) all_57_10 = e0 & op(e2, e0) = e0
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2471) implies:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2472) all_57_10 = e0
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2473) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2473) gives:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2474) all_57_9 = e3 & op(e3, e0) = e3
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2474) implies:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2475) all_57_9 = e3
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2453) gives:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2476) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27))
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2476) gives:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2477) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2477) implies:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2478) all_56_31 = e3
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2452), (2478) imply:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2479) op(e0, e0) = e3
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (208), (212), (2428),
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2429), (2452), (2453), (2475), (2479),
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #439.
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2480) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27)
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2480) implies:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2481) all_56_31 = e2
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2452), (2481) imply:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2482) op(e0, e0) = e2
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (208), (212), (2428),
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2475), (2482), (function-axioms) are inconsistent
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #635.
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2483) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (2429), (2436), (2483),
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #428.
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2484) all_57_10 = e3 & op(e2, e0) = e3
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2472), (2484) are inconsistent by sub-proof
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #377.
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2485) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2485) gives:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2486) all_57_11 = e3 & op(e1, e0) = e3
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (2363), (2486), (function-axioms) are
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #750.
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2487) all_57_15 = e3 & op(e0, e0) = e3
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2487) implies:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2488) op(e0, e0) = e3
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2489) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2489) gives:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2490) all_57_1 = e3 & op(e3, e2) = e3
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2462), (2490) are inconsistent by sub-proof
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #376.
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2491) all_57_3 = e3 & op(e2, e2) = e3
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2491) implies:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2492) all_57_3 = e3
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (233), (237), (1834), (2423), (2492),
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #360.
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2493) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2493) gives:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2494) all_57_7 = e3 & op(e1, e2) = e3
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2494) implies:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2495) op(e1, e2) = e3
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (2359), (2495), (function-axioms) are
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #654.
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2496) all_57_13 = e3 & op(e0, e2) = e3
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2496) implies:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2497) all_57_13 = e3
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2498) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2498) gives:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2499) all_57_12 = e1 & op(e0, e3) = e1
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2499) implies:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2500) all_57_12 = e1
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2501) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2501) gives:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2502) all_57_2 = e3 & op(e2, e3) = e3
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2502) implies:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2503) all_57_2 = e3
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (164), (165), (167), (225), (231),
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1825), (1834), (2417), (2418), (2423), (2467),
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2500), (2503), (function-axioms) are inconsistent
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #358.
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2504) all_57_3 = e3 & op(e2, e2) = e3
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2504) implies:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2505) all_57_3 = e3
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (233), (237), (1834), (2423), (2505),
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #360.
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2506) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2506) gives:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2507) all_57_5 = e3 & op(e2, e1) = e3
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (2361), (2507), (function-axioms) are
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547.
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2508) all_57_10 = e3 & op(e2, e0) = e3
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2472), (2508) are inconsistent by sub-proof
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #377.
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2509) all_57_13 = e1 & op(e0, e2) = e1
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2497), (2509) are inconsistent by sub-proof
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #389.
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2510) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2510) gives:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2511) all_57_14 = e1 & op(e0, e1) = e1
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2511) implies:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2512) all_57_14 = e1
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2435), (2512) are inconsistent by sub-proof
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #560.
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2513) all_57_15 = e1 & op(e0, e0) = e1
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2513) implies:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2514) op(e0, e0) = e1
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2488), (2514), (function-axioms) are
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #606.
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2515) all_57_11 = e0 & op(e1, e0) = e0
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2515) implies:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2516) all_57_11 = e0
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2428), (2516) imply:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2517) e2 = e0
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2517) implies:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2518) e2 = e0
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (164), (165), (167), (225), (1825), (2417),
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2418), (2467), (2518), (function-axioms) are
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #359.
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2519) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (165), (2417), (2428), (2439), (2457),
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2519), (function-axioms) are inconsistent by
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #357.
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2520) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2520) gives:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2521) all_57_4 = e0 & op(e3, e1) = e0
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2407), (2521) are inconsistent by sub-proof
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #672.
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2522) all_57_9 = e0 & op(e3, e0) = e0
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2439), (2522) are inconsistent by sub-proof
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #687.
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2523) all_57_10 = e1 & op(e2, e0) = e1
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2523) implies:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2524) all_57_10 = e1
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2525) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2525) gives:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2526) all_57_2 = e2 & op(e2, e3) = e2
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2526) implies:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2527) all_57_2 = e2
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (233), (237), (1834), (2423),
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2527), (function-axioms) are inconsistent by
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #393.
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2528) all_57_3 = e2 & op(e2, e2) = e2
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2528) implies:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2529) all_57_3 = e2
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2530) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2530) gives:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2531) all_57_2 = e3 & op(e2, e3) = e3
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2531) implies:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2532) all_57_2 = e3
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2533) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (1834), (2532), (2533),
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #356.
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2534) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2534) gives:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2535) all_57_6 = e1 & op(e1, e3) = e1
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2535) implies:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2536) op(e1, e3) = e1
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (2424), (2536), (function-axioms) are
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #517.
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2537) all_57_12 = e1 & op(e0, e3) = e1
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2537) implies:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2538) all_57_12 = e1
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (164), (165), (167), (225), (231),
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1825), (1834), (2417), (2418), (2423), (2529),
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2532), (2538), (function-axioms) are inconsistent
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #358.
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2539) all_57_3 = e3 & op(e2, e2) = e3
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2539) implies:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2540) all_57_3 = e3
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (233), (237), (1834), (2423), (2540),
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #360.
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2541) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2541) gives:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2542) all_57_5 = e3 & op(e2, e1) = e3
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (2361), (2542), (function-axioms) are
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547.
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2543) all_57_10 = e3 & op(e2, e0) = e3
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2524), (2543) are inconsistent by sub-proof
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #355.
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2544) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (165), (2417), (2418), (2544),
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #625.
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2545) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (371), (2429), (2545),
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #353.
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2546) all_57_15 = e2 & op(e0, e0) = e2
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2546) implies:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2547) op(e0, e0) = e2
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2548) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2548) gives:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2549) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1834), (2420), (2549), (function-axioms) are
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #444.
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2550) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (167), (1825), (1834), (2550),
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #443.
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2551) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2551) gives:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2552) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (165), (2417), (2424), (2552),
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #468.
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2553) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2553) gives:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2554) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2554) implies:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2555) op(e2, e0) = e2
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2418), (2555), (function-axioms) are
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2556) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (39), (372), (1836), (2547), (2556),
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #352.
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | (2557) all_57_7 = e2 & op(e1, e2) = e2
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (2416), (2557), (function-axioms) are
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #515.
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | (2558) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2558) gives:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | (2559) all_57_8 = e2 & op(e1, e1) = e2
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2559) implies:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | (2560) op(e1, e1) = e2
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (2560), (function-axioms) are
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | (2561) all_57_11 = e2 & op(e1, e0) = e2
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2561) implies:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | (2562) all_57_11 = e2
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | (2563) op(e1, e0) = e2
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | (2564) all_54_6 = e3
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (2564) imply:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | (2565) all_52_9 = e3
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2361), (2565) imply:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | (2566) $false
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2566) is inconsistent.
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | (2567) ~ (all_54_6 = e3)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | (2568) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2568) gives:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2569) all_54_6 = e2
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (2569) imply:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2570) all_52_9 = e2
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2417), (2570) imply:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2571) $false
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2571) is inconsistent.
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2572) ~ (all_54_6 = e2)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2573) all_54_6 = e1 | all_54_6 = e0
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2574) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (1829), (2417), (2574),
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #441.
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2575) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2575) gives:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2576) all_57_8 = e2 & op(e1, e1) = e2
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2576) implies:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2577) all_57_8 = e2
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (215), (216),
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218), (2359), (2562), (2577), (function-axioms)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #571.
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2578) all_57_14 = e2 & op(e0, e1) = e2
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2578) implies:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2579) all_57_14 = e2
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2580) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2580) gives:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2581) all_57_9 = e1 & op(e3, e0) = e1
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2581) implies:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2582) all_57_9 = e1
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2583) op(e3, e0) = e1
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2584) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2584) gives:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2585) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1834), (2420), (2585), (function-axioms) are
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #444.
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2586) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (167), (1825), (1834), (2586),
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #443.
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2587) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2587) gives:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2588) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2588) gives:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2589) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2589) implies:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2590) ~ (all_56_1 = e3)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2591) op(e3, e0) = all_56_25
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2592) op(e3, e3) = all_56_1
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2593) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2593) gives:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2594) all_57_0 = e3 & op(e3, e3) = e3
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2594) implies:
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2595) op(e3, e3) = e3
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2590), (2592), (2595), (function-axioms) are
% 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #766.
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2596) all_57_1 = e3 & op(e3, e2) = e3
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2596) implies:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2597) all_57_1 = e3
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2598) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2598) gives:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2599) all_57_0 = e0 & op(e3, e3) = e0
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2599) implies:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2600) op(e3, e3) = e0
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1834), (2600), (function-axioms) are
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495.
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2601) all_57_1 = e0 & op(e3, e2) = e0
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2597), (2601) are inconsistent by sub-proof
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #649.
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2602) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2602) gives:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2603) all_57_4 = e0 & op(e3, e1) = e0
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2407), (2603) are inconsistent by sub-proof
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #672.
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2604) all_57_9 = e0 & op(e3, e0) = e0
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2604) implies:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2605) op(e3, e0) = e0
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_25, e0, e3, simplifying with (2583), (2591)
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2606) all_56_25 = e1
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_25, e0, e3, simplifying with (2591), (2605)
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2607) all_56_25 = e0
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2606), (2607) imply:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2608) e1 = e0
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2608) implies:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2609) e1 = e0
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (2609) imply:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2610) $false
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2610) is inconsistent.
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2611) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2611) gives:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2612) all_57_4 = e3 & op(e3, e1) = e3
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (2360), (2369), (2612), (function-axioms)
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #379.
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2613) all_57_9 = e3 & op(e3, e0) = e3
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2613) implies:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2614) all_57_9 = e3
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2582), (2614) are inconsistent by sub-proof
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #690.
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2615) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2,
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2615) implies:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2616) op(e2, e1) = e2
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (2417), (2616), (function-axioms) are
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #770.
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2617) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2617) gives:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2618) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2618) implies:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2619) op(e2, e0) = e2
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2418), (2619), (function-axioms) are
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2620) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2620) gives:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2621) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2621) implies:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2622) op(e1, e1) = e2
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (2622), (function-axioms) are
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2623) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2623) implies:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2624) op(e0, e0) = all_56_31
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2625) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2573) gives:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2626) all_54_6 = e1
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (2626) imply:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2627) all_52_9 = e1
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2399), (2627) imply:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2628) $false
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2628) is inconsistent.
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2629) all_54_6 = e0
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (2629) imply:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2630) all_52_9 = e0
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (2630) imply:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2631) ~ (all_52_11 = e0)
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2631) implies:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2632) ~ (all_52_11 = e0)
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2361), (2630) imply:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2633) ~ (e3 = e0)
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2417), (2630) imply:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2634) ~ (e2 = e0)
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2399), (2630) imply:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2635) ~ (e1 = e0)
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2636) all_54_14 = e3
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (2362), (2636) are inconsistent by
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #760.
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2637) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2638) all_57_15 = e0 & op(e0, e0) = e0
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2638) implies:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2639) op(e0, e0) = e0
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (2624), (2625), (2639),
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #710.
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2640) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2640) implies:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2641) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2642) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2643) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2643) gives:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2644) all_57_0 = e0 & op(e3, e3) = e0
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2644) implies:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2645) op(e3, e3) = e0
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1834), (2645), (function-axioms) are
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495.
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2646) all_57_1 = e0 & op(e3, e2) = e0
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2646) implies:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2647) all_57_1 = e0
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2648) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2648) gives:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2649) all_57_2 = e2 & op(e2, e3) = e2
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2649) implies:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2650) op(e2, e3) = e2
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (1825), (2650), (function-axioms) are
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #779.
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2651) all_57_3 = e2 & op(e2, e2) = e2
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2651) implies:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2652) all_57_3 = e2
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2653) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2653) gives:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2654) all_57_1 = e3 & op(e3, e2) = e3
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2647), (2654) are inconsistent by sub-proof
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #376.
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2655) all_57_3 = e3 & op(e2, e2) = e3
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2655) implies:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2656) all_57_3 = e3
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2652), (2656) imply:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2657) e3 = e2
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2657) implies:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2658) e3 = e2
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2375), (2658) imply:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2659) all_57_8 = e2
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (215), (216),
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218), (2359), (2562), (2659), (function-axioms)
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #571.
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2660) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2660) gives:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2661) all_57_7 = e3 & op(e1, e2) = e3
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2661) implies:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2662) op(e1, e2) = e3
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (2359), (2662), (function-axioms) are
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #654.
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2663) all_57_13 = e3 & op(e0, e2) = e3
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2663) implies:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2664) all_57_13 = e3
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2665) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2665) gives:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2666) all_57_12 = e1 & op(e0, e3) = e1
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2666) implies:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2667) all_57_12 = e1
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2641) gives:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2668) all_57_12 = e0 & op(e0, e3) = e0
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2668) implies:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2669) all_57_12 = e0
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2667), (2669) are inconsistent by sub-proof
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #581.
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2670) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2670) gives:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2671) all_57_13 = e0 & op(e0, e2) = e0
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2671) implies:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2672) all_57_13 = e0
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2664), (2672) are inconsistent by sub-proof
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #484.
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2673) all_57_14 = e0 & op(e0, e1) = e0
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2673) implies:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2674) op(e0, e1) = e0
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (246), (2400), (2632), (2637), (2674),
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #351.
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2675) all_57_13 = e1 & op(e0, e2) = e1
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2664), (2675) are inconsistent by sub-proof
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #389.
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2676) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (371), (2579), (2676),
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #350.
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2677) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (165), (2417), (2562), (2582), (2642),
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2677), (function-axioms) are inconsistent by
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #357.
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2678) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2678) gives:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2679) all_57_4 = e0 & op(e3, e1) = e0
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2407), (2679) are inconsistent by sub-proof
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #672.
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2680) all_57_9 = e0 & op(e3, e0) = e0
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2582), (2680) are inconsistent by sub-proof
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #687.
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2681) all_57_10 = e1 & op(e2, e0) = e1
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2681) implies:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2682) all_57_10 = e1
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2683) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2683) gives:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2684) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1834), (2420), (2684), (function-axioms) are
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #444.
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2685) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2685) gives:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2686) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3,
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2686) implies:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2687) op(e3, e3) = e0
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1834), (2687), (function-axioms) are
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495.
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2688) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2,
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2688) implies:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2689) ~ (all_56_17 = e1)
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2690) op(e3, e1) = all_56_17
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2403), (2689), (2690), (function-axioms) are
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #349.
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2691) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2691) gives:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2692) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (2403), (2417), (2692), (function-axioms)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #348.
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2693) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2693) gives:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2694) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2694) implies:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2695) op(e2, e0) = e2
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2418), (2695), (function-axioms) are
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2696) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2696) gives:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2697) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2697) implies:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2698) op(e1, e1) = e2
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (2698), (function-axioms) are
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2699) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2699) implies:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2700) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2573) gives:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2701) all_54_6 = e1
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (2701) imply:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2702) all_52_9 = e1
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2399), (2702) imply:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2703) $false
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2703) is inconsistent.
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2704) all_54_6 = e0
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (2704) imply:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2705) all_52_9 = e0
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (2705) imply:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2706) ~ (all_52_11 = e0)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2706) implies:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2707) ~ (all_52_11 = e0)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2361), (2705) imply:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2708) ~ (e3 = e0)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2417), (2705) imply:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2709) ~ (e2 = e0)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2399), (2705) imply:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2710) ~ (e1 = e0)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2711) all_54_14 = e3
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (2362), (2711) are inconsistent by
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #760.
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2712) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2713) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2713) gives:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2714) all_57_2 = e3 & op(e2, e3) = e3
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2714) implies:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2715) op(e2, e3) = e3
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2700) gives:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2716) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27))
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2403), (2715), (2716), (function-axioms) are
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #346.
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2717) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2717) gives:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2718) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23)
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2718) implies:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2719) op(e1, e0) = e1
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2563), (2719), (function-axioms) are
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #720.
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2720) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2720) implies:
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2721) op(e0, e1) = e0
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (246), (2400), (2707), (2712), (2721),
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #351.
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2722) all_57_3 = e3 & op(e2, e2) = e3
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2722) implies:
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2723) all_57_3 = e3
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2724) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2724) gives:
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2725) all_57_1 = e2 & op(e3, e2) = e2
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (1828), (2725), (function-axioms) are
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #396.
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2726) all_57_3 = e2 & op(e2, e2) = e2
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2726) implies:
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2727) all_57_3 = e2
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2723), (2727) imply:
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2728) e3 = e2
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2375), (2728) imply:
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2729) all_57_8 = e2
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (215), (216),
% 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218), (2359), (2562), (2729), (function-axioms)
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #571.
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2730) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2730) gives:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2731) all_57_7 = e2 & op(e1, e2) = e2
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (2416), (2731), (function-axioms) are
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #515.
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2732) all_57_13 = e2 & op(e0, e2) = e2
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2732) implies:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2733) all_57_13 = e2
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (208), (209), (211),
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2579), (2733) are inconsistent by sub-proof #401.
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2734) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2734) gives:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2735) all_57_5 = e3 & op(e2, e1) = e3
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (2361), (2735), (function-axioms) are
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547.
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2736) all_57_10 = e3 & op(e2, e0) = e3
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2682), (2736) are inconsistent by sub-proof
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #355.
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2737) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (371), (2563), (2737),
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #353.
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | (2738) all_54_5 = e1 | all_54_5 = e0
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (373), (2409), (2738) are inconsistent by
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #624.
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | (2739) all_30_2 = e0
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (309), (2739) imply:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | (2740) all_8_2 = e0
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | SIMP: (2740) implies:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | (2741) all_8_2 = e0
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | REDUCE: (350), (2741) imply:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | (2742) ~ (all_52_4 = e0)
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | REDUCE: (354), (2741) imply:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | (2743) ~ (all_52_7 = e0)
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | REDUCE: (356), (2741) imply:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | (2744) ~ (all_52_9 = e0)
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (2741) imply:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | (2745) ~ (e1 = e0)
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (2741) imply:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | (2746) op(e2, e2) = e0
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | (2747) all_54_6 = e3
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (2747) imply:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | (2748) all_52_9 = e3
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2361), (2748) imply:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | (2749) $false
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2749) is inconsistent.
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | (2750) ~ (all_54_6 = e3)
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | (2751) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | (2752) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (170), (1834), (2742), (2752),
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | #421.
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | (2753) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2753) gives:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | (2754) all_57_4 = e0 & op(e3, e1) = e0
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2407), (2754) are inconsistent by sub-proof
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | #672.
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | (2755) all_57_9 = e0 & op(e3, e0) = e0
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2755) implies:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | (2756) all_57_9 = e0
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | (2757) op(e3, e0) = e0
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2751) gives:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | (2758) all_54_6 = e2
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (2758) imply:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | (2759) all_52_9 = e2
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (2759) imply:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | (2760) ~ (all_52_11 = e2)
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2760) implies:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | (2761) ~ (all_52_11 = e2)
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (2759) imply:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | (2762) ~ (all_52_13 = e2)
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2762) implies:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | (2763) ~ (all_52_13 = e2)
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (2764) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (1830), (2763), (2764),
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | #440.
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (2765) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2765) gives:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2766) all_57_11 = e2 & op(e1, e0) = e2
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2766) implies:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2767) op(e1, e0) = e2
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2768) all_54_1 = e3
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (2768) imply:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2769) all_52_4 = e3
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2769) implies:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2770) all_52_4 = e3
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (2770) imply:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2771) ~ (all_52_12 = e3)
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2771) implies:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2772) ~ (all_52_12 = e3)
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2773) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2773) gives:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2774) all_57_9 = e1 & op(e3, e0) = e1
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2774) implies:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2775) all_57_9 = e1
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2756), (2775) are inconsistent by sub-proof
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #383.
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2776) all_57_10 = e1 & op(e2, e0) = e1
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2776) implies:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2777) all_57_10 = e1
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2778) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2778) gives:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2779) all_57_9 = e3 & op(e3, e0) = e3
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2779) implies:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2780) op(e3, e0) = e3
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (2772), (2780), (function-axioms) are
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #733.
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2781) all_57_10 = e3 & op(e2, e0) = e3
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2777), (2781) are inconsistent by sub-proof
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #355.
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2782) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2782) gives:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2783) all_57_11 = e3 & op(e1, e0) = e3
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (2363), (2783), (function-axioms) are
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #750.
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2784) all_57_15 = e3 & op(e0, e0) = e3
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2784) implies:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2785) op(e0, e0) = e3
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2786) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2786) gives:
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2787) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2787) gives:
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2788) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2788) implies:
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2789) ~ (all_56_3 = e3)
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2790) op(e2, e3) = all_56_3
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2791) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2791) gives:
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2792) all_57_2 = e3 & op(e2, e3) = e3
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2792) implies:
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2793) op(e2, e3) = e3
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2789), (2790), (2793), (function-axioms) are
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #347.
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2794) all_57_3 = e3 & op(e2, e2) = e3
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2794) implies:
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2795) op(e2, e2) = e3
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2746), (2795), (function-axioms) are
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641.
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2796) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2796) gives:
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2797) all_57_5 = e3 & op(e2, e1) = e3
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (2361), (2797), (function-axioms) are
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547.
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2798) all_57_10 = e3 & op(e2, e0) = e3
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2777), (2798) are inconsistent by sub-proof
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #355.
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2799) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2799) implies:
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2800) op(e3, e3) = e1
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (236), (238), (2407),
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2756), (2800), (function-axioms) are inconsistent
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #668.
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2801) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (2746), (2772), (2801),
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #622.
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2802) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2802) gives:
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2803) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2746), (2757), (2803), (function-axioms) are
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #540.
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2804) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2804) gives:
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2805) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2805) implies:
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2806) op(e2, e0) = e2
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2763), (2806), (function-axioms) are
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2807) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (39), (158), (372), (2376), (2743),
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2757), (2785), (2807), (function-axioms) are
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #537.
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2808) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (371), (2767), (2808),
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #353.
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2809) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (271), (1828), (2398), (2742), (2809) are
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #701.
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2810) all_57_15 = e2 & op(e0, e0) = e2
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2810) implies:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2811) op(e0, e0) = e2
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2812) all_54_14 = e3
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (2362), (2812) are inconsistent by
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #760.
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2813) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2813) gives:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2814) all_54_14 = e2
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (2761), (2814) are inconsistent by
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #527.
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2815) all_54_14 = e1 | all_54_14 = e0
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2815) gives:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2816) all_54_14 = e1
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (2400), (2816) are inconsistent by
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #756.
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2817) all_54_14 = e0
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (2817) imply:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2818) all_52_11 = e0
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2818) implies:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2819) all_52_11 = e0
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (367), (2819) imply:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2820) ~ (all_4_2 = e0)
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2820) implies:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2821) ~ (all_4_2 = e0)
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2822) all_54_15 = e3
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (2822) imply:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2823) all_4_2 = e3
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2823) implies:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2824) all_4_2 = e3
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (2824) imply:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2825) op(e0, e0) = e3
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2811), (2825), (function-axioms) are
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #634.
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2826) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (371), (1836), (2821), (2826) are
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #746.
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | (2827) all_54_6 = e1 | all_54_6 = e0
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (2399), (2744), (2827) are inconsistent by
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #479.
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | (2828) all_57_9 = e1 & op(e3, e0) = e1
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | ALPHA: (2828) implies:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | (2829) all_57_9 = e1
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | (2830) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2830) gives:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | (2831) all_57_0 = e0 & op(e3, e3) = e0
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2831) implies:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | (2832) op(e3, e3) = e0
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1834), (2832), (function-axioms) are
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495.
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | (2833) all_57_1 = e0 & op(e3, e2) = e0
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2833) implies:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | (2834) all_57_1 = e0
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (169), (238), (1834), (2360),
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | (2369), (2829), (2834), (function-axioms) are
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #344.
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | (2835) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2835) gives:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | (2836) all_57_4 = e0 & op(e3, e1) = e0
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2836) implies:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | (2837) op(e3, e1) = e0
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2403), (2837), (function-axioms) are
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #343.
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | (2838) all_57_9 = e0 & op(e3, e0) = e0
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2829), (2838) are inconsistent by sub-proof
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | #687.
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.86 | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.86 | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.86 | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | (2839) all_54_2 = e0
% 132.56/18.86 | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2378), (2839) imply:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | (2840) all_36_0 = e0
% 132.56/18.86 | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | REDUCE: (2368), (2840) imply:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | (2841) $false
% 132.56/18.86 | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | CLOSE: (2841) is inconsistent.
% 132.56/18.86 | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | End of split
% 132.56/18.86 | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | End of split
% 132.56/18.86 | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | End of split
% 132.56/18.86 | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | Case 2:
% 132.56/18.86 | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | (2842) all_57_14 = e3 & op(e0, e1) = e3
% 132.56/18.86 | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | REF_CLOSE: (157), (2362), (2842), (function-axioms) are
% 132.56/18.86 | | | | | | | | | | | | | | | inconsistent by sub-proof #652.
% 132.56/18.86 | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | End of split
% 132.56/18.86 | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | End of split
% 132.56/18.86 | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | Case 2:
% 132.56/18.86 | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | (2843) ~ (all_36_1 = e2) & op(e3, e3) = all_36_1 &
% 132.56/18.86 | | | | | | | | | | | | | $i(all_36_1)
% 132.56/18.86 | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | REF_CLOSE: (1834), (2843), (function-axioms) are inconsistent
% 132.56/18.86 | | | | | | | | | | | | | by sub-proof #342.
% 132.56/18.86 | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | End of split
% 132.56/18.86 | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | End of split
% 132.56/18.86 | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | End of split
% 132.56/18.86 | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | Case 2:
% 132.56/18.86 | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | (2844) all_20_2 = e2
% 132.56/18.86 | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | COMBINE_EQS: (318), (2844) imply:
% 132.56/18.86 | | | | | | | | | | (2845) all_4_2 = e2
% 132.56/18.86 | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | SIMP: (2845) implies:
% 132.56/18.86 | | | | | | | | | | (2846) all_4_2 = e2
% 132.56/18.86 | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | COMBINE_EQS: (331), (2846) imply:
% 132.56/18.86 | | | | | | | | | | (2847) all_26_2 = e2
% 132.56/18.86 | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | REDUCE: (367), (2846) imply:
% 132.56/18.86 | | | | | | | | | | (2848) ~ (all_52_11 = e2)
% 132.56/18.86 | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | REDUCE: (370), (2846) imply:
% 132.56/18.86 | | | | | | | | | | (2849) ~ (all_52_14 = e2)
% 132.56/18.86 | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | REDUCE: (36), (2846) imply:
% 132.56/18.86 | | | | | | | | | | (2850) op(e0, e0) = e2
% 132.56/18.86 | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | BETA: splitting (221) gives:
% 132.56/18.86 | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | Case 1:
% 132.56/18.86 | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | (2851) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 132.56/18.86 | | | | | | | | | | | & op(e2, e1) = e2)
% 132.56/18.86 | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | BETA: splitting (2851) gives:
% 132.56/18.86 | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | Case 1:
% 132.56/18.86 | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | (2852) all_57_4 = e2 & op(e3, e1) = e2
% 132.56/18.86 | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | REF_CLOSE: (169), (1829), (2852), (function-axioms) are
% 132.56/18.86 | | | | | | | | | | | | inconsistent by sub-proof #442.
% 132.56/18.86 | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | Case 2:
% 132.56/18.86 | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | (2853) all_57_5 = e2 & op(e2, e1) = e2
% 132.56/18.86 | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | ALPHA: (2853) implies:
% 132.56/18.86 | | | | | | | | | | | | (2854) op(e2, e1) = e2
% 132.56/18.86 | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | BETA: splitting (217) gives:
% 132.56/18.86 | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | Case 1:
% 132.56/18.86 | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | (2855) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 132.56/18.86 | | | | | | | | | | | | | & op(e1, e2) = e2)
% 132.56/18.86 | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | BETA: splitting (2855) gives:
% 132.56/18.86 | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | Case 1:
% 132.56/18.86 | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | (2856) all_57_6 = e2 & op(e1, e3) = e2
% 132.56/18.86 | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | REF_CLOSE: (163), (1826), (2856), (function-axioms) are
% 132.56/18.86 | | | | | | | | | | | | | | inconsistent by sub-proof #341.
% 132.56/18.86 | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | Case 2:
% 132.56/18.86 | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | (2857) all_57_7 = e2 & op(e1, e2) = e2
% 132.56/18.86 | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | ALPHA: (2857) implies:
% 132.56/18.86 | | | | | | | | | | | | | | (2858) op(e1, e2) = e2
% 132.56/18.86 | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e2,
% 132.56/18.86 | | | | | | | | | | | | | | e2, e1, simplifying with (162), (2858) gives:
% 132.56/18.86 | | | | | | | | | | | | | | (2859) all_52_6 = e2
% 132.56/18.86 | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2,
% 132.56/18.86 | | | | | | | | | | | | | | e1, e2, simplifying with (165), (2854) gives:
% 132.56/18.86 | | | | | | | | | | | | | | (2860) all_52_9 = e2
% 132.56/18.86 | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | REDUCE: (117), (2860) imply:
% 132.56/18.86 | | | | | | | | | | | | | | (2861) ~ (all_52_13 = e2)
% 132.56/18.86 | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | SIMP: (2861) implies:
% 132.56/18.86 | | | | | | | | | | | | | | (2862) ~ (all_52_13 = e2)
% 132.56/18.86 | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | REDUCE: (356), (2860) imply:
% 132.56/18.86 | | | | | | | | | | | | | | (2863) ~ (all_8_2 = e2)
% 132.56/18.86 | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | SIMP: (2863) implies:
% 132.56/18.86 | | | | | | | | | | | | | | (2864) ~ (all_8_2 = e2)
% 132.56/18.86 | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | REDUCE: (362), (2860) imply:
% 132.56/18.86 | | | | | | | | | | | | | | (2865) ~ (all_6_2 = e2)
% 132.56/18.86 | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 132.56/18.86 | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | Case 1:
% 132.56/18.86 | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | (2866) all_54_5 = e3
% 132.56/18.86 | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | REF_CLOSE: (267), (376), (2866) are inconsistent by sub-proof
% 132.56/18.86 | | | | | | | | | | | | | | | #554.
% 132.56/18.86 | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | Case 2:
% 132.56/18.86 | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | (2867) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 132.56/18.86 | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | BETA: splitting (2867) gives:
% 132.56/18.86 | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | Case 1:
% 132.56/18.86 | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | (2868) all_54_5 = e2
% 132.56/18.86 | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | REF_CLOSE: (267), (2864), (2868) are inconsistent by
% 132.56/18.86 | | | | | | | | | | | | | | | | sub-proof #340.
% 132.56/18.86 | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | Case 2:
% 132.56/18.86 | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | (2869) ~ (all_54_5 = e2)
% 132.56/18.86 | | | | | | | | | | | | | | | | (2870) all_54_5 = e1 | all_54_5 = e0
% 132.56/18.86 | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | BETA: splitting (2870) gives:
% 132.56/18.86 | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.86 | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | (2871) all_54_5 = e1
% 132.56/18.86 | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (373), (2871) are inconsistent by sub-proof
% 132.56/18.86 | | | | | | | | | | | | | | | | | #339.
% 132.56/18.86 | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.86 | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | (2872) all_54_5 = e0
% 132.56/18.86 | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (2872) imply:
% 132.56/18.86 | | | | | | | | | | | | | | | | | (2873) all_8_2 = e0
% 132.56/18.86 | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | SIMP: (2873) implies:
% 132.56/18.86 | | | | | | | | | | | | | | | | | (2874) all_8_2 = e0
% 132.56/18.86 | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | REDUCE: (347), (2874) imply:
% 132.56/18.86 | | | | | | | | | | | | | | | | | (2875) ~ (all_52_1 = e0)
% 132.56/18.86 | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | REDUCE: (354), (2874) imply:
% 132.56/18.86 | | | | | | | | | | | | | | | | | (2876) ~ (all_52_7 = e0)
% 132.56/18.86 | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | REDUCE: (358), (2874) imply:
% 132.56/18.86 | | | | | | | | | | | | | | | | | (2877) ~ (all_52_13 = e0)
% 132.56/18.86 | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | REDUCE: (2864), (2874) imply:
% 132.56/18.86 | | | | | | | | | | | | | | | | | (2878) ~ (e2 = e0)
% 132.56/18.86 | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | REDUCE: (42), (2874) imply:
% 132.56/18.86 | | | | | | | | | | | | | | | | | (2879) op(e2, e2) = e0
% 132.56/18.86 | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | BETA: splitting (1823) gives:
% 132.56/18.86 | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.86 | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | (2880) ~ (all_16_0 = e1) & op(e2, e3) = all_16_0 &
% 132.56/18.86 | | | | | | | | | | | | | | | | | | $i(all_16_0)
% 132.56/18.86 | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | ALPHA: (2880) implies:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | (2881) ~ (all_16_0 = e1)
% 132.56/18.86 | | | | | | | | | | | | | | | | | | (2882) op(e2, e3) = all_16_0
% 132.56/18.86 | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 132.56/18.86 | | | | | | | | | | | | | | | | | | all_16_0, e3, e2, simplifying with (167), (2882)
% 132.56/18.86 | | | | | | | | | | | | | | | | | | gives:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | (2883) all_52_1 = all_16_0
% 132.56/18.86 | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (2883) imply:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | (2884) all_54_4 = all_16_0
% 132.56/18.86 | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | REDUCE: (149), (2883) imply:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | (2885) ~ (all_52_2 = all_16_0)
% 132.56/18.86 | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | SIMP: (2885) implies:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | (2886) ~ (all_52_2 = all_16_0)
% 132.56/18.86 | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | REDUCE: (145), (2883) imply:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | (2887) ~ (all_52_13 = all_16_0)
% 132.56/18.86 | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | SIMP: (2887) implies:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | (2888) ~ (all_52_13 = all_16_0)
% 132.56/18.86 | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | REDUCE: (1825), (2883) imply:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | (2889) ~ (all_16_0 = e2)
% 132.56/18.86 | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | REDUCE: (2875), (2883) imply:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | (2890) ~ (all_16_0 = e0)
% 132.56/18.86 | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 132.56/18.86 | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.86 | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | (2891) all_54_4 = e3
% 132.56/18.86 | | | | | | | | | | | | | | | | | | |
% 132.56/18.86 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2884), (2891) imply:
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | (2892) all_16_0 = e3
% 132.56/18.87 | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | REDUCE: (2886), (2892) imply:
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | (2893) ~ (all_52_2 = e3)
% 132.56/18.87 | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | REDUCE: (2888), (2892) imply:
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | (2894) ~ (all_52_13 = e3)
% 132.56/18.87 | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | REDUCE: (2882), (2892) imply:
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | (2895) op(e2, e3) = e3
% 132.56/18.87 | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 132.56/18.87 | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | (2896) all_54_7 = e3
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (2894), (2896) are inconsistent by
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | sub-proof #338.
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | (2897) ~ (all_54_7 = e3)
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | (2898) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2898) gives:
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | (2899) all_54_7 = e2
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (2862), (2899) are inconsistent by
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | sub-proof #337.
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | (2900) ~ (all_54_7 = e2)
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | (2901) all_54_7 = e1 | all_54_7 = e0
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2901) gives:
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | (2902) all_54_7 = e1
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (2902) imply:
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | (2903) all_52_13 = e1
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | SIMP: (2903) implies:
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | (2904) all_52_13 = e1
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (2904) imply:
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | (2905) ~ (all_52_14 = e1)
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | SIMP: (2905) implies:
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | (2906) ~ (all_52_14 = e1)
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2862), (2904) imply:
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | (2907) ~ (e2 = e1)
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (2904) imply:
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | (2908) op(e2, e0) = e1
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | (2909) ~ (all_26_2 = e2)
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2847), (2909) imply:
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | (2910) $false
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2910) is inconsistent.
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | (2911) ( ~ (all_26_0 = e1) & op(e2, e0) = all_26_0 &
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | $i(all_26_0)) | ( ~ (all_26_1 = e3) & op(e2, e2)
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | = all_26_1 & $i(all_26_1))
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2911) gives:
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | (2912) ~ (all_26_0 = e1) & op(e2, e0) = all_26_0 &
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_26_0)
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2912) implies:
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | (2913) ~ (all_26_0 = e1)
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | (2914) op(e2, e0) = all_26_0
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2908), (2913), (2914), (function-axioms) are
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #336.
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | (2915) ~ (all_26_1 = e3) & op(e2, e2) = all_26_1 &
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_26_1)
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2915) implies:
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | (2916) ~ (all_26_1 = e3)
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | (2917) op(e2, e2) = all_26_1
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | (2918) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2918) gives:
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | (2919) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1834), (2895), (2919), (function-axioms) are
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #335.
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (2920) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2920) gives:
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2921) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3,
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2921) implies:
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2922) op(e3, e3) = e0
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1834), (2922), (function-axioms) are
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495.
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2923) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2,
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2923) implies:
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2924) op(e2, e2) = e3
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2916), (2917), (2924), (function-axioms) are
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #334.
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | (2925) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2925) gives:
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (2926) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2926) gives:
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2927) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2927) implies:
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2928) ~ (all_56_25 = e0)
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2929) ~ (all_56_17 = e1)
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2930) op(e1, e1) = e3
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2931) op(e1, e3) = e1
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2932) op(e3, e0) = all_56_25
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2933) op(e3, e1) = all_56_17
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2934) op(e3, e3) = all_56_1
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, e3,
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e1, simplifying with (39), (2930) gives:
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2935) all_6_2 = e3
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1,
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (163), (2931) gives:
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2936) all_52_2 = e1
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_25, e0, e3, simplifying with (168), (2932)
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2937) all_56_25 = all_52_12
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_56_1,
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (1834), (2934) gives:
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2938) all_56_1 = e2
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (302), (2935) imply:
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2939) all_36_2 = e3
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2928), (2937) imply:
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2940) ~ (all_52_12 = e0)
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2893), (2936) imply:
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2941) ~ (e3 = e1)
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (2935) imply:
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2942) ~ (all_52_14 = e3)
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2943) ~ (all_36_2 = e3)
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2939), (2943) imply:
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2944) $false
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2944) is inconsistent.
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2945) ( ~ (all_36_0 = e0) & op(e3, e1) = all_36_0 &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_36_0)) | ( ~ (all_36_1 = e2) & op(e3, e3)
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_36_1 & $i(all_36_1))
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (160), (164), (168),
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (214), (232), (234), (1834), (2850), (2894),
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2929), (2933), (2940), (2942), (2945),
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #328.
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2946) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 =
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2,
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2946) implies:
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2947) op(e2, e2) = e1
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2879), (2947), (function-axioms) are
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675.
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (2948) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2948) gives:
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2949) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2949) implies:
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2950) op(e2, e0) = e2
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2862), (2950), (function-axioms) are
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2951) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2951) gives:
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2952) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2952) implies:
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2953) op(e1, e1) = e2
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (2953), (function-axioms) are
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2954) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2954) implies:
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2955) op(e0, e0) = all_56_31
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2956) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2956) gives:
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2957) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27))
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (158), (2850), (2876), (2955), (2957),
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #507.
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2958) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2958) gives:
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2959) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7)
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23)
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2959) implies:
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2960) op(e1, e0) = e1
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (2906), (2960), (function-axioms) are
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #327.
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2961) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2961) implies:
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2962) all_56_31 = e1
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2955), (2962) imply:
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2963) op(e0, e0) = e1
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2850), (2963), (function-axioms) are
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #636.
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | (2964) all_54_7 = e0
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (2877), (2964) are inconsistent by
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | sub-proof #326.
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.89 | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.89 | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | (2965) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 132.56/18.89 | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2881), (2884), (2889), (2890), (2965) are
% 132.56/18.89 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #381.
% 132.56/18.89 | | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.89 | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.89 | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | (2966) ~ (all_16_1 = e0) & op(e2, e2) = all_16_1 &
% 132.56/18.89 | | | | | | | | | | | | | | | | | | $i(all_16_1)
% 132.56/18.89 | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2879), (2966), (function-axioms) are inconsistent
% 132.56/18.89 | | | | | | | | | | | | | | | | | | by sub-proof #380.
% 132.56/18.89 | | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | | End of split
% 132.56/18.89 | | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | End of split
% 132.56/18.89 | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | End of split
% 132.56/18.89 | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | End of split
% 132.56/18.89 | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | End of split
% 132.56/18.89 | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | Case 2:
% 132.56/18.89 | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | (2967) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 132.56/18.89 | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 132.56/18.89 | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | REF_CLOSE: (39), (160), (372), (2849), (2967),
% 132.56/18.89 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.56/18.89 | | | | | | | | | | | | | #513.
% 132.56/18.89 | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | End of split
% 132.56/18.89 | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | End of split
% 132.56/18.89 | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | Case 2:
% 132.56/18.89 | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | (2968) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 132.56/18.89 | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 132.56/18.89 | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | REF_CLOSE: (39), (157), (372), (2848), (2968),
% 132.56/18.89 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.56/18.89 | | | | | | | | | | | #511.
% 132.56/18.89 | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | End of split
% 132.56/18.89 | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | End of split
% 132.56/18.89 | | | | | | | | |
% 132.56/18.89 | | | | | | | | Case 2:
% 132.56/18.89 | | | | | | | | |
% 132.56/18.89 | | | | | | | | | (2969) all_57_1 = e2 & op(e3, e2) = e2
% 132.56/18.89 | | | | | | | | |
% 132.56/18.89 | | | | | | | | | REF_CLOSE: (170), (1828), (2969), (function-axioms) are
% 132.56/18.89 | | | | | | | | | inconsistent by sub-proof #396.
% 132.56/18.89 | | | | | | | | |
% 132.56/18.89 | | | | | | | | End of split
% 132.56/18.89 | | | | | | | |
% 132.56/18.89 | | | | | | | Case 2:
% 132.56/18.89 | | | | | | | |
% 132.56/18.89 | | | | | | | | (2970) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 &
% 132.56/18.89 | | | | | | | | op(e3, e0) = e2)
% 132.56/18.89 | | | | | | | |
% 132.56/18.89 | | | | | | | | BETA: splitting (2970) gives:
% 132.56/18.89 | | | | | | | |
% 132.56/18.89 | | | | | | | | Case 1:
% 132.56/18.89 | | | | | | | | |
% 132.56/18.89 | | | | | | | | | (2971) all_57_4 = e2 & op(e3, e1) = e2
% 132.56/18.89 | | | | | | | | |
% 132.56/18.89 | | | | | | | | | REF_CLOSE: (169), (1829), (2971), (function-axioms) are
% 132.56/18.89 | | | | | | | | | inconsistent by sub-proof #442.
% 132.56/18.89 | | | | | | | | |
% 132.56/18.89 | | | | | | | | Case 2:
% 132.56/18.89 | | | | | | | | |
% 132.56/18.89 | | | | | | | | | (2972) all_57_9 = e2 & op(e3, e0) = e2
% 132.56/18.89 | | | | | | | | |
% 132.56/18.89 | | | | | | | | | REF_CLOSE: (168), (1830), (2972), (function-axioms) are
% 132.56/18.89 | | | | | | | | | inconsistent by sub-proof #460.
% 132.56/18.89 | | | | | | | | |
% 132.56/18.89 | | | | | | | | End of split
% 132.56/18.89 | | | | | | | |
% 132.56/18.89 | | | | | | | End of split
% 132.56/18.89 | | | | | | |
% 132.56/18.89 | | | | | | End of split
% 132.56/18.89 | | | | | |
% 132.56/18.89 | | | | | Case 2:
% 132.56/18.89 | | | | | |
% 132.56/18.89 | | | | | | (2973) all_14_2 = e3
% 132.56/18.89 | | | | | |
% 132.56/18.89 | | | | | | COMBINE_EQS: (329), (2973) imply:
% 132.56/18.89 | | | | | | (2974) all_8_2 = e3
% 132.56/18.89 | | | | | |
% 132.56/18.89 | | | | | | SIMP: (2974) implies:
% 132.56/18.89 | | | | | | (2975) all_8_2 = e3
% 132.56/18.89 | | | | | |
% 132.56/18.89 | | | | | | COMBINE_EQS: (322), (2975) imply:
% 132.56/18.89 | | | | | | (2976) all_22_2 = e3
% 132.56/18.89 | | | | | |
% 132.56/18.89 | | | | | | REDUCE: (347), (2975) imply:
% 132.56/18.89 | | | | | | (2977) ~ (all_52_1 = e3)
% 132.56/18.89 | | | | | |
% 132.56/18.89 | | | | | | REDUCE: (350), (2975) imply:
% 132.56/18.89 | | | | | | (2978) ~ (all_52_4 = e3)
% 132.56/18.89 | | | | | |
% 132.56/18.89 | | | | | | REDUCE: (352), (2975) imply:
% 132.56/18.89 | | | | | | (2979) ~ (all_52_6 = e3)
% 132.56/18.89 | | | | | |
% 132.56/18.89 | | | | | | REDUCE: (354), (2975) imply:
% 132.56/18.89 | | | | | | (2980) ~ (all_52_7 = e3)
% 132.56/18.89 | | | | | |
% 132.56/18.89 | | | | | | REDUCE: (356), (2975) imply:
% 132.56/18.89 | | | | | | (2981) ~ (all_52_9 = e3)
% 132.56/18.89 | | | | | |
% 132.56/18.89 | | | | | | REDUCE: (358), (2975) imply:
% 132.56/18.89 | | | | | | (2982) ~ (all_52_13 = e3)
% 132.56/18.89 | | | | | |
% 132.56/18.89 | | | | | | BETA: splitting (230) gives:
% 132.56/18.89 | | | | | |
% 132.56/18.89 | | | | | | Case 1:
% 132.56/18.89 | | | | | | |
% 132.56/18.89 | | | | | | | (2983) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 &
% 132.56/18.89 | | | | | | | op(e2, e2) = e3)
% 132.56/18.89 | | | | | | |
% 132.56/18.89 | | | | | | | BETA: splitting (2983) gives:
% 132.56/18.89 | | | | | | |
% 132.56/18.89 | | | | | | | Case 1:
% 132.56/18.89 | | | | | | | |
% 132.56/18.89 | | | | | | | | (2984) all_57_1 = e3 & op(e3, e2) = e3
% 132.56/18.89 | | | | | | | |
% 132.56/18.89 | | | | | | | | ALPHA: (2984) implies:
% 132.56/18.89 | | | | | | | | (2985) op(e3, e2) = e3
% 132.56/18.89 | | | | | | | |
% 132.56/18.89 | | | | | | | | REF_CLOSE: (170), (2978), (2985), (function-axioms) are
% 132.56/18.89 | | | | | | | | inconsistent by sub-proof #738.
% 132.56/18.89 | | | | | | | |
% 132.56/18.89 | | | | | | | Case 2:
% 132.56/18.89 | | | | | | | |
% 132.56/18.89 | | | | | | | | (2986) all_57_3 = e3 & op(e2, e2) = e3
% 132.56/18.89 | | | | | | | |
% 132.56/18.89 | | | | | | | | ALPHA: (2986) implies:
% 132.56/18.89 | | | | | | | | (2987) all_57_3 = e3
% 132.56/18.89 | | | | | | | | (2988) op(e2, e2) = e3
% 132.56/18.89 | | | | | | | |
% 132.56/18.89 | | | | | | | | BETA: splitting (55) gives:
% 132.56/18.89 | | | | | | | |
% 132.56/18.89 | | | | | | | | Case 1:
% 132.56/18.89 | | | | | | | | |
% 132.56/18.89 | | | | | | | | | (2989) ~ (all_16_2 = e2)
% 132.56/18.89 | | | | | | | | |
% 132.56/18.89 | | | | | | | | | REDUCE: (327), (2989) imply:
% 132.56/18.89 | | | | | | | | | (2990) ~ (all_10_2 = e2)
% 132.56/18.89 | | | | | | | | |
% 132.56/18.89 | | | | | | | | | BETA: splitting (61) gives:
% 132.56/18.89 | | | | | | | | |
% 132.56/18.89 | | | | | | | | | Case 1:
% 132.56/18.89 | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | (2991) ~ (all_20_2 = e2)
% 132.56/18.89 | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | REDUCE: (318), (2991) imply:
% 132.56/18.89 | | | | | | | | | | (2992) ~ (all_4_2 = e2)
% 132.56/18.89 | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | BETA: splitting (64) gives:
% 132.56/18.89 | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | Case 1:
% 132.56/18.89 | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | (2993) ~ (all_22_2 = e3)
% 132.56/18.89 | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | REDUCE: (2976), (2993) imply:
% 132.56/18.89 | | | | | | | | | | | (2994) $false
% 132.56/18.89 | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | CLOSE: (2994) is inconsistent.
% 132.56/18.89 | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | Case 2:
% 132.56/18.89 | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | (2995) ( ~ (all_22_0 = e0) & op(e3, e2) = all_22_0 &
% 132.56/18.89 | | | | | | | | | | | $i(all_22_0)) | ( ~ (all_22_1 = e1) & op(e3, e3)
% 132.56/18.89 | | | | | | | | | | | = all_22_1 & $i(all_22_1))
% 132.56/18.89 | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | BETA: splitting (73) gives:
% 132.56/18.89 | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | Case 1:
% 132.56/18.89 | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | (2996) ~ (all_28_2 = e3)
% 132.56/18.89 | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | REDUCE: (316), (2996) imply:
% 132.56/18.89 | | | | | | | | | | | | (2997) ~ (all_6_2 = e3)
% 132.56/18.89 | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | BETA: splitting (79) gives:
% 132.56/18.89 | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | Case 1:
% 132.56/18.89 | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | (2998) ~ (all_32_2 = e1)
% 132.56/18.89 | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | REDUCE: (312), (2998) imply:
% 132.56/18.89 | | | | | | | | | | | | | (2999) ~ (all_10_2 = e1)
% 132.56/18.89 | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | BETA: splitting (204) gives:
% 132.56/18.89 | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | Case 1:
% 132.56/18.89 | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | (3000) all_54_0 = e3
% 132.56/18.89 | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | COMBINE_EQS: (278), (3000) imply:
% 132.56/18.89 | | | | | | | | | | | | | | (3001) all_10_2 = e3
% 132.56/18.89 | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | REDUCE: (338), (3001) imply:
% 132.56/18.89 | | | | | | | | | | | | | | (3002) ~ (all_52_2 = e3)
% 132.56/18.89 | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | REDUCE: (346), (3001) imply:
% 132.56/18.89 | | | | | | | | | | | | | | (3003) ~ (all_52_12 = e3)
% 132.56/18.89 | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | REDUCE: (45), (3001) imply:
% 132.56/18.89 | | | | | | | | | | | | | | (3004) op(e3, e3) = e3
% 132.56/18.89 | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 132.56/18.89 | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | Case 1:
% 132.56/18.89 | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | (3005) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 132.56/18.89 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.56/18.89 | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 132.56/18.89 | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 132.56/18.89 | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.56/18.89 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 132.56/18.89 | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.56/18.89 | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.56/18.89 | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.56/18.89 | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 132.56/18.89 | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 132.56/18.89 | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.56/18.89 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 132.56/18.89 | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 132.56/18.89 | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.56/18.89 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.56/18.89 | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 132.56/18.89 | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 132.56/18.89 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.89 | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.56/18.89 | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.56/18.89 | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.56/18.89 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.56/18.89 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.89 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.56/18.89 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 132.56/18.89 | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.89 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 132.56/18.89 | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | BETA: splitting (3005) gives:
% 132.56/18.89 | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | Case 1:
% 132.56/18.89 | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | (3006) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 132.56/18.89 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.56/18.89 | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 132.56/18.89 | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 132.56/18.89 | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.56/18.89 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 132.56/18.89 | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.56/18.89 | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.56/18.89 | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.56/18.89 | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 132.56/18.89 | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 132.56/18.89 | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.56/18.89 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 132.56/18.89 | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 132.56/18.89 | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (3004), (3006), (function-axioms) are
% 132.56/18.89 | | | | | | | | | | | | | | | | inconsistent by sub-proof #623.
% 132.56/18.89 | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | Case 2:
% 132.56/18.89 | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | (3007) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.56/18.89 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.56/18.89 | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 132.56/18.89 | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 132.56/18.89 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.89 | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.56/18.89 | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.56/18.89 | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.56/18.89 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.56/18.89 | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.89 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.56/18.89 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 132.56/18.89 | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.89 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 132.56/18.89 | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | REF_CLOSE: (168), (3003), (3004), (3007), (function-axioms)
% 132.56/18.89 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #553.
% 132.56/18.89 | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | End of split
% 132.56/18.89 | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | Case 2:
% 132.56/18.89 | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | (3008) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.56/18.89 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.56/18.89 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.89 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.56/18.89 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 132.56/18.89 | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.89 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 132.56/18.89 | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 132.56/18.89 | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 132.56/18.89 | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 132.56/18.89 | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.56/18.89 | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 132.56/18.89 | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.56/18.89 | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 132.56/18.89 | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 132.56/18.89 | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.56/18.89 | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 132.56/18.89 | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.56/18.89 | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 132.56/18.89 | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.56/18.89 | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 132.56/18.89 | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 132.56/18.89 | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 132.56/18.89 | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.56/18.89 | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 132.56/18.89 | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 132.56/18.89 | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 132.56/18.89 | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 132.56/18.89 | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 132.56/18.89 | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 132.56/18.89 | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 132.56/18.89 | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.89 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 132.56/18.89 | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 132.56/18.89 | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.89 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 132.56/18.89 | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 132.56/18.89 | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 132.56/18.89 | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.56/18.89 | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.56/18.89 | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 132.56/18.89 | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 132.56/18.89 | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 132.56/18.89 | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 132.56/18.89 | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 132.56/18.89 | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 132.56/18.89 | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 132.56/18.89 | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 132.56/18.89 | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 132.56/18.89 | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.56/18.89 | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.56/18.89 | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.56/18.89 | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.56/18.89 | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.56/18.89 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.56/18.89 | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.56/18.89 | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.56/18.89 | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | BETA: splitting (3008) gives:
% 132.56/18.89 | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | Case 1:
% 132.56/18.89 | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | (3009) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.56/18.89 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.56/18.89 | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.89 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.56/18.89 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 132.56/18.89 | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.89 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 132.56/18.89 | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 132.56/18.89 | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 132.56/18.89 | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 132.56/18.89 | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.56/18.89 | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 132.56/18.89 | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.56/18.89 | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 132.56/18.89 | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (2988), (2997), (3009),
% 132.56/18.89 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.56/18.89 | | | | | | | | | | | | | | | | #324.
% 132.56/18.89 | | | | | | | | | | | | | | | |
% 132.56/18.89 | | | | | | | | | | | | | | | Case 2:
% 132.56/18.89 | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | (3010) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 132.56/18.90 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.56/18.90 | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 132.56/18.90 | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 132.56/18.90 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.90 | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.56/18.90 | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.56/18.90 | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.56/18.90 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.56/18.90 | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 132.56/18.90 | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.56/18.90 | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 132.56/18.90 | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 132.56/18.90 | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.56/18.90 | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.56/18.90 | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 132.56/18.90 | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 132.56/18.90 | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.56/18.90 | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 132.56/18.90 | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 132.56/18.90 | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 132.56/18.90 | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 132.56/18.90 | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 132.56/18.90 | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 132.56/18.90 | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 132.56/18.90 | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 132.56/18.90 | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 132.56/18.90 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 132.56/18.90 | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 132.56/18.90 | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 132.56/18.90 | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.56/18.90 | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.56/18.90 | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.56/18.90 | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.56/18.90 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.90 | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 132.56/18.90 | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.56/18.90 | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.56/18.90 | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.56/18.90 | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.56/18.90 | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.56/18.90 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.56/18.90 | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.56/18.90 | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.56/18.90 | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | BETA: splitting (3010) gives:
% 132.56/18.90 | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.90 | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | (3011) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 132.56/18.90 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 132.56/18.90 | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 132.56/18.90 | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.56/18.90 | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 132.56/18.90 | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.56/18.90 | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 132.56/18.90 | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | ALPHA: (3011) implies:
% 132.56/18.90 | | | | | | | | | | | | | | | | | (3012) op(e2, e2) = e0
% 132.56/18.90 | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2988), (3012), (function-axioms) are
% 132.56/18.90 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641.
% 132.56/18.90 | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.90 | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | (3013) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.56/18.90 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.56/18.90 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 132.56/18.90 | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.56/18.90 | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 132.56/18.90 | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 132.56/18.90 | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.56/18.90 | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.56/18.90 | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 132.56/18.90 | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 132.56/18.90 | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.56/18.90 | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 132.56/18.90 | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 132.56/18.90 | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 132.56/18.90 | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 132.56/18.90 | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 132.56/18.90 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 132.56/18.90 | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 132.56/18.90 | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 132.56/18.90 | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.56/18.90 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.56/18.90 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.56/18.90 | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.56/18.90 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 132.56/18.90 | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.56/18.90 | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.56/18.90 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.56/18.90 | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.56/18.90 | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.56/18.90 | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.56/18.90 | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | BETA: splitting (3013) gives:
% 132.56/18.90 | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.90 | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | (3014) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.56/18.90 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 132.56/18.90 | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 132.56/18.90 | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 132.56/18.90 | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | ALPHA: (3014) implies:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | (3015) op(e1, e1) = e2
% 132.56/18.90 | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (3015), (function-axioms) are
% 132.56/18.90 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 132.56/18.90 | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.90 | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | (3016) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 132.56/18.90 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 132.56/18.90 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.56/18.90 | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 132.56/18.90 | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 132.56/18.90 | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 132.56/18.90 | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 132.56/18.90 | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 132.56/18.90 | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.56/18.90 | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 132.56/18.90 | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 132.56/18.90 | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.56/18.90 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.56/18.90 | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.56/18.90 | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.56/18.90 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 132.56/18.90 | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 132.56/18.90 | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 132.56/18.90 | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 132.56/18.90 | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 132.56/18.90 | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | ALPHA: (3016) implies:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | (3017) op(e0, e0) = all_56_31
% 132.56/18.90 | | | | | | | | | | | | | | | | | | (3018) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 132.56/18.90 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.56/18.90 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 132.56/18.90 | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 132.56/18.90 | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 132.56/18.90 | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 132.56/18.90 | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.56/18.90 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.56/18.90 | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 132.56/18.90 | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.56/18.90 | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 132.56/18.90 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.56/18.90 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 132.56/18.90 | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 132.56/18.90 | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 132.56/18.90 | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 132.56/18.90 | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 132.56/18.90 | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | (3019) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 132.56/18.90 | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (163), (2979), (3002), (3019),
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | #323.
% 132.56/18.90 | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | (3020) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 132.56/18.90 | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | BETA: splitting (3020) gives:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3021) all_57_8 = e3 & op(e1, e1) = e3
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | ALPHA: (3021) implies:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3022) op(e1, e1) = e3
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (2997), (3022), (function-axioms) are
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #771.
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3023) all_57_11 = e3 & op(e1, e0) = e3
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | ALPHA: (3023) implies:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3024) op(e1, e0) = e3
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | all_56_31, e0, e0, simplifying with (36), (3017)
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | gives:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3025) all_56_31 = all_4_2
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | e3, e0, e1, simplifying with (160), (3024) gives:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3026) all_52_14 = e3
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | REDUCE: (370), (3026) imply:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3027) ~ (all_4_2 = e3)
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | SIMP: (3027) implies:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3028) ~ (all_4_2 = e3)
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (189), (245), (371), (2992), (3018), (3025),
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3028) are inconsistent by sub-proof #322.
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.90 | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.90 | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | End of split
% 132.56/18.90 | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | End of split
% 132.56/18.90 | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | End of split
% 132.56/18.90 | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | End of split
% 132.56/18.90 | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | Case 2:
% 132.56/18.90 | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | (3029) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 132.56/18.90 | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | REF_CLOSE: (278), (374), (2990), (2999), (3029) are
% 132.56/18.90 | | | | | | | | | | | | | | inconsistent by sub-proof #777.
% 132.56/18.90 | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | End of split
% 132.56/18.90 | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | Case 2:
% 132.56/18.90 | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | (3030) all_32_2 = e1
% 132.56/18.90 | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | COMBINE_EQS: (312), (3030) imply:
% 132.56/18.90 | | | | | | | | | | | | | (3031) all_10_2 = e1
% 132.56/18.90 | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | SIMP: (3031) implies:
% 132.56/18.90 | | | | | | | | | | | | | (3032) all_10_2 = e1
% 132.56/18.90 | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | REDUCE: (336), (3032) imply:
% 132.56/18.90 | | | | | | | | | | | | | (3033) ~ (all_52_1 = e1)
% 132.56/18.90 | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | REDUCE: (342), (3032) imply:
% 132.56/18.90 | | | | | | | | | | | | | (3034) ~ (all_52_4 = e1)
% 132.56/18.90 | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | REDUCE: (344), (3032) imply:
% 132.56/18.90 | | | | | | | | | | | | | (3035) ~ (all_52_8 = e1)
% 132.56/18.90 | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | REDUCE: (346), (3032) imply:
% 132.56/18.90 | | | | | | | | | | | | | (3036) ~ (all_52_12 = e1)
% 132.56/18.90 | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | REDUCE: (45), (3032) imply:
% 132.56/18.90 | | | | | | | | | | | | | (3037) op(e3, e3) = e1
% 132.56/18.90 | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | BETA: splitting (2995) gives:
% 132.56/18.90 | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | Case 1:
% 132.56/18.90 | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | (3038) ~ (all_22_0 = e0) & op(e3, e2) = all_22_0 &
% 132.56/18.90 | | | | | | | | | | | | | | $i(all_22_0)
% 132.56/18.90 | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | ALPHA: (3038) implies:
% 132.56/18.90 | | | | | | | | | | | | | | (3039) ~ (all_22_0 = e0)
% 132.56/18.90 | | | | | | | | | | | | | | (3040) op(e3, e2) = all_22_0
% 132.56/18.90 | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4,
% 132.56/18.90 | | | | | | | | | | | | | | all_22_0, e2, e3, simplifying with (170), (3040)
% 132.56/18.90 | | | | | | | | | | | | | | gives:
% 132.56/18.90 | | | | | | | | | | | | | | (3041) all_52_4 = all_22_0
% 132.56/18.90 | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | COMBINE_EQS: (271), (3041) imply:
% 132.56/18.90 | | | | | | | | | | | | | | (3042) all_54_1 = all_22_0
% 132.56/18.90 | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | REDUCE: (134), (3041) imply:
% 132.56/18.90 | | | | | | | | | | | | | | (3043) ~ (all_52_8 = all_22_0)
% 132.56/18.90 | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | SIMP: (3043) implies:
% 132.56/18.90 | | | | | | | | | | | | | | (3044) ~ (all_52_8 = all_22_0)
% 132.56/18.90 | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | REDUCE: (133), (3041) imply:
% 132.56/18.90 | | | | | | | | | | | | | | (3045) ~ (all_52_12 = all_22_0)
% 132.56/18.90 | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | SIMP: (3045) implies:
% 132.56/18.90 | | | | | | | | | | | | | | (3046) ~ (all_52_12 = all_22_0)
% 132.56/18.90 | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | REDUCE: (2978), (3041) imply:
% 132.56/18.90 | | | | | | | | | | | | | | (3047) ~ (all_22_0 = e3)
% 132.56/18.90 | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | REDUCE: (3034), (3041) imply:
% 132.56/18.90 | | | | | | | | | | | | | | (3048) ~ (all_22_0 = e1)
% 132.56/18.90 | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 132.56/18.90 | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | Case 1:
% 132.56/18.90 | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | (3049) all_54_1 = e3
% 132.56/18.90 | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | COMBINE_EQS: (3042), (3049) imply:
% 132.56/18.90 | | | | | | | | | | | | | | | (3050) all_22_0 = e3
% 132.56/18.90 | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | REDUCE: (3047), (3050) imply:
% 132.56/18.90 | | | | | | | | | | | | | | | (3051) $false
% 132.56/18.90 | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | CLOSE: (3051) is inconsistent.
% 132.56/18.90 | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | Case 2:
% 132.56/18.90 | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | (3052) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 132.56/18.90 | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | BETA: splitting (3052) gives:
% 132.56/18.90 | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | Case 1:
% 132.56/18.90 | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | (3053) all_54_1 = e2
% 132.56/18.90 | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | COMBINE_EQS: (3042), (3053) imply:
% 132.56/18.90 | | | | | | | | | | | | | | | | (3054) all_22_0 = e2
% 132.56/18.90 | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | REDUCE: (3044), (3054) imply:
% 132.56/18.90 | | | | | | | | | | | | | | | | (3055) ~ (all_52_8 = e2)
% 132.56/18.90 | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | REDUCE: (3046), (3054) imply:
% 132.56/18.90 | | | | | | | | | | | | | | | | (3056) ~ (all_52_12 = e2)
% 132.56/18.90 | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 132.56/18.90 | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.90 | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | (3057) ~ (all_34_2 = e3)
% 132.56/18.90 | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | REDUCE: (307), (3057) imply:
% 132.56/18.90 | | | | | | | | | | | | | | | | | (3058) ~ (all_4_2 = e3)
% 132.56/18.90 | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 132.56/18.90 | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.90 | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | (3059) all_54_15 = e3
% 132.56/18.90 | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (3059) imply:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | (3060) all_4_2 = e3
% 132.56/18.90 | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | REDUCE: (3058), (3060) imply:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | (3061) $false
% 132.56/18.90 | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | CLOSE: (3061) is inconsistent.
% 132.56/18.90 | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.90 | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | (3062) ~ (all_54_15 = e3)
% 132.56/18.90 | | | | | | | | | | | | | | | | | | (3063) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 132.56/18.90 | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | BETA: splitting (3063) gives:
% 132.56/18.90 | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | (3064) all_54_15 = e2
% 132.56/18.90 | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (3064) imply:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | (3065) all_4_2 = e2
% 132.56/18.90 | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | REDUCE: (2992), (3065) imply:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | (3066) $false
% 132.56/18.90 | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | CLOSE: (3066) is inconsistent.
% 132.56/18.90 | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | (3067) ~ (all_54_15 = e2)
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | (3068) all_54_15 = e1 | all_54_15 = e0
% 132.56/18.90 | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | BETA: splitting (3068) gives:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3069) all_54_15 = e1
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (3069) imply:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3070) all_4_2 = e1
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (3070) imply:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3071) $false
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | CLOSE: (3071) is inconsistent.
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3072) all_54_15 = e0
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (3072) imply:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3073) all_4_2 = e0
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (3073) imply:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3074) ~ (all_52_12 = e0)
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (3073) imply:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3075) ~ (all_52_13 = e0)
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | REDUCE: (3058), (3073) imply:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3076) ~ (e3 = e0)
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | REDUCE: (2992), (3073) imply:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3077) ~ (e2 = e0)
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (3073) imply:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3078) ~ (e1 = e0)
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (3073) imply:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3079) op(e0, e0) = e0
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | (3080) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3080) gives:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | (3081) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (120), (169), (201), (269), (3036), (3037),
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | (3056), (3074), (3081), (function-axioms) are
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #318.
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | (3082) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3082) gives:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | (3083) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3,
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3083) implies:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | (3084) op(e3, e3) = e0
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3037), (3084), (function-axioms) are
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #717.
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | (3085) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2,
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3085) implies:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | (3086) op(e2, e3) = e2
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | (3087) all_54_3 = e3
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (3087) imply:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | (3088) all_52_12 = e3
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (3088) imply:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | (3089) ~ (all_52_8 = e3)
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (3088) imply:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | (3090) ~ (all_52_13 = e3)
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | | (3091) all_54_2 = e3
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (3091) imply:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | | (3092) all_52_8 = e3
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3089), (3092) imply:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | | (3093) $false
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3093) is inconsistent.
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | | (3094) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3094) gives:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | (3095) all_54_2 = e2
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (3055), (3095) are inconsistent by
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #317.
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | (3096) all_54_2 = e1 | all_54_2 = e0
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3096) gives:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3097) all_54_2 = e1
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (3035), (3097) are inconsistent by
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #316.
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3098) all_54_2 = e0
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (3098) imply:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3099) all_52_8 = e0
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3099) implies:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3100) all_52_8 = e0
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (3100) imply:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3101) ~ (all_52_9 = e0)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3101) implies:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3102) ~ (all_52_9 = e0)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3103) all_54_6 = e3
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (2981), (3103) are inconsistent by
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #315.
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3104) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3104) gives:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3105) all_54_6 = e2
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (3105) imply:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3106) all_52_9 = e2
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3106) implies:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3107) all_52_9 = e2
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (3107) imply:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3108) ~ (all_52_1 = e2)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (3086), (3108), (function-axioms) are
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #779.
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3109) all_54_6 = e1 | all_54_6 = e0
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (117), (145), (167), (197), (259), (260), (2982),
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3075), (3086), (3102), (3109), (function-axioms)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #311.
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | (3110) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (3036), (3056), (3074), (3110) are
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #320.
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | (3111) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3111) gives:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | (3112) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (2988), (2997), (3112),
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | #324.
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | (3113) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3113) gives:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | (3114) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3114) implies:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | (3115) op(e2, e2) = e0
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2988), (3115), (function-axioms) are
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641.
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | (3116) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3116) gives:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | (3117) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3117) implies:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | (3118) op(e1, e1) = e2
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (3118), (function-axioms) are
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | (3119) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3119) implies:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | (3120) op(e0, e0) = all_56_31
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | (3121) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3121) gives:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | (3122) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27))
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (3079), (3120), (3122),
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | #713.
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | (3123) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3123) gives:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | (3124) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3124) implies:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | (3125) op(e1, e1) = e0
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3126) all_54_3 = e3
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (3126) imply:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3127) all_52_12 = e3
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (3127) imply:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3128) ~ (all_52_8 = e3)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3129) all_54_2 = e3
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (3129) imply:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3130) all_52_8 = e3
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3128), (3130) imply:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3131) $false
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3131) is inconsistent.
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3132) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (194), (270), (334), (361), (372), (2997),
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3035), (3055), (3125), (3132), (function-axioms)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #476.
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3133) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (3036), (3056), (3074), (3133) are
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #320.
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | (3134) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3134) implies:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | (3135) op(e0, e1) = e0
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3136) all_54_3 = e3
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (3136) imply:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3137) all_52_12 = e3
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (3137) imply:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3138) ~ (all_52_8 = e3)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (3137) imply:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3139) ~ (all_52_13 = e3)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (3137) imply:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3140) ~ (all_52_14 = e3)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3140) implies:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3141) ~ (all_52_14 = e3)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3142) all_54_2 = e3
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (3142) imply:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3143) all_52_8 = e3
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3138), (3143) imply:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3144) $false
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3144) is inconsistent.
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3145) ~ (all_54_2 = e3)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3146) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3146) gives:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3147) all_54_2 = e2
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (3147) imply:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3148) all_52_8 = e2
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3055), (3148) imply:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3149) $false
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3149) is inconsistent.
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3150) all_54_2 = e1 | all_54_2 = e0
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3150) gives:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3151) all_54_2 = e1
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (3151) imply:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3152) all_52_8 = e1
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3035), (3152) imply:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3153) $false
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3153) is inconsistent.
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3154) all_54_2 = e0
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (3154) imply:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3155) all_52_8 = e0
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (3155) imply:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3156) ~ (all_52_9 = e0)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3156) implies:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3157) ~ (all_52_9 = e0)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (3155) imply:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3158) ~ (all_6_2 = e0)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3158) implies:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3159) ~ (all_6_2 = e0)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3160) all_54_10 = e3
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (2997), (3160) are inconsistent by
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #742.
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3161) ~ (all_54_10 = e3)
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3162) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3162) gives:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3163) all_54_10 = e2
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (372), (3163) are inconsistent by sub-proof
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #741.
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3164) all_54_10 = e1 | all_54_10 = e0
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3164) gives:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3165) all_54_10 = e1
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (3165) imply:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3166) all_6_2 = e1
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3166) implies:
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3167) all_6_2 = e1
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (3167) imply:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3168) ~ (all_52_9 = e1)
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2997), (3167) imply:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3169) ~ (e3 = e1)
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (3167) imply:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3170) op(e1, e1) = e1
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3171) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3171) gives:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3172) all_57_9 = e3 & op(e3, e0) = e3
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3172) implies:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3173) all_57_9 = e3
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3174) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (2981), (3138), (3174),
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #310.
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3175) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3175) gives:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3176) all_57_8 = e3 & op(e1, e1) = e3
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3176) implies:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3177) op(e1, e1) = e3
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (3170), (3177), (function-axioms) are
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #662.
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3178) all_57_14 = e3 & op(e0, e1) = e3
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3178) implies:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3179) op(e0, e1) = e3
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3180) all_54_6 = e3
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (3180) imply:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3181) all_52_9 = e3
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2981), (3181) imply:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3182) $false
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3182) is inconsistent.
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3183) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3183) gives:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3184) all_54_6 = e2
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (3184) imply:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3185) all_52_9 = e2
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (3185) imply:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3186) ~ (all_52_1 = e2)
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3187) all_54_4 = e3
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (3187) imply:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3188) all_52_1 = e3
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2977), (3188) imply:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3189) $false
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3189) is inconsistent.
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3190) ~ (all_54_4 = e3)
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3191) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3191) gives:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3192) all_54_4 = e2
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (3192) imply:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3193) all_52_1 = e2
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3186), (3193) imply:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3194) $false
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3194) is inconsistent.
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3195) all_54_4 = e1 | all_54_4 = e0
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3195) gives:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3196) all_54_4 = e1
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (3196) imply:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3197) all_52_1 = e1
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3033), (3197) imply:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3198) $false
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3198) is inconsistent.
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3199) all_54_4 = e0
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (3199) imply:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3200) all_52_1 = e0
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e3, e1,
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, simplifying with (3135), (3179) gives:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3201) e3 = e0
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3173), (3201) imply:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3202) all_57_9 = e0
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (160), (164), (214), (2982), (3079), (3141),
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3202), (function-axioms) are inconsistent by
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #386.
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3203) all_54_6 = e1 | all_54_6 = e0
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (3157), (3168), (3203) are inconsistent by
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #479.
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3204) all_57_10 = e3 & op(e2, e0) = e3
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2982), (3204), (function-axioms) are
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749.
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3205) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (160), (3079), (3141), (3205),
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #387.
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3206) all_54_10 = e0
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (3159), (3206) are inconsistent by
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #506.
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3207) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (3036), (3056), (3074), (3207) are
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #320.
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.92 | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | (3208) all_34_2 = e3
% 132.56/18.92 | | | | | | | | | | | | | | | | | (3209) ( ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 &
% 132.56/18.92 | | | | | | | | | | | | | | | | | $i(all_34_0)) | ( ~ (all_34_1 = e1) & op(e3, e3)
% 132.56/18.92 | | | | | | | | | | | | | | | | | = all_34_1 & $i(all_34_1))
% 132.56/18.92 | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (3208) imply:
% 132.56/18.92 | | | | | | | | | | | | | | | | | (3210) all_4_2 = e3
% 132.56/18.92 | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | SIMP: (3210) implies:
% 132.56/18.92 | | | | | | | | | | | | | | | | | (3211) all_4_2 = e3
% 132.56/18.92 | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | REDUCE: (367), (3211) imply:
% 132.56/18.92 | | | | | | | | | | | | | | | | | (3212) ~ (all_52_11 = e3)
% 132.56/18.92 | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | REDUCE: (368), (3211) imply:
% 132.56/18.92 | | | | | | | | | | | | | | | | | (3213) ~ (all_52_12 = e3)
% 132.56/18.92 | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | REDUCE: (370), (3211) imply:
% 132.56/18.92 | | | | | | | | | | | | | | | | | (3214) ~ (all_52_14 = e3)
% 132.56/18.92 | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | REDUCE: (36), (3211) imply:
% 132.56/18.92 | | | | | | | | | | | | | | | | | (3215) op(e0, e0) = e3
% 132.56/18.92 | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 132.56/18.92 | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.92 | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | (3216) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 132.56/18.92 | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 132.56/18.92 | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | BETA: splitting (3216) gives:
% 132.56/18.92 | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | (3217) all_57_6 = e3 & op(e1, e3) = e3
% 132.56/18.92 | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | ALPHA: (3217) implies:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | (3218) all_57_6 = e3
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | (3219) op(e1, e3) = e3
% 132.56/18.92 | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | (3220) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | BETA: splitting (3220) gives:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | (3221) all_57_4 = e3 & op(e3, e1) = e3
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | ALPHA: (3221) implies:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | (3222) all_57_4 = e3
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | (3223) all_54_3 = e3
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (3223) imply:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | (3224) all_52_12 = e3
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3213), (3224) imply:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | (3225) $false
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3225) is inconsistent.
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | (3226) ~ (all_54_3 = e3)
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | (3227) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | (3228) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3228) gives:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | (3229) all_57_6 = e2 & op(e1, e3) = e2
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3229) implies:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | (3230) all_57_6 = e2
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3218), (3230) imply:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | (3231) e3 = e2
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (3231) imply:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | (3232) $false
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3232) is inconsistent.
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | (3233) all_57_7 = e2 & op(e1, e2) = e2
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3233) implies:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | (3234) all_57_7 = e2
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (227), (228),
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | (232), (236), (238), (2978), (2988), (3037),
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | (3039), (3040), (3234), (function-axioms) are
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #308.
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | (3235) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3235) gives:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | (3236) all_57_8 = e2 & op(e1, e1) = e2
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3236) implies:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | (3237) op(e1, e1) = e2
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (3237), (function-axioms) are
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | (3238) all_57_11 = e2 & op(e1, e0) = e2
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3238) implies:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | (3239) all_57_11 = e2
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | (3240) op(e1, e0) = e2
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | (3241) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3037), (3039), (3040), (3241),
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | #307.
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | (3242) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3242) gives:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (3243) all_57_4 = e0 & op(e3, e1) = e0
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3222), (3243) are inconsistent by sub-proof
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | #384.
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (3244) all_57_9 = e0 & op(e3, e0) = e0
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3244) implies:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (3245) all_57_9 = e0
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3209) gives:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3246) ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 &
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_34_0)
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3246) implies:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3247) ~ (all_34_0 = e2)
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3248) op(e3, e0) = all_34_0
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3249) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3249) gives:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3250) all_57_9 = e1 & op(e3, e0) = e1
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3250) implies:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3251) all_57_9 = e1
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3245), (3251) are inconsistent by sub-proof
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #383.
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3252) all_57_10 = e1 & op(e2, e0) = e1
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3252) implies:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3253) op(e2, e0) = e1
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3227) gives:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3254) all_54_3 = e2
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (3254) imply:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3255) all_52_12 = e2
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3056), (3255) imply:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3256) $false
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3256) is inconsistent.
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3257) all_54_3 = e1 | all_54_3 = e0
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3257) gives:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3258) all_54_3 = e1
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (3258) imply:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3259) all_52_12 = e1
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3036), (3259) imply:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3260) $false
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3260) is inconsistent.
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3261) all_54_3 = e0
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (3261) imply:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3262) all_52_12 = e0
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (3262) imply:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3263) ~ (all_52_13 = e0)
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3263) implies:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3264) ~ (all_52_13 = e0)
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3213), (3262) imply:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3265) ~ (e3 = e0)
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (3262) imply:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3266) op(e3, e0) = e0
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (39), (110), (160), (163), (164), (168),
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206), (208), (212), (214), (366), (2982), (2988),
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3037), (3213), (3214), (3219), (3239), (3240),
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3247), (3248), (3253), (3264), (3266),
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #631.
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3267) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (3215), (3240), (3267),
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #557.
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3268) ~ (all_34_1 = e1) & op(e3, e3) = all_34_1 &
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_34_1)
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3268) implies:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3269) ~ (all_34_1 = e1)
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3270) op(e3, e3) = all_34_1
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3037), (3269), (3270), (function-axioms) are
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #626.
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | (3271) all_57_5 = e3 & op(e2, e1) = e3
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (2981), (3271), (function-axioms) are
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547.
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | (3272) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (157), (2997), (3212), (3272),
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | | #651.
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | (3273) all_57_7 = e3 & op(e1, e2) = e3
% 132.56/18.92 | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | ALPHA: (3273) implies:
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | (3274) op(e1, e2) = e3
% 132.56/18.92 | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (2979), (3274), (function-axioms) are
% 132.56/18.92 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #654.
% 132.56/18.92 | | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.92 | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | (3275) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 132.56/18.92 | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 132.56/18.92 | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (160), (2997), (3214), (3275),
% 132.56/18.92 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.56/18.92 | | | | | | | | | | | | | | | | | | #653.
% 132.56/18.92 | | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | Case 2:
% 132.56/18.92 | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | (3276) all_54_1 = e1 | all_54_1 = e0
% 132.56/18.92 | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | | REF_CLOSE: (3039), (3042), (3048), (3276) are inconsistent by
% 132.56/18.92 | | | | | | | | | | | | | | | | sub-proof #306.
% 132.56/18.92 | | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | Case 2:
% 132.56/18.92 | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | (3277) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 &
% 132.56/18.92 | | | | | | | | | | | | | | $i(all_22_1)
% 132.56/18.92 | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | | REF_CLOSE: (3037), (3277), (function-axioms) are inconsistent
% 132.56/18.92 | | | | | | | | | | | | | | by sub-proof #305.
% 132.56/18.92 | | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | End of split
% 132.56/18.92 | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | Case 2:
% 132.56/18.92 | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | (3278) all_28_2 = e3
% 132.56/18.92 | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | COMBINE_EQS: (316), (3278) imply:
% 132.56/18.92 | | | | | | | | | | | | (3279) all_6_2 = e3
% 132.56/18.92 | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | SIMP: (3279) implies:
% 132.56/18.92 | | | | | | | | | | | | (3280) all_6_2 = e3
% 132.56/18.92 | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | REDUCE: (348), (3280) imply:
% 132.56/18.92 | | | | | | | | | | | | (3281) ~ (all_52_2 = e3)
% 132.56/18.92 | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | REDUCE: (361), (3280) imply:
% 132.56/18.92 | | | | | | | | | | | | (3282) ~ (all_52_8 = e3)
% 132.56/18.92 | | | | | | | | | | | |
% 132.56/18.92 | | | | | | | | | | | | REDUCE: (364), (3280) imply:
% 132.56/18.93 | | | | | | | | | | | | (3283) ~ (all_52_11 = e3)
% 132.56/18.93 | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | REDUCE: (39), (3280) imply:
% 132.56/18.93 | | | | | | | | | | | | (3284) op(e1, e1) = e3
% 132.56/18.93 | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | BETA: splitting (79) gives:
% 132.56/18.93 | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | Case 1:
% 132.56/18.93 | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | (3285) ~ (all_32_2 = e1)
% 132.56/18.93 | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | REDUCE: (312), (3285) imply:
% 132.56/18.93 | | | | | | | | | | | | | (3286) ~ (all_10_2 = e1)
% 132.56/18.93 | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | BETA: splitting (204) gives:
% 132.56/18.93 | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | Case 1:
% 132.56/18.93 | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | (3287) all_54_0 = e3
% 132.56/18.93 | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | COMBINE_EQS: (278), (3287) imply:
% 132.56/18.93 | | | | | | | | | | | | | | (3288) all_10_2 = e3
% 132.56/18.93 | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | SIMP: (3288) implies:
% 132.56/18.93 | | | | | | | | | | | | | | (3289) all_10_2 = e3
% 132.56/18.93 | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | REDUCE: (340), (3289) imply:
% 132.56/18.93 | | | | | | | | | | | | | | (3290) ~ (all_52_3 = e3)
% 132.56/18.93 | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | REDUCE: (346), (3289) imply:
% 132.56/18.93 | | | | | | | | | | | | | | (3291) ~ (all_52_12 = e3)
% 132.56/18.93 | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | REDUCE: (45), (3289) imply:
% 132.56/18.93 | | | | | | | | | | | | | | (3292) op(e3, e3) = e3
% 132.56/18.93 | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 132.56/18.93 | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | Case 1:
% 132.56/18.93 | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | (3293) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 132.56/18.93 | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 132.56/18.93 | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | BETA: splitting (3293) gives:
% 132.56/18.93 | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | Case 1:
% 132.56/18.93 | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | (3294) all_57_12 = e3 & op(e0, e3) = e3
% 132.56/18.93 | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | REF_CLOSE: (159), (3290), (3294), (function-axioms) are
% 132.56/18.93 | | | | | | | | | | | | | | | | inconsistent by sub-proof #628.
% 132.56/18.93 | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | Case 2:
% 132.56/18.93 | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | (3295) all_57_13 = e3 & op(e0, e2) = e3
% 132.56/18.93 | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | REF_CLOSE: (158), (2980), (3295), (function-axioms) are
% 132.56/18.93 | | | | | | | | | | | | | | | | inconsistent by sub-proof #556.
% 132.56/18.93 | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | End of split
% 132.56/18.93 | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | Case 2:
% 132.56/18.93 | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | (3296) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 132.56/18.93 | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 132.56/18.93 | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | BETA: splitting (3296) gives:
% 132.56/18.93 | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | Case 1:
% 132.56/18.93 | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | (3297) all_57_14 = e3 & op(e0, e1) = e3
% 132.56/18.93 | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | REF_CLOSE: (157), (3283), (3297), (function-axioms) are
% 132.56/18.93 | | | | | | | | | | | | | | | | inconsistent by sub-proof #652.
% 132.56/18.93 | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | Case 2:
% 132.56/18.93 | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | (3298) all_57_15 = e3 & op(e0, e0) = e3
% 132.56/18.93 | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | ALPHA: (3298) implies:
% 132.56/18.93 | | | | | | | | | | | | | | | | (3299) op(e0, e0) = e3
% 132.56/18.93 | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 132.56/18.93 | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.93 | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | (3300) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 132.56/18.93 | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.56/18.93 | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 132.56/18.93 | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 132.56/18.93 | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 132.56/18.93 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.56/18.93 | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.56/18.93 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 132.56/18.93 | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | BETA: splitting (3300) gives:
% 132.56/18.93 | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.93 | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | (3301) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 132.56/18.93 | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 132.56/18.93 | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 132.56/18.93 | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (3292), (3301), (function-axioms) are
% 132.56/18.93 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #623.
% 132.56/18.93 | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.93 | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | (3302) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 132.56/18.93 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.56/18.93 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 132.56/18.93 | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | BETA: splitting (3302) gives:
% 132.56/18.93 | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.93 | | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | (3303) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3,
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 132.56/18.93 | | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | ALPHA: (3303) implies:
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | (3304) op(e3, e0) = e3
% 132.56/18.93 | | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (3291), (3304), (function-axioms) are
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #733.
% 132.56/18.93 | | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.93 | | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | (3305) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2,
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 132.56/18.93 | | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | ALPHA: (3305) implies:
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | (3306) ~ (all_56_1 = e3)
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | (3307) op(e3, e3) = all_56_1
% 132.56/18.93 | | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_56_1,
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (3292), (3307) gives:
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | (3308) all_56_1 = e3
% 132.56/18.93 | | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | REDUCE: (3306), (3308) imply:
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | (3309) $false
% 132.56/18.93 | | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | CLOSE: (3309) is inconsistent.
% 132.56/18.93 | | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.93 | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | End of split
% 132.56/18.93 | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.93 | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | (3310) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.56/18.93 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 132.56/18.93 | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 132.56/18.93 | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 132.56/18.93 | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 132.56/18.93 | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.56/18.93 | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 132.56/18.93 | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 132.56/18.93 | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 132.56/18.93 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.56/18.93 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 132.56/18.93 | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.56/18.93 | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 132.56/18.93 | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 132.56/18.93 | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 132.56/18.93 | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 132.56/18.93 | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 132.56/18.93 | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 132.56/18.93 | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 132.56/18.93 | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 132.56/18.93 | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 132.56/18.93 | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 132.56/18.93 | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 132.56/18.93 | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.56/18.93 | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 132.56/18.93 | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 132.56/18.93 | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 132.56/18.93 | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.56/18.93 | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.56/18.93 | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.56/18.93 | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.56/18.93 | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.56/18.93 | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | BETA: splitting (3310) gives:
% 132.56/18.93 | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.93 | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | (3311) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.56/18.93 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 132.56/18.93 | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 132.56/18.93 | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 132.56/18.93 | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 132.56/18.93 | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 132.56/18.93 | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 132.56/18.93 | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | BETA: splitting (3311) gives:
% 132.56/18.93 | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.93 | | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | (3312) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 132.56/18.93 | | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | ALPHA: (3312) implies:
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | (3313) ~ (all_56_1 = e3)
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | (3314) op(e3, e3) = all_56_1
% 132.56/18.93 | | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3292), (3313), (3314), (function-axioms) are
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #766.
% 132.56/18.93 | | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.93 | | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | (3315) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2,
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 132.56/18.93 | | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | ALPHA: (3315) implies:
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | (3316) op(e2, e2) = e1
% 132.56/18.93 | | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2988), (3316), (function-axioms) are
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #325.
% 132.56/18.93 | | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.93 | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.93 | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | (3317) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 132.56/18.93 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 132.56/18.93 | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 132.56/18.93 | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 132.56/18.93 | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 132.56/18.93 | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 132.56/18.93 | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 132.56/18.93 | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 132.56/18.93 | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 132.56/18.93 | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.56/18.93 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.56/18.93 | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.56/18.93 | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.56/18.93 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.56/18.93 | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.56/18.93 | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.56/18.93 | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.56/18.93 | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.56/18.93 | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | BETA: splitting (3317) gives:
% 132.56/18.93 | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.93 | | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | (3318) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 132.56/18.93 | | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | ALPHA: (3318) implies:
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | (3319) op(e2, e2) = e0
% 132.56/18.93 | | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2988), (3319), (function-axioms) are
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641.
% 132.56/18.93 | | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.93 | | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | (3320) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.56/18.93 | | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | BETA: splitting (3320) gives:
% 132.56/18.93 | | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | (3321) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | ALPHA: (3321) implies:
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | (3322) op(e1, e1) = e2
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (3322), (function-axioms) are
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | (3323) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | ALPHA: (3323) implies:
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | (3324) op(e0, e0) = all_56_31
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | (3325) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (371), (2992), (3284), (3292), (3299),
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | (3324), (3325), (function-axioms) are inconsistent
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | | by sub-proof #751.
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.93 | | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.93 | | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | | End of split
% 132.56/18.93 | | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | | End of split
% 132.56/18.93 | | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | | End of split
% 132.56/18.93 | | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | End of split
% 132.56/18.93 | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | Case 2:
% 132.56/18.93 | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | (3326) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 132.56/18.93 | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | REF_CLOSE: (278), (374), (2990), (3286), (3326) are
% 132.56/18.93 | | | | | | | | | | | | | | inconsistent by sub-proof #777.
% 132.56/18.93 | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | End of split
% 132.56/18.93 | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | Case 2:
% 132.56/18.93 | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | (3327) all_32_2 = e1
% 132.56/18.93 | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | COMBINE_EQS: (312), (3327) imply:
% 132.56/18.93 | | | | | | | | | | | | | (3328) all_10_2 = e1
% 132.56/18.93 | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | SIMP: (3328) implies:
% 132.56/18.93 | | | | | | | | | | | | | (3329) all_10_2 = e1
% 132.56/18.93 | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | REDUCE: (338), (3329) imply:
% 132.56/18.93 | | | | | | | | | | | | | (3330) ~ (all_52_2 = e1)
% 132.56/18.93 | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | REDUCE: (342), (3329) imply:
% 132.56/18.93 | | | | | | | | | | | | | (3331) ~ (all_52_4 = e1)
% 132.56/18.93 | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | REDUCE: (344), (3329) imply:
% 132.56/18.93 | | | | | | | | | | | | | (3332) ~ (all_52_8 = e1)
% 132.56/18.93 | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | REDUCE: (346), (3329) imply:
% 132.56/18.93 | | | | | | | | | | | | | (3333) ~ (all_52_12 = e1)
% 132.56/18.93 | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | REDUCE: (45), (3329) imply:
% 132.56/18.93 | | | | | | | | | | | | | (3334) op(e3, e3) = e1
% 132.56/18.93 | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | BETA: splitting (2995) gives:
% 132.56/18.93 | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | Case 1:
% 132.56/18.93 | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | (3335) ~ (all_22_0 = e0) & op(e3, e2) = all_22_0 &
% 132.56/18.93 | | | | | | | | | | | | | | $i(all_22_0)
% 132.56/18.93 | | | | | | | | | | | | | |
% 132.56/18.93 | | | | | | | | | | | | | | ALPHA: (3335) implies:
% 132.56/18.93 | | | | | | | | | | | | | | (3336) ~ (all_22_0 = e0)
% 132.56/18.94 | | | | | | | | | | | | | | (3337) op(e3, e2) = all_22_0
% 132.56/18.94 | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 132.56/18.94 | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | Case 1:
% 132.56/18.94 | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | (3338) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 132.56/18.94 | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 132.56/18.94 | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | BETA: splitting (3338) gives:
% 132.56/18.94 | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | Case 1:
% 132.56/18.94 | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | (3339) all_57_0 = e3 & op(e3, e3) = e3
% 132.56/18.94 | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | ALPHA: (3339) implies:
% 132.56/18.94 | | | | | | | | | | | | | | | | (3340) op(e3, e3) = e3
% 132.56/18.94 | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3334), (3340), (function-axioms) are
% 132.56/18.94 | | | | | | | | | | | | | | | | inconsistent by sub-proof #775.
% 132.56/18.94 | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | Case 2:
% 132.56/18.94 | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | (3341) all_57_2 = e3 & op(e2, e3) = e3
% 132.56/18.94 | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | ALPHA: (3341) implies:
% 132.56/18.94 | | | | | | | | | | | | | | | | (3342) op(e2, e3) = e3
% 132.56/18.94 | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | REF_CLOSE: (167), (2977), (3342), (function-axioms) are
% 132.56/18.94 | | | | | | | | | | | | | | | | inconsistent by sub-proof #763.
% 132.56/18.94 | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | End of split
% 132.56/18.94 | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | Case 2:
% 132.56/18.94 | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | (3343) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 132.56/18.94 | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 132.56/18.94 | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | BETA: splitting (3343) gives:
% 132.56/18.94 | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | Case 1:
% 132.56/18.94 | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | (3344) all_57_6 = e3 & op(e1, e3) = e3
% 132.56/18.94 | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | REF_CLOSE: (163), (3281), (3344), (function-axioms) are
% 132.56/18.94 | | | | | | | | | | | | | | | | inconsistent by sub-proof #761.
% 132.56/18.94 | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | Case 2:
% 132.56/18.94 | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | (3345) all_57_12 = e3 & op(e0, e3) = e3
% 132.56/18.94 | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | ALPHA: (3345) implies:
% 132.56/18.94 | | | | | | | | | | | | | | | | (3346) all_57_12 = e3
% 132.56/18.94 | | | | | | | | | | | | | | | | (3347) op(e0, e3) = e3
% 132.56/18.94 | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 132.56/18.94 | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.94 | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | (3348) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 132.56/18.94 | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 132.56/18.94 | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (170), (2978), (3334), (3348),
% 132.56/18.94 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.56/18.94 | | | | | | | | | | | | | | | | | #737.
% 132.56/18.94 | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.94 | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | (3349) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 132.56/18.94 | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 132.56/18.94 | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | BETA: splitting (3349) gives:
% 132.56/18.94 | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.94 | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | (3350) all_57_4 = e3 & op(e3, e1) = e3
% 132.56/18.94 | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | ALPHA: (3350) implies:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | (3351) op(e3, e1) = e3
% 132.56/18.94 | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (3282), (3351), (function-axioms) are
% 132.56/18.94 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #705.
% 132.56/18.94 | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.94 | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | (3352) all_57_9 = e3 & op(e3, e0) = e3
% 132.56/18.94 | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | ALPHA: (3352) implies:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | (3353) all_57_9 = e3
% 132.56/18.94 | | | | | | | | | | | | | | | | | | (3354) op(e3, e0) = e3
% 132.56/18.94 | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e3,
% 132.56/18.94 | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (159), (3347) gives:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | (3355) all_52_3 = e3
% 132.56/18.94 | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 132.56/18.94 | | | | | | | | | | | | | | | | | | e3, e0, e3, simplifying with (168), (3354) gives:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | (3356) all_52_12 = e3
% 132.56/18.94 | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4,
% 132.56/18.94 | | | | | | | | | | | | | | | | | | all_22_0, e2, e3, simplifying with (170), (3337)
% 132.56/18.94 | | | | | | | | | | | | | | | | | | gives:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | (3357) all_52_4 = all_22_0
% 132.56/18.94 | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (3357) imply:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | (3358) all_54_1 = all_22_0
% 132.56/18.94 | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | REDUCE: (140), (3355) imply:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | (3359) ~ (all_52_7 = e3)
% 132.56/18.94 | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | REDUCE: (139), (3355) imply:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | (3360) ~ (all_52_11 = e3)
% 132.56/18.94 | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | REDUCE: (135), (3357) imply:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | (3361) ~ (all_52_7 = all_22_0)
% 132.56/18.94 | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | SIMP: (3361) implies:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | (3362) ~ (all_52_7 = all_22_0)
% 132.56/18.94 | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | REDUCE: (134), (3357) imply:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | (3363) ~ (all_52_8 = all_22_0)
% 132.56/18.94 | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | SIMP: (3363) implies:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | (3364) ~ (all_52_8 = all_22_0)
% 132.56/18.94 | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | REDUCE: (2978), (3357) imply:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | (3365) ~ (all_22_0 = e3)
% 132.56/18.94 | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | REDUCE: (3331), (3357) imply:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | (3366) ~ (all_22_0 = e1)
% 132.56/18.94 | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | REDUCE: (113), (3356) imply:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | (3367) ~ (all_52_13 = e3)
% 132.56/18.94 | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | REDUCE: (368), (3356) imply:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | (3368) ~ (all_4_2 = e3)
% 132.56/18.94 | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | SIMP: (3368) implies:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | (3369) ~ (all_4_2 = e3)
% 132.56/18.94 | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 132.56/18.94 | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | (3370) all_54_15 = e3
% 132.56/18.94 | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (3369), (3370) are inconsistent by
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | sub-proof #601.
% 132.56/18.94 | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | (3371) ~ (all_54_15 = e3)
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | (3372) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 132.56/18.94 | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | (3373) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3334), (3336), (3337), (3373),
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | #307.
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | (3374) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | BETA: splitting (3374) gives:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | (3375) all_57_4 = e0 & op(e3, e1) = e0
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | ALPHA: (3375) implies:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | (3376) all_57_4 = e0
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | (3377) all_54_1 = e3
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3358), (3377) imply:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | (3378) all_22_0 = e3
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3365), (3378) imply:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | (3379) $false
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3379) is inconsistent.
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | (3380) ~ (all_54_1 = e3)
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | (3381) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3381) gives:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | (3382) all_54_1 = e2
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3358), (3382) imply:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | (3383) all_22_0 = e2
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3362), (3383) imply:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | (3384) ~ (all_52_7 = e2)
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3364), (3383) imply:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | (3385) ~ (all_52_8 = e2)
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3365), (3383) imply:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | (3386) ~ (e3 = e2)
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3372) gives:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | (3387) all_54_15 = e2
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (2992), (3387) are inconsistent by
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #748.
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | (3388) ~ (all_54_15 = e2)
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | (3389) all_54_15 = e1 | all_54_15 = e0
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | (3390) all_54_2 = e3
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (3390) imply:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | (3391) all_52_8 = e3
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3282), (3391) imply:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | (3392) $false
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3392) is inconsistent.
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | (3393) ~ (all_54_2 = e3)
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | (3394) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (3395) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3395) gives:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3396) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (169), (3282), (3334), (3396),
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | #552.
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3397) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3397) gives:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3398) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3,
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3398) implies:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3399) op(e3, e3) = e0
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3334), (3399), (function-axioms) are
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #717.
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3400) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2,
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3400) implies:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3401) op(e2, e3) = e2
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3389) gives:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3402) all_54_15 = e1
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (371), (3402) are inconsistent by sub-proof
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #747.
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3403) all_54_15 = e0
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (3403) imply:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3404) all_4_2 = e0
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3404) implies:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3405) all_4_2 = e0
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (3405) imply:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3406) ~ (all_52_7 = e0)
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (3405) imply:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3407) ~ (all_52_13 = e0)
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3408) all_54_13 = e3
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (3408) imply:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3409) all_52_7 = e3
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3409) implies:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3410) all_52_7 = e3
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2980), (3410) imply:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3411) $false
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3411) is inconsistent.
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3412) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3412) gives:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3413) all_54_13 = e2
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (3384), (3413) are inconsistent by
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #472.
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3414) all_54_13 = e1 | all_54_13 = e0
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3414) gives:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3415) all_54_13 = e1
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (3415) imply:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3416) all_52_7 = e1
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3416) implies:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3417) all_52_7 = e1
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (3417) imply:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3418) ~ (all_52_11 = e1)
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3418) implies:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3419) ~ (all_52_11 = e1)
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3394) gives:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3420) all_54_2 = e2
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (3420) imply:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3421) all_52_8 = e2
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3385), (3421) imply:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3422) $false
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3422) is inconsistent.
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3423) all_54_2 = e1 | all_54_2 = e0
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3423) gives:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3424) all_54_2 = e1
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (3424) imply:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3425) all_52_8 = e1
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3332), (3425) imply:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3426) $false
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3426) is inconsistent.
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3427) all_54_2 = e0
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (3427) imply:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3428) all_52_8 = e0
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (3428) imply:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3429) ~ (all_52_9 = e0)
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3429) implies:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3430) ~ (all_52_9 = e0)
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (3428) imply:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3431) ~ (all_52_11 = e0)
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3431) implies:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3432) ~ (all_52_11 = e0)
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3433) all_54_14 = e3
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (3283), (3433) are inconsistent by
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #760.
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3434) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3434) gives:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3435) all_54_14 = e2
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (3435) imply:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3436) all_52_11 = e2
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3436) implies:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3437) all_52_11 = e2
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (3437) imply:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3438) ~ (all_52_9 = e2)
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3439) all_54_6 = e3
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (2981), (3439) are inconsistent by
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #315.
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3440) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3440) gives:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3441) all_54_6 = e2
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (3441) imply:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3442) all_52_9 = e2
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3442) implies:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3443) all_52_9 = e2
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3438), (3443) imply:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3444) $false
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3444) is inconsistent.
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3445) all_54_6 = e1 | all_54_6 = e0
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (117), (145), (167), (197), (259), (260), (2982),
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3401), (3407), (3430), (3445), (function-axioms)
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #311.
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3446) all_54_14 = e1 | all_54_14 = e0
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (3419), (3432), (3446) are inconsistent by
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #755.
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3447) all_54_13 = e0
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (3406), (3447) are inconsistent by
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #471.
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (3448) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3448) gives:
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3449) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (163), (2988), (3330), (3449),
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | #304.
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3450) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3450) gives:
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3451) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3451) implies:
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3452) op(e2, e2) = e0
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2988), (3452), (function-axioms) are
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641.
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3453) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3453) gives:
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3454) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3454) implies:
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3455) op(e1, e1) = e2
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (3455), (function-axioms) are
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3456) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3456) implies:
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3457) op(e0, e0) = all_56_31
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3458) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3459) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3459) gives:
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3460) all_57_0 = e2 & op(e3, e3) = e2
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3460) implies:
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3461) op(e3, e3) = e2
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3334), (3461), (function-axioms) are
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743.
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3462) all_57_1 = e2 & op(e3, e2) = e2
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3462) implies:
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3463) all_57_1 = e2
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3389) gives:
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3464) all_54_15 = e1
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (371), (3464) are inconsistent by sub-proof
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #747.
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3465) all_54_15 = e0
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (3465) imply:
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3466) all_4_2 = e0
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3466) implies:
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3467) all_4_2 = e0
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3369), (3467) imply:
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3468) ~ (e3 = e0)
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2992), (3467) imply:
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3469) ~ (e2 = e0)
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (3467) imply:
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3470) ~ (e1 = e0)
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (3467) imply:
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3471) op(e0, e0) = e0
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (210), (227), (228),
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2987), (3284), (3346), (3457), (3458), (3463),
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3471), (function-axioms) are inconsistent by
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #300.
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3472) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3472) gives:
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3473) all_57_4 = e2 & op(e3, e1) = e2
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3376), (3473) are inconsistent by sub-proof
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #689.
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3474) all_57_9 = e2 & op(e3, e0) = e2
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3474) implies:
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3475) all_57_9 = e2
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3353), (3475) imply:
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3476) e3 = e2
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (3476) imply:
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3477) $false
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3477) is inconsistent.
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | (3478) all_54_1 = e1 | all_54_1 = e0
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3336), (3358), (3366), (3478) are inconsistent by
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #306.
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | (3479) all_57_9 = e0 & op(e3, e0) = e0
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3353), (3479) are inconsistent by sub-proof
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | #299.
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.95 | | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.95 | | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | End of split
% 132.91/18.95 | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | End of split
% 132.91/18.95 | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | End of split
% 132.91/18.95 | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | End of split
% 132.91/18.95 | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | Case 2:
% 132.91/18.95 | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | (3480) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 &
% 132.91/18.95 | | | | | | | | | | | | | | $i(all_22_1)
% 132.91/18.95 | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | REF_CLOSE: (3334), (3480), (function-axioms) are inconsistent
% 132.91/18.95 | | | | | | | | | | | | | | by sub-proof #305.
% 132.91/18.95 | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | End of split
% 132.91/18.95 | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | End of split
% 132.91/18.95 | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | End of split
% 132.91/18.95 | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | End of split
% 132.91/18.95 | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | Case 2:
% 132.91/18.95 | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | (3481) all_20_2 = e2
% 132.91/18.95 | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | COMBINE_EQS: (318), (3481) imply:
% 132.91/18.95 | | | | | | | | | | (3482) all_4_2 = e2
% 132.91/18.95 | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | SIMP: (3482) implies:
% 132.91/18.95 | | | | | | | | | | (3483) all_4_2 = e2
% 132.91/18.95 | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | COMBINE_EQS: (331), (3483) imply:
% 132.91/18.95 | | | | | | | | | | (3484) all_26_2 = e2
% 132.91/18.95 | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | REDUCE: (367), (3483) imply:
% 132.91/18.95 | | | | | | | | | | (3485) ~ (all_52_11 = e2)
% 132.91/18.95 | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | REDUCE: (368), (3483) imply:
% 132.91/18.95 | | | | | | | | | | (3486) ~ (all_52_12 = e2)
% 132.91/18.95 | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | REDUCE: (369), (3483) imply:
% 132.91/18.95 | | | | | | | | | | (3487) ~ (all_52_13 = e2)
% 132.91/18.95 | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | REDUCE: (370), (3483) imply:
% 132.91/18.95 | | | | | | | | | | (3488) ~ (all_52_14 = e2)
% 132.91/18.95 | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | REDUCE: (36), (3483) imply:
% 132.91/18.95 | | | | | | | | | | (3489) op(e0, e0) = e2
% 132.91/18.95 | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | BETA: splitting (70) gives:
% 132.91/18.95 | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | Case 1:
% 132.91/18.95 | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | (3490) ~ (all_26_2 = e2)
% 132.91/18.95 | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | REDUCE: (3484), (3490) imply:
% 132.91/18.95 | | | | | | | | | | | (3491) $false
% 132.91/18.95 | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | CLOSE: (3491) is inconsistent.
% 132.91/18.95 | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | Case 2:
% 132.91/18.95 | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | (3492) ( ~ (all_26_0 = e1) & op(e2, e0) = all_26_0 &
% 132.91/18.95 | | | | | | | | | | | $i(all_26_0)) | ( ~ (all_26_1 = e3) & op(e2, e2)
% 132.91/18.95 | | | | | | | | | | | = all_26_1 & $i(all_26_1))
% 132.91/18.95 | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | BETA: splitting (3492) gives:
% 132.91/18.95 | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | Case 1:
% 132.91/18.95 | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | (3493) ~ (all_26_0 = e1) & op(e2, e0) = all_26_0 &
% 132.91/18.95 | | | | | | | | | | | | $i(all_26_0)
% 132.91/18.95 | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | ALPHA: (3493) implies:
% 132.91/18.95 | | | | | | | | | | | | (3494) ~ (all_26_0 = e1)
% 132.91/18.95 | | | | | | | | | | | | (3495) op(e2, e0) = all_26_0
% 132.91/18.95 | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 132.91/18.95 | | | | | | | | | | | | all_26_0, e0, e2, simplifying with (164), (3495)
% 132.91/18.95 | | | | | | | | | | | | gives:
% 132.91/18.95 | | | | | | | | | | | | (3496) all_52_13 = all_26_0
% 132.91/18.95 | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | COMBINE_EQS: (259), (3496) imply:
% 132.91/18.95 | | | | | | | | | | | | (3497) all_54_7 = all_26_0
% 132.91/18.95 | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | REDUCE: (113), (3496) imply:
% 132.91/18.95 | | | | | | | | | | | | (3498) ~ (all_52_12 = all_26_0)
% 132.91/18.95 | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | REDUCE: (110), (3496) imply:
% 132.91/18.95 | | | | | | | | | | | | (3499) ~ (all_52_14 = all_26_0)
% 132.91/18.95 | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | SIMP: (3499) implies:
% 132.91/18.95 | | | | | | | | | | | | (3500) ~ (all_52_14 = all_26_0)
% 132.91/18.95 | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | REDUCE: (2982), (3496) imply:
% 132.91/18.95 | | | | | | | | | | | | (3501) ~ (all_26_0 = e3)
% 132.91/18.95 | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | REDUCE: (3487), (3496) imply:
% 132.91/18.95 | | | | | | | | | | | | (3502) ~ (all_26_0 = e2)
% 132.91/18.95 | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | BETA: splitting (197) gives:
% 132.91/18.95 | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | Case 1:
% 132.91/18.95 | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | (3503) all_54_7 = e3
% 132.91/18.95 | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | COMBINE_EQS: (3497), (3503) imply:
% 132.91/18.95 | | | | | | | | | | | | | (3504) all_26_0 = e3
% 132.91/18.95 | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | REDUCE: (3501), (3504) imply:
% 132.91/18.95 | | | | | | | | | | | | | (3505) $false
% 132.91/18.95 | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | CLOSE: (3505) is inconsistent.
% 132.91/18.95 | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | Case 2:
% 132.91/18.95 | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | (3506) ~ (all_54_7 = e3)
% 132.91/18.95 | | | | | | | | | | | | | (3507) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 132.91/18.95 | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | BETA: splitting (3507) gives:
% 132.91/18.95 | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | Case 1:
% 132.91/18.95 | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | (3508) all_54_7 = e2
% 132.91/18.95 | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | COMBINE_EQS: (3497), (3508) imply:
% 132.91/18.95 | | | | | | | | | | | | | | (3509) all_26_0 = e2
% 132.91/18.95 | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | REDUCE: (3502), (3509) imply:
% 132.91/18.95 | | | | | | | | | | | | | | (3510) $false
% 132.91/18.95 | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | CLOSE: (3510) is inconsistent.
% 132.91/18.95 | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | Case 2:
% 132.91/18.95 | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | (3511) ~ (all_54_7 = e2)
% 132.91/18.95 | | | | | | | | | | | | | | (3512) all_54_7 = e1 | all_54_7 = e0
% 132.91/18.95 | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | BETA: splitting (3512) gives:
% 132.91/18.95 | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | Case 1:
% 132.91/18.95 | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | (3513) all_54_7 = e1
% 132.91/18.95 | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | COMBINE_EQS: (3497), (3513) imply:
% 132.91/18.95 | | | | | | | | | | | | | | | (3514) all_26_0 = e1
% 132.91/18.95 | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | REDUCE: (3494), (3514) imply:
% 132.91/18.95 | | | | | | | | | | | | | | | (3515) $false
% 132.91/18.95 | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | CLOSE: (3515) is inconsistent.
% 132.91/18.95 | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | Case 2:
% 132.91/18.95 | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | (3516) all_54_7 = e0
% 132.91/18.95 | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | COMBINE_EQS: (3497), (3516) imply:
% 132.91/18.95 | | | | | | | | | | | | | | | (3517) all_26_0 = e0
% 132.91/18.95 | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | REDUCE: (3498), (3517) imply:
% 132.91/18.95 | | | | | | | | | | | | | | | (3518) ~ (all_52_12 = e0)
% 132.91/18.95 | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | REDUCE: (3500), (3517) imply:
% 132.91/18.95 | | | | | | | | | | | | | | | (3519) ~ (all_52_14 = e0)
% 132.91/18.95 | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | REDUCE: (3501), (3517) imply:
% 132.91/18.95 | | | | | | | | | | | | | | | (3520) ~ (e3 = e0)
% 132.91/18.95 | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | REDUCE: (3502), (3517) imply:
% 132.91/18.95 | | | | | | | | | | | | | | | (3521) ~ (e2 = e0)
% 132.91/18.95 | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | REDUCE: (3494), (3517) imply:
% 132.91/18.95 | | | | | | | | | | | | | | | (3522) ~ (e1 = e0)
% 132.91/18.95 | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | REDUCE: (3495), (3517) imply:
% 132.91/18.95 | | | | | | | | | | | | | | | (3523) op(e2, e0) = e0
% 132.91/18.95 | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 132.91/18.95 | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | Case 1:
% 132.91/18.95 | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | (3524) all_57_15 = e0 & op(e0, e0) = e0
% 132.91/18.95 | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | ALPHA: (3524) implies:
% 132.91/18.95 | | | | | | | | | | | | | | | | (3525) op(e0, e0) = e0
% 132.91/18.95 | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3489), (3525), (function-axioms) are
% 132.91/18.95 | | | | | | | | | | | | | | | | inconsistent by sub-proof #714.
% 132.91/18.95 | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | Case 2:
% 132.91/18.95 | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | (3526) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 132.91/18.95 | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 132.91/18.95 | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 132.91/18.95 | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 132.91/18.95 | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 132.91/18.95 | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | ALPHA: (3526) implies:
% 132.91/18.95 | | | | | | | | | | | | | | | | (3527) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 132.91/18.95 | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 132.91/18.95 | | | | | | | | | | | | | | | | e0) = e0)
% 132.91/18.95 | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | BETA: splitting (3527) gives:
% 132.91/18.95 | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.95 | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | (3528) all_57_9 = e0 & op(e3, e0) = e0
% 132.91/18.95 | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | ALPHA: (3528) implies:
% 132.91/18.95 | | | | | | | | | | | | | | | | | (3529) all_57_9 = e0
% 132.91/18.95 | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (208), (212),
% 132.91/18.95 | | | | | | | | | | | | | | | | | (214), (223), (224), (225), (2982), (2987),
% 132.91/18.95 | | | | | | | | | | | | | | | | | (2988), (3489), (3523), (3529), (function-axioms)
% 132.91/18.95 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #291.
% 132.91/18.95 | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.95 | | | | | | | | | | | | | | | | |
% 132.91/18.95 | | | | | | | | | | | | | | | | | (3530) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 132.91/18.95 | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 132.91/18.95 | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | BETA: splitting (3530) gives:
% 132.91/18.96 | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.96 | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | (3531) all_57_10 = e0 & op(e2, e0) = e0
% 132.91/18.96 | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | ALPHA: (3531) implies:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | (3532) all_57_10 = e0
% 132.91/18.96 | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 132.91/18.96 | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | (3533) ~ (all_22_2 = e3)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | REDUCE: (2976), (3533) imply:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | (3534) $false
% 132.91/18.96 | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | CLOSE: (3534) is inconsistent.
% 132.91/18.96 | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | (3535) ( ~ (all_22_0 = e0) & op(e3, e2) = all_22_0 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | $i(all_22_0)) | ( ~ (all_22_1 = e1) & op(e3, e3)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | = all_22_1 & $i(all_22_1))
% 132.91/18.96 | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | (3536) ~ (all_28_2 = e3)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | REDUCE: (316), (3536) imply:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | (3537) ~ (all_6_2 = e3)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (3538) ~ (all_32_2 = e1)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | REDUCE: (312), (3538) imply:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (3539) ~ (all_10_2 = e1)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | (3540) all_54_0 = e3
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (3540) imply:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | (3541) all_10_2 = e3
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (346), (3541) imply:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | (3542) ~ (all_52_12 = e3)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (3541) imply:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | (3543) op(e3, e3) = e3
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (3544) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3544) gives:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | (3545) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3545) gives:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | (3546) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3546) implies:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | (3547) op(e3, e3) = e2
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (91), (118),
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | (145), (146), (149), (157), (158), (163), (164),
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | (165), (167), (170), (190), (197), (200), (206),
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | (208), (209), (210), (211), (212), (214), (217),
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | (221), (223), (224), (225), (227), (228), (231),
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | (232), (233), (234), (237), (238), (246), (259),
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | (268), (332), (362), (364), (372), (2977), (2978),
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | (2980), (2981), (2982), (2987), (2988), (3487),
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | (3489), (3494), (3495), (3547), (function-axioms)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #267.
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | (3548) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3548) implies:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | (3549) op(e3, e3) = e1
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3543), (3549), (function-axioms) are
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #775.
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | (3550) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (3542), (3543), (3550), (function-axioms)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #553.
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (3551) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3551) gives:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | (3552) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (2988), (3537), (3552),
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | #324.
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | (3553) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (39), (91), (157), (190), (246),
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | (332), (364), (372), (2988), (3485), (3489),
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | (3523), (3553), (function-axioms) are inconsistent
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #265.
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | (3554) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (374), (2990), (3539), (3554) are
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #777.
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (3555) all_32_2 = e1
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (312), (3555) imply:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (3556) all_10_2 = e1
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | SIMP: (3556) implies:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (3557) all_10_2 = e1
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | REDUCE: (338), (3557) imply:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (3558) ~ (all_52_2 = e1)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | REDUCE: (346), (3557) imply:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (3559) ~ (all_52_12 = e1)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | REDUCE: (2990), (3557) imply:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (3560) ~ (e2 = e1)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (39), (45), (91), (118), (120),
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (133), (145), (146), (149), (157), (158), (163),
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (164), (165), (167), (169), (170), (190), (197),
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (200), (201), (204), (206), (208), (209), (210),
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (211), (212), (214), (217), (221), (223), (224),
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (225), (227), (228), (231), (232), (233), (234),
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (237), (238), (246), (259), (268), (269), (278),
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (332), (346), (362), (364), (372), (374), (2977),
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (2980), (2981), (2982), (2987), (2988), (2990),
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (3485), (3486), (3487), (3489), (3494), (3495),
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (3518), (3523), (3532), (3535), (3558), (3559),
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | #261.
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | (3561) all_28_2 = e3
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (316), (3561) imply:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | (3562) all_6_2 = e3
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | SIMP: (3562) implies:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | (3563) all_6_2 = e3
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (3563) imply:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | (3564) ~ (all_52_14 = e3)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (3565) all_54_11 = e3
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (3564), (3565) are inconsistent by
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | sub-proof #260.
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (3566) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3566) gives:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | (3567) all_54_11 = e2
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (3488), (3567) are inconsistent by
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | sub-proof #259.
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | (3568) ~ (all_54_11 = e2)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | (3569) all_54_11 = e1 | all_54_11 = e0
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3569) gives:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (3570) all_54_11 = e1
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (3570) imply:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (3571) all_52_14 = e1
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3571) implies:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (3572) all_52_14 = e1
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (3572) imply:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (3573) ~ (all_52_2 = e1)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (3572) imply:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (3574) ~ (all_52_12 = e1)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3488), (3572) imply:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (3575) ~ (e2 = e1)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (39), (45), (91), (118), (120),
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (133), (145), (146), (149), (157), (158), (163),
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (164), (165), (167), (169), (170), (190), (197),
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (200), (201), (204), (206), (208), (209), (210),
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (211), (212), (214), (217), (221), (223), (224),
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (225), (227), (228), (231), (232), (233), (234),
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (237), (238), (246), (259), (268), (269), (278),
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (332), (346), (362), (364), (372), (374), (2977),
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (2980), (2981), (2982), (2987), (2988), (2990),
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (3485), (3486), (3487), (3489), (3494), (3495),
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (3518), (3523), (3532), (3535), (3573), (3574),
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | #261.
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (3576) all_54_11 = e0
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (3519), (3576) are inconsistent by
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #258.
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.96 | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.96 | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.96 | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | (3577) all_57_11 = e0 & op(e1, e0) = e0
% 132.91/18.96 | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | ALPHA: (3577) implies:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | (3578) all_57_11 = e0
% 132.91/18.96 | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 132.91/18.96 | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | (3579) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | BETA: splitting (3579) gives:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | (3580) all_57_9 = e3 & op(e3, e0) = e3
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | ALPHA: (3580) implies:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | (3581) all_57_9 = e3
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (212), (3489), (3523), (3578),
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | (3581), (function-axioms) are inconsistent by
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | sub-proof #257.
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | (3582) all_57_10 = e3 & op(e2, e0) = e3
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2982), (3582), (function-axioms) are
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749.
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.96 | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.96 | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | (3583) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 132.91/18.96 | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (3489), (3578), (3583),
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.91/18.96 | | | | | | | | | | | | | | | | | | | #255.
% 132.91/18.96 | | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.96 | | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | | End of split
% 132.91/18.96 | | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | | End of split
% 132.91/18.96 | | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | | End of split
% 132.91/18.96 | | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | | End of split
% 132.91/18.96 | | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | | End of split
% 132.91/18.96 | | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | End of split
% 132.91/18.96 | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | Case 2:
% 132.91/18.96 | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | (3584) ~ (all_26_1 = e3) & op(e2, e2) = all_26_1 &
% 132.91/18.96 | | | | | | | | | | | | $i(all_26_1)
% 132.91/18.96 | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | ALPHA: (3584) implies:
% 132.91/18.96 | | | | | | | | | | | | (3585) ~ (all_26_1 = e3)
% 132.91/18.96 | | | | | | | | | | | | (3586) op(e2, e2) = all_26_1
% 132.91/18.96 | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | | REF_CLOSE: (2988), (3585), (3586), (function-axioms) are
% 132.91/18.96 | | | | | | | | | | | | inconsistent by sub-proof #334.
% 132.91/18.96 | | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | End of split
% 132.91/18.96 | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | End of split
% 132.91/18.96 | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | End of split
% 132.91/18.96 | | | | | | | | |
% 132.91/18.96 | | | | | | | | Case 2:
% 132.91/18.96 | | | | | | | | |
% 132.91/18.96 | | | | | | | | | (3587) all_16_2 = e2
% 132.91/18.96 | | | | | | | | |
% 132.91/18.96 | | | | | | | | | COMBINE_EQS: (327), (3587) imply:
% 132.91/18.96 | | | | | | | | | (3588) all_10_2 = e2
% 132.91/18.96 | | | | | | | | |
% 132.91/18.96 | | | | | | | | | REDUCE: (336), (3588) imply:
% 132.91/18.96 | | | | | | | | | (3589) ~ (all_52_1 = e2)
% 132.91/18.96 | | | | | | | | |
% 132.91/18.96 | | | | | | | | | REDUCE: (342), (3588) imply:
% 132.91/18.96 | | | | | | | | | (3590) ~ (all_52_4 = e2)
% 132.91/18.96 | | | | | | | | |
% 132.91/18.96 | | | | | | | | | REDUCE: (344), (3588) imply:
% 132.91/18.96 | | | | | | | | | (3591) ~ (all_52_8 = e2)
% 132.91/18.96 | | | | | | | | |
% 132.91/18.96 | | | | | | | | | REDUCE: (346), (3588) imply:
% 132.91/18.96 | | | | | | | | | (3592) ~ (all_52_12 = e2)
% 132.91/18.96 | | | | | | | | |
% 132.91/18.96 | | | | | | | | | REDUCE: (45), (3588) imply:
% 132.91/18.96 | | | | | | | | | (3593) op(e3, e3) = e2
% 132.91/18.96 | | | | | | | | |
% 132.91/18.96 | | | | | | | | | BETA: splitting (61) gives:
% 132.91/18.96 | | | | | | | | |
% 132.91/18.96 | | | | | | | | | Case 1:
% 132.91/18.96 | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | (3594) ~ (all_20_2 = e2)
% 132.91/18.96 | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | REDUCE: (318), (3594) imply:
% 132.91/18.96 | | | | | | | | | | (3595) ~ (all_4_2 = e2)
% 132.91/18.96 | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | BETA: splitting (73) gives:
% 132.91/18.96 | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | Case 1:
% 132.91/18.96 | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | (3596) ~ (all_28_2 = e3)
% 132.91/18.96 | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | REDUCE: (316), (3596) imply:
% 132.91/18.96 | | | | | | | | | | | (3597) ~ (all_6_2 = e3)
% 132.91/18.96 | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | BETA: splitting (206) gives:
% 132.91/18.96 | | | | | | | | | | |
% 132.91/18.96 | | | | | | | | | | | Case 1:
% 132.91/18.96 | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | (3598) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 132.91/18.97 | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.91/18.97 | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 132.91/18.97 | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 132.91/18.97 | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.91/18.97 | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 132.91/18.97 | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.91/18.97 | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.91/18.97 | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.91/18.97 | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 132.91/18.97 | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 132.91/18.97 | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.91/18.97 | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 132.91/18.97 | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 132.91/18.97 | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.91/18.97 | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.91/18.97 | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 132.91/18.97 | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 132.91/18.97 | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.91/18.97 | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.91/18.97 | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.91/18.97 | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.91/18.97 | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.91/18.97 | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.91/18.97 | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.91/18.97 | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 132.91/18.97 | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.91/18.97 | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 132.91/18.97 | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | BETA: splitting (3598) gives:
% 132.91/18.97 | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | Case 1:
% 132.91/18.97 | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | (3599) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 132.91/18.97 | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.91/18.97 | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 132.91/18.97 | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 132.91/18.97 | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.91/18.97 | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 132.91/18.97 | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.91/18.97 | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.91/18.97 | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.91/18.97 | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 132.91/18.97 | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 132.91/18.97 | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.91/18.97 | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 132.91/18.97 | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 132.91/18.97 | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | REF_CLOSE: (6), (170), (2978), (3593), (3599),
% 132.91/18.97 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.91/18.97 | | | | | | | | | | | | | #254.
% 132.91/18.97 | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | Case 2:
% 132.91/18.97 | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | (3600) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.91/18.97 | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.91/18.97 | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 132.91/18.97 | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 132.91/18.97 | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.91/18.97 | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.91/18.97 | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.91/18.97 | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.91/18.97 | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.91/18.97 | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.91/18.97 | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.91/18.97 | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 132.91/18.97 | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.91/18.97 | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 132.91/18.97 | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | BETA: splitting (3600) gives:
% 132.91/18.97 | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | Case 1:
% 132.91/18.97 | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | (3601) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.91/18.97 | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 132.91/18.97 | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3,
% 132.91/18.97 | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.91/18.97 | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 132.91/18.97 | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.91/18.97 | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 132.91/18.97 | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | ALPHA: (3601) implies:
% 132.91/18.97 | | | | | | | | | | | | | | (3602) op(e3, e3) = e0
% 132.91/18.97 | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | REF_CLOSE: (5), (3593), (3602), (function-axioms) are
% 132.91/18.97 | | | | | | | | | | | | | | inconsistent by sub-proof #495.
% 132.91/18.97 | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | Case 2:
% 132.91/18.97 | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | (3603) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.91/18.97 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 132.91/18.97 | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.91/18.97 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.91/18.97 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2,
% 132.91/18.97 | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.91/18.97 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 132.91/18.97 | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | ALPHA: (3603) implies:
% 132.91/18.97 | | | | | | | | | | | | | | (3604) op(e2, e3) = e2
% 132.91/18.97 | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 132.91/18.97 | | | | | | | | | | | | | | e3, e2, simplifying with (167), (3604) gives:
% 132.91/18.97 | | | | | | | | | | | | | | (3605) all_52_1 = e2
% 132.91/18.97 | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | REDUCE: (3589), (3605) imply:
% 132.91/18.97 | | | | | | | | | | | | | | (3606) $false
% 132.91/18.97 | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | CLOSE: (3606) is inconsistent.
% 132.91/18.97 | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | End of split
% 132.91/18.97 | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | End of split
% 132.91/18.97 | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | Case 2:
% 132.91/18.97 | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | (3607) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.91/18.97 | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.91/18.97 | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.91/18.97 | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.91/18.97 | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 132.91/18.97 | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.91/18.97 | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 132.91/18.97 | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 132.91/18.97 | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 132.91/18.97 | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 132.91/18.97 | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.91/18.97 | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 132.91/18.97 | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.91/18.97 | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 132.91/18.97 | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 132.91/18.97 | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.91/18.97 | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 132.91/18.97 | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.91/18.97 | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 132.91/18.97 | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.91/18.97 | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 132.91/18.97 | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 132.91/18.97 | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 132.91/18.97 | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.91/18.97 | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 132.91/18.97 | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 132.91/18.97 | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 132.91/18.97 | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 132.91/18.97 | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 132.91/18.97 | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 132.91/18.97 | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 132.91/18.97 | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.91/18.97 | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 132.91/18.97 | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 132.91/18.97 | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 132.91/18.97 | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 132.91/18.97 | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 132.91/18.97 | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 132.91/18.97 | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.91/18.97 | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.91/18.97 | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 132.91/18.97 | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 132.91/18.97 | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 132.91/18.97 | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 132.91/18.97 | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 132.91/18.97 | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 132.91/18.97 | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 132.91/18.97 | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 132.91/18.97 | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 132.91/18.97 | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.91/18.97 | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.91/18.97 | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.91/18.97 | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.91/18.97 | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.91/18.97 | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.91/18.97 | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.91/18.97 | | | | | | | | | | | | & $i(all_56_29))))
% 132.91/18.97 | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | BETA: splitting (3607) gives:
% 132.91/18.97 | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | Case 1:
% 132.91/18.97 | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | (3608) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.91/18.97 | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.91/18.97 | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.91/18.97 | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.91/18.97 | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 132.91/18.97 | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.91/18.97 | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 132.91/18.97 | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 132.91/18.97 | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 132.91/18.97 | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 132.91/18.97 | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.91/18.97 | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 132.91/18.97 | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.91/18.97 | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 132.91/18.97 | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | REF_CLOSE: (8), (39), (2988), (3597), (3608),
% 132.91/18.97 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.91/18.97 | | | | | | | | | | | | | #324.
% 132.91/18.97 | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | Case 2:
% 132.91/18.97 | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | (3609) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 132.91/18.97 | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.91/18.97 | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 132.91/18.97 | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 132.91/18.97 | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.91/18.97 | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.91/18.97 | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.91/18.97 | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.91/18.97 | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.91/18.97 | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 132.91/18.97 | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.91/18.97 | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 132.91/18.97 | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 132.91/18.97 | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.91/18.97 | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.91/18.97 | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 132.91/18.97 | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 132.91/18.97 | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.91/18.97 | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 132.91/18.97 | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 132.91/18.97 | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 132.91/18.97 | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 132.91/18.97 | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 132.91/18.97 | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 132.91/18.97 | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 132.91/18.97 | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 132.91/18.97 | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 132.91/18.97 | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 132.91/18.97 | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 132.91/18.97 | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 132.91/18.97 | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.91/18.97 | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.91/18.97 | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.91/18.97 | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.91/18.97 | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.91/18.97 | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 132.91/18.97 | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.91/18.97 | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.91/18.97 | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.91/18.97 | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.91/18.97 | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.91/18.97 | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.91/18.97 | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.91/18.97 | | | | | | | | | | | | | & $i(all_56_29))))
% 132.91/18.97 | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | BETA: splitting (3609) gives:
% 132.91/18.97 | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | Case 1:
% 132.91/18.97 | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | (3610) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 132.91/18.97 | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 132.91/18.97 | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 132.91/18.97 | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.91/18.97 | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 132.91/18.97 | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.91/18.97 | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 132.91/18.97 | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | ALPHA: (3610) implies:
% 132.91/18.97 | | | | | | | | | | | | | | (3611) op(e2, e2) = e0
% 132.91/18.97 | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, e0, e2,
% 132.91/18.97 | | | | | | | | | | | | | | e2, simplifying with (2988), (3611) gives:
% 132.91/18.97 | | | | | | | | | | | | | | (3612) e3 = e0
% 132.91/18.97 | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | REDUCE: (7), (3612) imply:
% 132.91/18.97 | | | | | | | | | | | | | | (3613) $false
% 132.91/18.97 | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | CLOSE: (3613) is inconsistent.
% 132.91/18.97 | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | Case 2:
% 132.91/18.97 | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | (3614) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.91/18.97 | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.91/18.97 | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 132.91/18.97 | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.91/18.97 | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 132.91/18.97 | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 132.91/18.97 | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.91/18.97 | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.91/18.97 | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 132.91/18.97 | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 132.91/18.97 | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.91/18.97 | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 132.91/18.97 | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 132.91/18.97 | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 132.91/18.97 | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 132.91/18.97 | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 132.91/18.97 | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 132.91/18.97 | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 132.91/18.97 | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 132.91/18.97 | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 132.91/18.97 | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 132.91/18.97 | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 132.91/18.97 | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 132.91/18.97 | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.91/18.97 | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.91/18.97 | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.91/18.97 | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.91/18.97 | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.91/18.97 | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 132.91/18.97 | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.91/18.97 | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.91/18.97 | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.91/18.97 | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.91/18.97 | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.91/18.97 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.91/18.97 | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.91/18.97 | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.91/18.97 | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | BETA: splitting (3614) gives:
% 132.91/18.97 | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | Case 1:
% 132.91/18.97 | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | (3615) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.91/18.97 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 132.91/18.97 | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.91/18.97 | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.91/18.97 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 132.91/18.97 | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 132.91/18.97 | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 132.91/18.97 | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | ALPHA: (3615) implies:
% 132.91/18.97 | | | | | | | | | | | | | | | (3616) op(e1, e1) = e2
% 132.91/18.97 | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (3616), (function-axioms) are
% 132.91/18.97 | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 132.91/18.97 | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | Case 2:
% 132.91/18.97 | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | (3617) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.91/18.97 | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 132.91/18.97 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 132.91/18.97 | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.91/18.97 | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 132.91/18.97 | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 132.91/18.97 | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 132.91/18.97 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 132.91/18.97 | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 132.91/18.97 | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 132.91/18.97 | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.91/18.97 | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.91/18.97 | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 132.91/18.97 | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 132.91/18.97 | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 132.91/18.97 | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.91/18.97 | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.91/18.97 | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.91/18.97 | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.91/18.97 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.91/18.97 | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 132.91/18.97 | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 132.91/18.97 | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 132.91/18.97 | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 132.91/18.97 | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 132.91/18.97 | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 132.91/18.97 | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 132.91/18.97 | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 132.91/18.97 | | | | | | | | | | | | | | | $i(all_56_29)))
% 132.91/18.97 | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | ALPHA: (3617) implies:
% 132.91/18.97 | | | | | | | | | | | | | | | (3618) op(e0, e0) = all_56_31
% 132.91/18.97 | | | | | | | | | | | | | | | (3619) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 132.91/18.97 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.91/18.97 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.91/18.97 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.91/18.97 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 132.91/18.97 | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 132.91/18.97 | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 132.91/18.97 | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 132.91/18.97 | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 132.91/18.97 | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 132.91/18.97 | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 132.91/18.97 | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 132.91/18.97 | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 132.91/18.97 | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.91/18.97 | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.91/18.97 | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 132.91/18.97 | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.91/18.97 | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 132.91/18.97 | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 132.91/18.97 | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 132.91/18.97 | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.91/18.97 | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 132.91/18.97 | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 132.91/18.97 | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 132.91/18.97 | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 132.91/18.97 | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 132.91/18.97 | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 132.91/18.97 | | | | | | | | | | | | | | | all_56_31, e0, e0, simplifying with (36), (3618)
% 132.91/18.97 | | | | | | | | | | | | | | | gives:
% 132.91/18.97 | | | | | | | | | | | | | | | (3620) all_56_31 = all_4_2
% 132.91/18.97 | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 132.91/18.97 | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | Case 1:
% 132.91/18.97 | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | (3621) ~ (all_34_2 = e3)
% 132.91/18.97 | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | REDUCE: (307), (3621) imply:
% 132.91/18.97 | | | | | | | | | | | | | | | | (3622) ~ (all_4_2 = e3)
% 132.91/18.97 | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | REF_CLOSE: (189), (245), (371), (3595), (3619), (3620),
% 132.91/18.97 | | | | | | | | | | | | | | | | (3622) are inconsistent by sub-proof #322.
% 132.91/18.97 | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | Case 2:
% 132.91/18.97 | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | (3623) all_34_2 = e3
% 132.91/18.97 | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (3623) imply:
% 132.91/18.97 | | | | | | | | | | | | | | | | (3624) all_4_2 = e3
% 132.91/18.97 | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | SIMP: (3624) implies:
% 132.91/18.97 | | | | | | | | | | | | | | | | (3625) all_4_2 = e3
% 132.91/18.97 | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (3625) imply:
% 132.91/18.97 | | | | | | | | | | | | | | | | (3626) all_44_2 = e3
% 132.91/18.97 | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | COMBINE_EQS: (3620), (3625) imply:
% 132.91/18.97 | | | | | | | | | | | | | | | | (3627) all_56_31 = e3
% 132.91/18.97 | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | REDUCE: (368), (3625) imply:
% 132.91/18.97 | | | | | | | | | | | | | | | | (3628) ~ (all_52_12 = e3)
% 132.91/18.97 | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | REDUCE: (36), (3625) imply:
% 132.91/18.97 | | | | | | | | | | | | | | | | (3629) op(e0, e0) = e3
% 132.91/18.97 | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 132.91/18.97 | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.97 | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | (3630) ~ (all_44_2 = e3)
% 132.91/18.97 | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | REDUCE: (3626), (3630) imply:
% 132.91/18.97 | | | | | | | | | | | | | | | | | (3631) $false
% 132.91/18.97 | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | CLOSE: (3631) is inconsistent.
% 132.91/18.97 | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.97 | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | (3632) ( ~ (all_44_0 = e1) & op(e3, e0) = all_44_0 &
% 132.91/18.97 | | | | | | | | | | | | | | | | | $i(all_44_0)) | ( ~ (all_44_1 = e2) & op(e3, e3)
% 132.91/18.97 | | | | | | | | | | | | | | | | | = all_44_1 & $i(all_44_1))
% 132.91/18.97 | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | BETA: splitting (3632) gives:
% 132.91/18.97 | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.97 | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | (3633) ~ (all_44_0 = e1) & op(e3, e0) = all_44_0 &
% 132.91/18.97 | | | | | | | | | | | | | | | | | | $i(all_44_0)
% 132.91/18.97 | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | ALPHA: (3633) implies:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | (3634) ~ (all_44_0 = e1)
% 132.91/18.97 | | | | | | | | | | | | | | | | | | (3635) op(e3, e0) = all_44_0
% 132.91/18.97 | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 132.91/18.97 | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | (3636) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 132.91/18.97 | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | BETA: splitting (3636) gives:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | (3637) all_57_4 = e3 & op(e3, e1) = e3
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | ALPHA: (3637) implies:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | (3638) all_57_4 = e3
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | (3639) op(e3, e1) = e3
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | all_44_0, e0, e3, simplifying with (168), (3635)
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | gives:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | (3640) all_52_12 = all_44_0
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e3,
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (169), (3639) gives:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | (3641) all_52_8 = e3
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (3640) imply:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | (3642) all_54_3 = all_44_0
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (3640) imply:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | (3643) ~ (all_52_4 = all_44_0)
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (3641) imply:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | (3644) ~ (all_52_11 = e3)
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | SIMP: (3644) implies:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | (3645) ~ (all_52_11 = e3)
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | REDUCE: (3628), (3640) imply:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | (3646) ~ (all_44_0 = e3)
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | REDUCE: (3592), (3640) imply:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | (3647) ~ (all_44_0 = e2)
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | (3648) all_54_3 = e3
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3642), (3648) imply:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | (3649) all_44_0 = e3
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | REDUCE: (3646), (3649) imply:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | (3650) $false
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | CLOSE: (3650) is inconsistent.
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | (3651) ~ (all_54_3 = e3)
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | (3652) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3652) gives:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | (3653) all_54_3 = e2
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3642), (3653) imply:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | (3654) all_44_0 = e2
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3647), (3654) imply:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | (3655) $false
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3655) is inconsistent.
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | (3656) ~ (all_54_3 = e2)
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | (3657) all_54_3 = e1 | all_54_3 = e0
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3657) gives:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | (3658) all_54_3 = e1
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3642), (3658) imply:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | (3659) all_44_0 = e1
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3634), (3659) imply:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | (3660) $false
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3660) is inconsistent.
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | (3661) all_54_3 = e0
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3642), (3661) imply:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | (3662) all_44_0 = e0
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3643), (3662) imply:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | (3663) ~ (all_52_4 = e0)
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3646), (3662) imply:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | (3664) ~ (e3 = e0)
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3647), (3662) imply:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | (3665) ~ (e2 = e0)
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3634), (3662) imply:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | (3666) ~ (e1 = e0)
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3635), (3662) imply:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | (3667) op(e3, e0) = e0
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3619) gives:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | (3668) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27))
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3668) gives:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3669) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3669) implies:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3670) ~ (all_56_25 = e0)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3671) op(e3, e0) = all_56_25
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3667), (3670), (3671), (function-axioms) are
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #642.
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3672) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3672) implies:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3673) all_56_31 = e2
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3627), (3673) imply:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3674) e3 = e2
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3674) implies:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3675) e3 = e2
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3638), (3675) imply:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3676) all_57_4 = e2
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (234),
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (238), (2978), (3593), (3676), (function-axioms)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #278.
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | (3677) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3677) gives:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3678) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3678) implies:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3679) ~ (all_56_23 = e1)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3680) op(e0, e1) = all_56_23
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3681) op(e1, e1) = e0
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (3682) all_54_1 = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (271), (2978), (3682) are inconsistent by
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #740.
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (3683) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (100), (157), (190), (246), (271), (295),
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (364), (3590), (3629), (3645), (3663), (3679),
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (3680), (3681), (3683), (function-axioms) are
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #607.
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3684) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3684) implies:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3685) all_56_31 = e1
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3627), (3685) are inconsistent by sub-proof
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | #253.
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | (3686) all_57_5 = e3 & op(e2, e1) = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (2981), (3686), (function-axioms) are
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547.
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.98 | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | (3687) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | BETA: splitting (3687) gives:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | (3688) all_57_8 = e3 & op(e1, e1) = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | ALPHA: (3688) implies:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | (3689) op(e1, e1) = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (3597), (3689), (function-axioms) are
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #771.
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | (3690) all_57_14 = e3 & op(e0, e1) = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | ALPHA: (3690) implies:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | (3691) all_57_14 = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | (3692) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3692) gives:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | (3693) all_57_12 = e2 & op(e0, e3) = e2
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3693) implies:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | (3694) all_57_12 = e2
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | (3593), (3694), (function-axioms) are inconsistent
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #290.
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | (3695) all_57_13 = e2 & op(e0, e2) = e2
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3695) implies:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | (3696) all_57_13 = e2
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | (3697) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3697) gives:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | (3698) all_57_0 = e3 & op(e3, e3) = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3698) implies:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | (3699) op(e3, e3) = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3593), (3699), (function-axioms) are
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #778.
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | (3700) all_57_2 = e3 & op(e2, e3) = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3700) implies:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | (3701) all_57_2 = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3702) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (170), (2978), (3593), (3702),
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | #282.
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3703) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3703) gives:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (3704) all_57_4 = e3 & op(e3, e1) = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (170), (219),
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (220), (221), (232), (234), (238), (372), (2978),
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (3593), (3691), (3704), (function-axioms) are
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #251.
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (3705) all_57_9 = e3 & op(e3, e0) = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3705) implies:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (3706) all_57_9 = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3707) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3707) gives:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3708) all_57_4 = e2 & op(e3, e1) = e2
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3708) implies:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3709) all_57_4 = e2
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (232), (234), (3593),
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3706), (3709), (function-axioms) are inconsistent
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #279.
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3710) all_57_5 = e2 & op(e2, e1) = e2
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3710) implies:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3711) all_57_5 = e2
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (223), (224), (2987),
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3701), (3711) are inconsistent by sub-proof #368.
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3712) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (158), (170),
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (208), (209), (211), (232), (234), (238), (372),
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2978), (2980), (3593), (3696), (3706), (3712),
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | #249.
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | (3713) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3713) gives:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | (3714) all_57_6 = e3 & op(e1, e3) = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3714) implies:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | (3715) all_57_6 = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3716) all_57_15 = e0 & op(e0, e0) = e0
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3716) implies:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3717) op(e0, e0) = e0
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3629), (3717), (function-axioms) are
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #715.
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3718) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3718) implies:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3719) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (3720) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (170), (2978), (3593), (3720),
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | #282.
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (3721) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3721) gives:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3722) all_57_4 = e3 & op(e3, e1) = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (170), (219),
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (220), (221), (232), (234), (238), (372), (2978),
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3593), (3691), (3722), (function-axioms) are
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #251.
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3723) all_57_9 = e3 & op(e3, e0) = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3723) implies:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3724) all_57_9 = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (158), (170),
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (208), (209), (211), (213), (221), (223), (224),
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (232), (233), (234), (237), (238), (372), (2978),
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2980), (2987), (2988), (3593), (3629), (3691),
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3696), (3715), (3719), (3724), (function-axioms)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #246.
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | (3725) all_57_12 = e3 & op(e0, e3) = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3725) implies:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | (3726) all_57_12 = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3727) all_57_15 = e0 & op(e0, e0) = e0
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3727) implies:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3728) all_57_15 = e0
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (3729) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (3696), (3726), (3729) are inconsistent
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #245.
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (3730) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3730) gives:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3731) all_57_14 = e1 & op(e0, e1) = e1
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3731) implies:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3732) all_57_14 = e1
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3691), (3732) are inconsistent by sub-proof
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | #561.
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3733) all_57_15 = e1 & op(e0, e0) = e1
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3733) implies:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3734) all_57_15 = e1
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3728), (3734) imply:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3735) e1 = e0
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (3735) imply:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3736) $false
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3736) is inconsistent.
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3737) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3737) implies:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3738) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (3739) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (170), (2978), (3593), (3739),
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | #282.
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (3740) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3740) gives:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3741) all_57_4 = e3 & op(e3, e1) = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (170), (219),
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (220), (221), (232), (234), (238), (372), (2978),
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3593), (3691), (3741), (function-axioms) are
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #251.
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3742) all_57_9 = e3 & op(e3, e0) = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3742) implies:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3743) all_57_9 = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3744) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3744) gives:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3745) all_57_6 = e3 & op(e1, e3) = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3745) implies:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3746) all_57_6 = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (158), (170),
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (208), (209), (211), (213), (221), (223), (224),
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232), (233), (234), (237), (238), (372), (2978),
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2980), (2987), (2988), (3593), (3629), (3691),
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3696), (3738), (3743), (3746), (function-axioms)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #246.
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3747) all_57_7 = e3 & op(e1, e2) = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3747) implies:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3748) op(e1, e2) = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (2979), (3748), (function-axioms) are
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #654.
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3749) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3749) gives:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3750) all_57_8 = e3 & op(e1, e1) = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3750) implies:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3751) op(e1, e1) = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (3597), (3751), (function-axioms) are
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #771.
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3752) all_57_11 = e3 & op(e1, e0) = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3752) implies:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3753) all_57_11 = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3754) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3754) gives:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3755) all_57_4 = e2 & op(e3, e1) = e2
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3755) implies:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3756) all_57_4 = e2
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3757) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (170), (2978), (3593), (3757),
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #282.
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3740) gives:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3758) all_57_4 = e3 & op(e3, e1) = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3758) implies:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3759) all_57_4 = e3
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3756), (3759) imply:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3760) e3 = e2
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3726), (3760) imply:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3761) all_57_12 = e2
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3593), (3761), (function-axioms) are inconsistent
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #290.
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (232), (234), (3593),
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3743), (3756), (function-axioms) are inconsistent
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #279.
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3762) all_57_5 = e2 & op(e2, e1) = e2
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3762) implies:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3763) all_57_5 = e2
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3764) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3764) gives:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3765) all_57_6 = e2 & op(e1, e3) = e2
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3765) implies:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3766) all_57_6 = e2
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (231),
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (237), (2987), (3593), (3763), (3766),
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #366.
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3767) all_57_7 = e2 & op(e1, e2) = e2
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3767) implies:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3768) all_57_7 = e2
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (227), (228), (2987),
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3696), (3768) are inconsistent by sub-proof #287.
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3769) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3769) gives:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3770) all_57_8 = e2 & op(e1, e1) = e2
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3770) implies:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3771) op(e1, e1) = e2
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (3771), (function-axioms) are
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3772) all_57_11 = e2 & op(e1, e0) = e2
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3772) implies:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3773) all_57_11 = e2
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3753), (3773) imply:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3774) e3 = e2
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3743), (3774) imply:
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3775) all_57_9 = e2
% 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (234),
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (2978), (3593), (3775), (function-axioms)
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #250.
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3776) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3776) gives:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3777) all_57_8 = e2 & op(e1, e1) = e2
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3777) implies:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3778) op(e1, e1) = e2
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (3778), (function-axioms) are
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3779) all_57_14 = e2 & op(e0, e1) = e2
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3779) implies:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3780) all_57_14 = e2
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (3696), (3726), (3738), (3780) are
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #410.
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | (3781) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3781) gives:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | (3782) all_57_14 = e2 & op(e0, e1) = e2
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3691), (3782) are inconsistent by sub-proof
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | #397.
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | (3783) all_57_15 = e2 & op(e0, e0) = e2
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3783) implies:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | (3784) op(e0, e0) = e2
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3629), (3784), (function-axioms) are
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #634.
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.99 | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | (3785) ~ (all_44_1 = e2) & op(e3, e3) = all_44_1 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | $i(all_44_1)
% 132.91/18.99 | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | REF_CLOSE: (3593), (3785), (function-axioms) are inconsistent
% 132.91/18.99 | | | | | | | | | | | | | | | | | | by sub-proof #431.
% 132.91/18.99 | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | Case 2:
% 132.91/18.99 | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | (3786) all_28_2 = e3
% 132.91/18.99 | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | COMBINE_EQS: (316), (3786) imply:
% 132.91/18.99 | | | | | | | | | | | (3787) all_6_2 = e3
% 132.91/18.99 | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | COMBINE_EQS: (302), (3787) imply:
% 132.91/18.99 | | | | | | | | | | | (3788) all_36_2 = e3
% 132.91/18.99 | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | REDUCE: (348), (3787) imply:
% 132.91/18.99 | | | | | | | | | | | (3789) ~ (all_52_2 = e3)
% 132.91/18.99 | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | REDUCE: (361), (3787) imply:
% 132.91/18.99 | | | | | | | | | | | (3790) ~ (all_52_8 = e3)
% 132.91/18.99 | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | REDUCE: (39), (3787) imply:
% 132.91/18.99 | | | | | | | | | | | (3791) op(e1, e1) = e3
% 132.91/18.99 | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | BETA: splitting (85) gives:
% 132.91/18.99 | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | Case 1:
% 132.91/18.99 | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | (3792) ~ (all_36_2 = e3)
% 132.91/18.99 | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | REDUCE: (3788), (3792) imply:
% 132.91/18.99 | | | | | | | | | | | | (3793) $false
% 132.91/18.99 | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | CLOSE: (3793) is inconsistent.
% 132.91/18.99 | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | Case 2:
% 132.91/18.99 | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | (3794) ( ~ (all_36_0 = e0) & op(e3, e1) = all_36_0 &
% 132.91/18.99 | | | | | | | | | | | | $i(all_36_0)) | ( ~ (all_36_1 = e2) & op(e3, e3)
% 132.91/18.99 | | | | | | | | | | | | = all_36_1 & $i(all_36_1))
% 132.91/18.99 | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | BETA: splitting (3794) gives:
% 132.91/18.99 | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | Case 1:
% 132.91/18.99 | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | (3795) ~ (all_36_0 = e0) & op(e3, e1) = all_36_0 &
% 132.91/18.99 | | | | | | | | | | | | | $i(all_36_0)
% 132.91/18.99 | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | ALPHA: (3795) implies:
% 132.91/18.99 | | | | | | | | | | | | | (3796) ~ (all_36_0 = e0)
% 132.91/18.99 | | | | | | | | | | | | | (3797) op(e3, e1) = all_36_0
% 132.91/18.99 | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | BETA: splitting (237) gives:
% 132.91/18.99 | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | Case 1:
% 132.91/18.99 | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | (3798) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 132.91/18.99 | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 132.91/18.99 | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | BETA: splitting (3798) gives:
% 132.91/18.99 | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | Case 1:
% 132.91/18.99 | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | (3799) all_57_0 = e3 & op(e3, e3) = e3
% 132.91/18.99 | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | ALPHA: (3799) implies:
% 132.91/18.99 | | | | | | | | | | | | | | | (3800) op(e3, e3) = e3
% 132.91/18.99 | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | REF_CLOSE: (9), (3593), (3800), (function-axioms) are
% 132.91/18.99 | | | | | | | | | | | | | | | inconsistent by sub-proof #778.
% 132.91/18.99 | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | Case 2:
% 132.91/18.99 | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | (3801) all_57_2 = e3 & op(e2, e3) = e3
% 132.91/18.99 | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | ALPHA: (3801) implies:
% 132.91/18.99 | | | | | | | | | | | | | | | (3802) op(e2, e3) = e3
% 132.91/18.99 | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | REF_CLOSE: (167), (2977), (3802), (function-axioms) are
% 132.91/18.99 | | | | | | | | | | | | | | | inconsistent by sub-proof #763.
% 132.91/18.99 | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | Case 2:
% 132.91/18.99 | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | (3803) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 132.91/18.99 | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 132.91/18.99 | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | BETA: splitting (3803) gives:
% 132.91/18.99 | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | Case 1:
% 132.91/18.99 | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | (3804) all_57_6 = e3 & op(e1, e3) = e3
% 132.91/18.99 | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | REF_CLOSE: (163), (3789), (3804), (function-axioms) are
% 132.91/18.99 | | | | | | | | | | | | | | | inconsistent by sub-proof #761.
% 132.91/18.99 | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | Case 2:
% 132.91/18.99 | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | (3805) all_57_12 = e3 & op(e0, e3) = e3
% 132.91/18.99 | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | ALPHA: (3805) implies:
% 132.91/18.99 | | | | | | | | | | | | | | | (3806) all_57_12 = e3
% 132.91/18.99 | | | | | | | | | | | | | | | (3807) op(e0, e3) = e3
% 132.91/18.99 | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 132.91/18.99 | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | Case 1:
% 132.91/18.99 | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | (3808) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 132.91/18.99 | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 132.91/18.99 | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | REF_CLOSE: (9), (170), (2978), (3593), (3808),
% 132.91/18.99 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.91/18.99 | | | | | | | | | | | | | | | | #282.
% 132.91/18.99 | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | Case 2:
% 132.91/18.99 | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | (3809) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 132.91/18.99 | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 132.91/18.99 | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | BETA: splitting (3809) gives:
% 132.91/18.99 | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.99 | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | (3810) all_57_4 = e3 & op(e3, e1) = e3
% 132.91/18.99 | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (3790), (3797), (3810), (function-axioms)
% 132.91/18.99 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #379.
% 132.91/18.99 | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.99 | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | (3811) all_57_9 = e3 & op(e3, e0) = e3
% 132.91/18.99 | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | ALPHA: (3811) implies:
% 132.91/18.99 | | | | | | | | | | | | | | | | | (3812) all_57_9 = e3
% 132.91/18.99 | | | | | | | | | | | | | | | | | (3813) op(e3, e0) = e3
% 132.91/18.99 | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e3,
% 132.91/18.99 | | | | | | | | | | | | | | | | | e3, e0, simplifying with (159), (3807) gives:
% 132.91/18.99 | | | | | | | | | | | | | | | | | (3814) all_52_3 = e3
% 132.91/18.99 | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 132.91/18.99 | | | | | | | | | | | | | | | | | e3, e0, e3, simplifying with (168), (3813) gives:
% 132.91/18.99 | | | | | | | | | | | | | | | | | (3815) all_52_12 = e3
% 132.91/18.99 | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8,
% 132.91/18.99 | | | | | | | | | | | | | | | | | all_36_0, e1, e3, simplifying with (169), (3797)
% 132.91/18.99 | | | | | | | | | | | | | | | | | gives:
% 132.91/18.99 | | | | | | | | | | | | | | | | | (3816) all_52_8 = all_36_0
% 132.91/18.99 | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (3816) imply:
% 132.91/18.99 | | | | | | | | | | | | | | | | | (3817) all_54_2 = all_36_0
% 132.91/18.99 | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | REDUCE: (140), (3814) imply:
% 132.91/18.99 | | | | | | | | | | | | | | | | | (3818) ~ (all_52_7 = e3)
% 132.91/18.99 | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | REDUCE: (139), (3814) imply:
% 132.91/18.99 | | | | | | | | | | | | | | | | | (3819) ~ (all_52_11 = e3)
% 132.91/18.99 | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | SIMP: (3819) implies:
% 132.91/18.99 | | | | | | | | | | | | | | | | | (3820) ~ (all_52_11 = e3)
% 132.91/18.99 | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | REDUCE: (134), (3816) imply:
% 132.91/18.99 | | | | | | | | | | | | | | | | | (3821) ~ (all_52_4 = all_36_0)
% 132.91/18.99 | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | REDUCE: (123), (3816) imply:
% 132.91/18.99 | | | | | | | | | | | | | | | | | (3822) ~ (all_52_9 = all_36_0)
% 132.91/18.99 | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | SIMP: (3822) implies:
% 132.91/18.99 | | | | | | | | | | | | | | | | | (3823) ~ (all_52_9 = all_36_0)
% 132.91/18.99 | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | REDUCE: (121), (3816) imply:
% 132.91/18.99 | | | | | | | | | | | | | | | | | (3824) ~ (all_52_11 = all_36_0)
% 132.91/18.99 | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | SIMP: (3824) implies:
% 132.91/18.99 | | | | | | | | | | | | | | | | | (3825) ~ (all_52_11 = all_36_0)
% 132.91/18.99 | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | REDUCE: (3790), (3816) imply:
% 132.91/18.99 | | | | | | | | | | | | | | | | | (3826) ~ (all_36_0 = e3)
% 132.91/18.99 | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | REDUCE: (3591), (3816) imply:
% 132.91/18.99 | | | | | | | | | | | | | | | | | (3827) ~ (all_36_0 = e2)
% 132.91/18.99 | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | REDUCE: (368), (3815) imply:
% 132.91/18.99 | | | | | | | | | | | | | | | | | (3828) ~ (all_4_2 = e3)
% 132.91/18.99 | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | SIMP: (3828) implies:
% 132.91/18.99 | | | | | | | | | | | | | | | | | (3829) ~ (all_4_2 = e3)
% 132.91/18.99 | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 132.91/18.99 | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.99 | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | (3830) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 132.91/18.99 | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 132.91/18.99 | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | BETA: splitting (3830) gives:
% 132.91/18.99 | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | (3831) all_57_0 = e0 & op(e3, e3) = e0
% 132.91/18.99 | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | ALPHA: (3831) implies:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | (3832) op(e3, e3) = e0
% 132.91/18.99 | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3593), (3832), (function-axioms) are
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495.
% 132.91/18.99 | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | (3833) all_57_1 = e0 & op(e3, e2) = e0
% 132.91/18.99 | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | ALPHA: (3833) implies:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | (3834) all_57_1 = e0
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | (3835) op(e3, e2) = e0
% 132.91/18.99 | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | (3836) all_54_15 = e3
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (3829), (3836) are inconsistent by
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | sub-proof #601.
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | (3837) ~ (all_54_15 = e3)
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | (3838) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | (3839) all_54_2 = e3
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3817), (3839) imply:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | (3840) all_36_0 = e3
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | REDUCE: (3826), (3840) imply:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | (3841) $false
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | CLOSE: (3841) is inconsistent.
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | (3842) ~ (all_54_2 = e3)
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | (3843) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | (3844) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3844) gives:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | (3845) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (170), (2978), (3593), (3845),
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | #254.
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | (3846) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (167), (3589), (3593), (3846),
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | #443.
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | (3847) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3847) gives:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | (3848) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3848) gives:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | (3849) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3849) implies:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | (3850) op(e1, e3) = e1
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3843) gives:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | (3851) all_54_2 = e2
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3817), (3827), (3851) are inconsistent by
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #244.
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | (3852) all_54_2 = e1 | all_54_2 = e0
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3838) gives:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (3853) all_54_15 = e2
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (3595), (3853) are inconsistent by
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #748.
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (3854) all_54_15 = e1 | all_54_15 = e0
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3854) gives:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3855) all_54_15 = e1
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (371), (3855) are inconsistent by sub-proof
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | #747.
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3856) all_54_15 = e0
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (3856) imply:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3857) all_4_2 = e0
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3857) implies:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3858) all_4_2 = e0
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (367), (3858) imply:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3859) ~ (all_52_11 = e0)
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3852) gives:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3860) all_54_2 = e1
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3817), (3860) imply:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3861) all_36_0 = e1
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3861) implies:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3862) all_36_0 = e1
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3823), (3862) imply:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3863) ~ (all_52_9 = e1)
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3825), (3862) imply:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3864) ~ (all_52_11 = e1)
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3865) all_54_14 = e3
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (3820), (3865) are inconsistent by
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #760.
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3866) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3866) gives:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3867) all_54_14 = e2
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (3867) imply:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3868) all_52_11 = e2
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3868) implies:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3869) all_52_11 = e2
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (3869) imply:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3870) ~ (all_52_9 = e2)
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3871) all_54_6 = e3
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (3871) imply:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3872) all_52_9 = e3
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2981), (3872) imply:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3873) $false
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3873) is inconsistent.
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3874) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3874) gives:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3875) all_54_6 = e2
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (3875) imply:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3876) all_52_9 = e2
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3870), (3876) imply:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3877) $false
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3877) is inconsistent.
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3878) all_54_6 = e1 | all_54_6 = e0
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3878) gives:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3879) all_54_6 = e1
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (3879) imply:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3880) all_52_9 = e1
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3863), (3880) imply:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3881) $false
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3881) is inconsistent.
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3882) all_54_6 = e0
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (3882) imply:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3883) all_52_9 = e0
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (3883) imply:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3884) ~ (all_52_1 = e0)
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3885) all_54_4 = e3
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (3885) imply:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3886) all_52_1 = e3
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2977), (3886) imply:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3887) $false
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3887) is inconsistent.
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3888) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3888) gives:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3889) all_54_4 = e2
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (3889) imply:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3890) all_52_1 = e2
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3589), (3890) imply:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3891) $false
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3891) is inconsistent.
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3892) all_54_4 = e1 | all_54_4 = e0
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (163), (268), (3850), (3884), (3892),
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #243.
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3893) all_54_14 = e1 | all_54_14 = e0
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (3859), (3864), (3893) are inconsistent by
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #755.
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3894) all_54_2 = e0
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3796), (3817), (3894) are inconsistent by
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #242.
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | (3895) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2,
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3895) implies:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | (3896) op(e2, e2) = e1
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2988), (3896), (function-axioms) are
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #325.
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | (3897) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3897) gives:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | (3898) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3898) implies:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | (3899) op(e2, e2) = e0
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2988), (3899), (function-axioms) are
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641.
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | (3900) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3900) gives:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | (3901) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3901) implies:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | (3902) op(e1, e1) = e2
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (3902), (function-axioms) are
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | (3903) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3903) implies:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | (3904) op(e0, e0) = all_56_31
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | (3905) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | (3906) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (3593), (3835), (3906),
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | #241.
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | (3907) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3907) gives:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3908) all_57_4 = e1 & op(e3, e1) = e1
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3908) implies:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3909) all_57_4 = e1
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3843) gives:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3910) all_54_2 = e2
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3817), (3827), (3910) are inconsistent by
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #244.
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3911) ~ (all_54_2 = e2)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3912) all_54_2 = e1 | all_54_2 = e0
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3912) gives:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3913) all_54_2 = e1
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3817), (3913) imply:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3914) all_36_0 = e1
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3914) implies:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3915) all_36_0 = e1
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3825), (3915) imply:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3916) ~ (all_52_11 = e1)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3826), (3915) imply:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3917) ~ (e3 = e1)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3827), (3915) imply:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3918) ~ (e2 = e1)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3919) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3919) gives:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3920) all_57_12 = e1 & op(e0, e3) = e1
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3920) implies:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3921) all_57_12 = e1
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3806), (3921) are inconsistent by sub-proof
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #591.
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3922) all_57_13 = e1 & op(e0, e2) = e1
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3922) implies:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3923) all_57_13 = e1
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3924) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3924) gives:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3925) all_57_12 = e2 & op(e0, e3) = e2
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3925) implies:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3926) all_57_12 = e2
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3593), (3926), (function-axioms) are inconsistent
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #290.
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3927) all_57_13 = e2 & op(e0, e2) = e2
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3927) implies:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3928) all_57_13 = e2
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3923), (3928) are inconsistent by sub-proof
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #567.
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3929) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3929) gives:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3930) all_57_14 = e2 & op(e0, e1) = e2
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3930) implies:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3931) all_57_14 = e2
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3932) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3932) gives:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3933) all_57_1 = e2 & op(e3, e2) = e2
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3933) implies:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3934) all_57_1 = e2
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (234),
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (2978), (3593), (3812), (3934),
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #237.
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3935) all_57_3 = e2 & op(e2, e2) = e2
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (234),
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (2978), (2987), (3593), (3812), (3935),
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #236.
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3936) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3936) gives:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3937) all_57_7 = e2 & op(e1, e2) = e2
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3937) implies:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3938) all_57_7 = e2
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3838) gives:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3939) all_54_15 = e2
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (3595), (3939) are inconsistent by
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #748.
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3940) ~ (all_54_15 = e2)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3941) all_54_15 = e1 | all_54_15 = e0
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3942) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3942) gives:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3943) all_57_4 = e0 & op(e3, e1) = e0
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3943) implies:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3944) all_57_4 = e0
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (170), (203), (234), (271), (2978),
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3590), (3593), (3796), (3812), (3817), (3821),
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3827), (3843), (3944), (function-axioms) are
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #234.
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3945) all_57_5 = e0 & op(e2, e1) = e0
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3945) implies:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3946) all_57_5 = e0
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3941) gives:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3947) all_54_15 = e1
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (371), (3947) are inconsistent by sub-proof
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #747.
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3948) all_54_15 = e0
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (3948) imply:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3949) all_4_2 = e0
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3949) implies:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3950) all_4_2 = e0
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (367), (3950) imply:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3951) ~ (all_52_11 = e0)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3829), (3950) imply:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3952) ~ (e3 = e0)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3595), (3950) imply:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3953) ~ (e2 = e0)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (3950) imply:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3954) ~ (e1 = e0)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (3950) imply:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3955) op(e0, e0) = e0
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3956) all_54_14 = e3
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (3820), (3956) are inconsistent by
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #760.
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3957) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3958) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3958) gives:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3959) all_57_2 = e2 & op(e2, e3) = e2
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3959) implies:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3960) all_57_2 = e2
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (231), (233), (3593),
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3806), (3960), (function-axioms) are inconsistent
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #489.
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3961) all_57_3 = e2 & op(e2, e2) = e2
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (234),
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (2978), (2987), (3593), (3812), (3961),
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #236.
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3962) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3962) gives:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3963) all_57_5 = e2 & op(e2, e1) = e2
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3963) implies:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3964) all_57_5 = e2
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3946), (3964) are inconsistent by sub-proof
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #372.
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3965) all_57_10 = e2 & op(e2, e0) = e2
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3965) implies:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3966) all_57_10 = e2
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3905) gives:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3967) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27))
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3967) gives:
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3968) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3968) implies:
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3969) all_56_31 = e3
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3904), (3969) imply:
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3970) op(e0, e0) = e3
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3955), (3970), (function-axioms) are
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #715.
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3971) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27)
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3971) implies:
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3972) all_56_31 = e2
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3904), (3972) imply:
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3973) op(e0, e0) = e2
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (158), (170),
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (208), (209), (210), (211), (221), (223), (224),
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227), (228), (231), (232), (233), (234), (237),
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (372), (2978), (2980), (2987), (3593),
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3938), (3966), (3973), (function-axioms) are
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #269.
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3974) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3974) gives:
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3975) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7)
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23)
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3975) implies:
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3976) op(e1, e1) = e0
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3791), (3976), (function-axioms) are
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753.
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3977) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3977) implies:
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3978) op(e0, e1) = e0
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (246), (3916), (3951), (3957), (3978),
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #351.
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3979) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3979) gives:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3980) all_57_8 = e0 & op(e1, e1) = e0
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3980) implies:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3981) op(e1, e1) = e0
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3791), (3981), (function-axioms) are
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753.
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3982) all_57_14 = e0 & op(e0, e1) = e0
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3982) implies:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3983) op(e0, e1) = e0
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (190), (245), (246), (367), (371), (3820),
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3916), (3941), (3983), (function-axioms) are
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #233.
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3984) all_57_13 = e2 & op(e0, e2) = e2
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3984) implies:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3985) all_57_13 = e2
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (208), (209), (3806),
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3931), (3985) are inconsistent by sub-proof #409.
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3986) all_57_15 = e2 & op(e0, e0) = e2
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3986) implies:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3987) op(e0, e0) = e2
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3988) all_57_15 = e0 & op(e0, e0) = e0
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3988) implies:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3989) op(e0, e0) = e0
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3987), (3989), (function-axioms) are
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #714.
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3990) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3990) implies:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3991) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3991) gives:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3992) all_57_12 = e0 & op(e0, e3) = e0
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3806), (3992) are inconsistent by sub-proof
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #436.
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3993) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3993) gives:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3994) all_57_13 = e0 & op(e0, e2) = e0
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3994) implies:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3995) all_57_13 = e0
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3923), (3995) imply:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3996) e1 = e0
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3909), (3996) imply:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3997) all_57_4 = e0
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (170), (203), (234), (271), (2978),
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3590), (3593), (3796), (3812), (3817), (3821),
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3827), (3843), (3997), (function-axioms) are
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #234.
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3998) all_57_14 = e0 & op(e0, e1) = e0
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3998) implies:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3999) op(e0, e1) = e0
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (190), (245), (246), (367), (371), (3595),
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3820), (3838), (3916), (3999), (function-axioms)
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #232.
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4000) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4000) gives:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4001) all_57_14 = e1 & op(e0, e1) = e1
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4001) implies:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4002) all_57_14 = e1
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4003) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4003) gives:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4004) all_57_4 = e2 & op(e3, e1) = e2
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4004) implies:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4005) all_57_4 = e2
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (234), (3593), (3812), (3834),
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4005), (function-axioms) are inconsistent by
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #280.
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4006) all_57_5 = e2 & op(e2, e1) = e2
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4006) implies:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4007) all_57_5 = e2
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4008) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4008) gives:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4009) all_57_4 = e0 & op(e3, e1) = e0
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4009) implies:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4010) all_57_4 = e0
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (170), (203), (234), (271), (2978),
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3590), (3593), (3796), (3812), (3817), (3821),
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3827), (3843), (4010), (function-axioms) are
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #234.
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4011) all_57_5 = e0 & op(e2, e1) = e0
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4011) implies:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4012) all_57_5 = e0
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4007), (4012) are inconsistent by sub-proof
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #372.
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4013) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4013) gives:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4014) all_57_8 = e0 & op(e1, e1) = e0
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4014) implies:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4015) op(e1, e1) = e0
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3791), (4015), (function-axioms) are
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753.
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4016) all_57_14 = e0 & op(e0, e1) = e0
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4016) implies:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4017) all_57_14 = e0
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4002), (4017) imply:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4018) e1 = e0
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3909), (4018) imply:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4019) all_57_4 = e0
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (39), (220), (3791), (4007),
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4017), (4019), (function-axioms) are inconsistent
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #230.
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4020) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (39), (372), (4002), (4020),
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #559.
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4021) all_57_15 = e1 & op(e0, e0) = e1
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4021) implies:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4022) op(e0, e0) = e1
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3838) gives:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4023) all_54_15 = e2
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (3595), (4023) are inconsistent by
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #748.
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4024) all_54_15 = e1 | all_54_15 = e0
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3905) gives:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4025) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27))
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4025) gives:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4026) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4026) implies:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4027) all_56_31 = e3
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3904), (4027) imply:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4028) op(e0, e0) = e3
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4022), (4028), (function-axioms) are
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #606.
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4029) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27)
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4029) implies:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4030) all_56_31 = e2
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3904), (4030) imply:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4031) op(e0, e0) = e2
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4022), (4031), (function-axioms) are
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #636.
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4032) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4032) gives:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4033) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7)
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23)
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4033) implies:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4034) op(e1, e1) = e0
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3791), (4034), (function-axioms) are
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753.
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4035) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4035) implies:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4036) op(e0, e1) = e0
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (190), (245), (246), (367), (371), (3820),
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3916), (4024), (4036), (function-axioms) are
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #233.
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4037) all_54_2 = e0
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3796), (3817), (4037) are inconsistent by
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #242.
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4038) all_57_9 = e1 & op(e3, e0) = e1
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4038) implies:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4039) all_57_9 = e1
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3812), (4039) are inconsistent by sub-proof
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | #690.
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | Case 2:
% 133.16/19.01 | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | (4040) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 133.16/19.01 | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 133.16/19.01 | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | BETA: splitting (4040) gives:
% 133.16/19.01 | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | Case 1:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | (4041) all_57_4 = e0 & op(e3, e1) = e0
% 133.16/19.01 | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | ALPHA: (4041) implies:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | (4042) all_57_4 = e0
% 133.16/19.01 | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | (4043) all_54_2 = e3
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3817), (4043) imply:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | (4044) all_36_0 = e3
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | REDUCE: (3826), (4044) imply:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | (4045) $false
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | CLOSE: (4045) is inconsistent.
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | (4046) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (170), (203), (234), (271), (2978),
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | (3590), (3593), (3796), (3812), (3817), (3821),
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | (3827), (4042), (4046), (function-axioms) are
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #234.
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | Case 2:
% 133.16/19.01 | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | (4047) all_57_9 = e0 & op(e3, e0) = e0
% 133.16/19.01 | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3812), (4047) are inconsistent by sub-proof
% 133.16/19.01 | | | | | | | | | | | | | | | | | | | #299.
% 133.16/19.01 | | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | Case 2:
% 133.16/19.01 | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | (4048) ~ (all_36_1 = e2) & op(e3, e3) = all_36_1 &
% 133.16/19.01 | | | | | | | | | | | | | $i(all_36_1)
% 133.16/19.01 | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | | REF_CLOSE: (3593), (4048), (function-axioms) are inconsistent
% 133.16/19.01 | | | | | | | | | | | | | by sub-proof #342.
% 133.16/19.01 | | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | Case 2:
% 133.16/19.01 | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | (4049) all_20_2 = e2
% 133.16/19.01 | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | COMBINE_EQS: (318), (4049) imply:
% 133.16/19.01 | | | | | | | | | | (4050) all_4_2 = e2
% 133.16/19.01 | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | COMBINE_EQS: (331), (4050) imply:
% 133.16/19.01 | | | | | | | | | | (4051) all_26_2 = e2
% 133.16/19.01 | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | REDUCE: (369), (4050) imply:
% 133.16/19.01 | | | | | | | | | | (4052) ~ (all_52_13 = e2)
% 133.16/19.01 | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | REDUCE: (36), (4050) imply:
% 133.16/19.01 | | | | | | | | | | (4053) op(e0, e0) = e2
% 133.16/19.01 | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | BETA: splitting (70) gives:
% 133.16/19.01 | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | Case 1:
% 133.16/19.01 | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | (4054) ~ (all_26_2 = e2)
% 133.16/19.01 | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | REDUCE: (4051), (4054) imply:
% 133.16/19.01 | | | | | | | | | | | (4055) $false
% 133.16/19.01 | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | CLOSE: (4055) is inconsistent.
% 133.16/19.01 | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | Case 2:
% 133.16/19.01 | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | (4056) ( ~ (all_26_0 = e1) & op(e2, e0) = all_26_0 &
% 133.16/19.01 | | | | | | | | | | | $i(all_26_0)) | ( ~ (all_26_1 = e3) & op(e2, e2)
% 133.16/19.01 | | | | | | | | | | | = all_26_1 & $i(all_26_1))
% 133.16/19.01 | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | BETA: splitting (4056) gives:
% 133.16/19.01 | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | Case 1:
% 133.16/19.01 | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | (4057) ~ (all_26_0 = e1) & op(e2, e0) = all_26_0 &
% 133.16/19.01 | | | | | | | | | | | | $i(all_26_0)
% 133.16/19.01 | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | ALPHA: (4057) implies:
% 133.16/19.01 | | | | | | | | | | | | (4058) ~ (all_26_0 = e1)
% 133.16/19.01 | | | | | | | | | | | | (4059) op(e2, e0) = all_26_0
% 133.16/19.01 | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (91), (118),
% 133.16/19.01 | | | | | | | | | | | | (145), (146), (149), (157), (158), (163), (164),
% 133.16/19.01 | | | | | | | | | | | | (165), (167), (170), (190), (197), (200), (206),
% 133.16/19.01 | | | | | | | | | | | | (208), (209), (210), (211), (212), (214), (217),
% 133.16/19.01 | | | | | | | | | | | | (221), (223), (224), (225), (227), (228), (231),
% 133.16/19.01 | | | | | | | | | | | | (232), (233), (234), (237), (238), (246), (259),
% 133.16/19.01 | | | | | | | | | | | | (268), (332), (362), (364), (372), (2977), (2978),
% 133.16/19.01 | | | | | | | | | | | | (2980), (2981), (2982), (2987), (2988), (3593),
% 133.16/19.01 | | | | | | | | | | | | (4052), (4053), (4058), (4059), (function-axioms)
% 133.16/19.01 | | | | | | | | | | | | are inconsistent by sub-proof #267.
% 133.16/19.01 | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | Case 2:
% 133.16/19.01 | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | (4060) ~ (all_26_1 = e3) & op(e2, e2) = all_26_1 &
% 133.16/19.01 | | | | | | | | | | | | $i(all_26_1)
% 133.16/19.01 | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | ALPHA: (4060) implies:
% 133.16/19.01 | | | | | | | | | | | | (4061) ~ (all_26_1 = e3)
% 133.16/19.01 | | | | | | | | | | | | (4062) op(e2, e2) = all_26_1
% 133.16/19.01 | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | | REF_CLOSE: (2988), (4061), (4062), (function-axioms) are
% 133.16/19.01 | | | | | | | | | | | | inconsistent by sub-proof #334.
% 133.16/19.01 | | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | | |
% 133.16/19.01 | | | | | | | | | End of split
% 133.16/19.01 | | | | | | | | |
% 133.16/19.01 | | | | | | | | End of split
% 133.16/19.01 | | | | | | | |
% 133.16/19.01 | | | | | | | End of split
% 133.16/19.01 | | | | | | |
% 133.16/19.01 | | | | | | Case 2:
% 133.16/19.01 | | | | | | |
% 133.16/19.01 | | | | | | | (4063) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 &
% 133.16/19.01 | | | | | | | op(e0, e2) = e3)
% 133.16/19.01 | | | | | | |
% 133.16/19.01 | | | | | | | REF_CLOSE: (158), (162), (2979), (2980), (4063), (function-axioms)
% 133.16/19.01 | | | | | | | are inconsistent by sub-proof #555.
% 133.16/19.01 | | | | | | |
% 133.16/19.01 | | | | | | End of split
% 133.16/19.01 | | | | | |
% 133.16/19.01 | | | | | End of split
% 133.16/19.01 | | | | |
% 133.16/19.01 | | | | Case 2:
% 133.16/19.01 | | | | |
% 133.16/19.01 | | | | | (4064) all_10_2 = e0
% 133.16/19.01 | | | | |
% 133.16/19.01 | | | | | COMBINE_EQS: (319), (4064) imply:
% 133.16/19.01 | | | | | (4065) all_24_2 = e0
% 133.16/19.01 | | | | |
% 133.16/19.01 | | | | | REDUCE: (336), (4064) imply:
% 133.16/19.01 | | | | | (4066) ~ (all_52_1 = e0)
% 133.16/19.01 | | | | |
% 133.16/19.01 | | | | | REDUCE: (340), (4064) imply:
% 133.16/19.01 | | | | | (4067) ~ (all_52_3 = e0)
% 133.16/19.01 | | | | |
% 133.16/19.01 | | | | | REDUCE: (342), (4064) imply:
% 133.16/19.01 | | | | | (4068) ~ (all_52_4 = e0)
% 133.16/19.01 | | | | |
% 133.16/19.01 | | | | | REDUCE: (344), (4064) imply:
% 133.16/19.01 | | | | | (4069) ~ (all_52_8 = e0)
% 133.16/19.01 | | | | |
% 133.16/19.01 | | | | | REDUCE: (346), (4064) imply:
% 133.16/19.01 | | | | | (4070) ~ (all_52_12 = e0)
% 133.16/19.01 | | | | |
% 133.16/19.01 | | | | | REDUCE: (45), (4064) imply:
% 133.16/19.01 | | | | | (4071) op(e3, e3) = e0
% 133.16/19.01 | | | | |
% 133.16/19.01 | | | | | BETA: splitting (52) gives:
% 133.16/19.01 | | | | |
% 133.16/19.01 | | | | | Case 1:
% 133.16/19.01 | | | | | |
% 133.16/19.01 | | | | | | (4072) ~ (all_14_2 = e3)
% 133.16/19.01 | | | | | |
% 133.16/19.01 | | | | | | REDUCE: (329), (4072) imply:
% 133.16/19.01 | | | | | | (4073) ~ (all_8_2 = e3)
% 133.16/19.01 | | | | | |
% 133.16/19.01 | | | | | | BETA: splitting (61) gives:
% 133.16/19.01 | | | | | |
% 133.16/19.01 | | | | | | Case 1:
% 133.16/19.01 | | | | | | |
% 133.16/19.01 | | | | | | | (4074) ~ (all_20_2 = e2)
% 133.16/19.01 | | | | | | |
% 133.16/19.01 | | | | | | | REDUCE: (318), (4074) imply:
% 133.16/19.01 | | | | | | | (4075) ~ (all_4_2 = e2)
% 133.16/19.01 | | | | | | |
% 133.16/19.01 | | | | | | | BETA: splitting (73) gives:
% 133.16/19.01 | | | | | | |
% 133.16/19.01 | | | | | | | Case 1:
% 133.16/19.01 | | | | | | | |
% 133.16/19.01 | | | | | | | | (4076) ~ (all_28_2 = e3)
% 133.16/19.01 | | | | | | | |
% 133.16/19.01 | | | | | | | | REDUCE: (316), (4076) imply:
% 133.16/19.01 | | | | | | | | (4077) ~ (all_6_2 = e3)
% 133.16/19.01 | | | | | | | |
% 133.16/19.01 | | | | | | | | BETA: splitting (76) gives:
% 133.16/19.01 | | | | | | | |
% 133.16/19.01 | | | | | | | | Case 1:
% 133.16/19.01 | | | | | | | | |
% 133.16/19.01 | | | | | | | | | (4078) ~ (all_30_2 = e0)
% 133.16/19.01 | | | | | | | | |
% 133.16/19.01 | | | | | | | | | REDUCE: (309), (4078) imply:
% 133.16/19.02 | | | | | | | | | (4079) ~ (all_8_2 = e0)
% 133.16/19.02 | | | | | | | | |
% 133.16/19.02 | | | | | | | | | BETA: splitting (199) gives:
% 133.16/19.02 | | | | | | | | |
% 133.16/19.02 | | | | | | | | | Case 1:
% 133.16/19.02 | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | (4080) all_54_5 = e3
% 133.16/19.02 | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | REF_CLOSE: (267), (4073), (4080) are inconsistent by
% 133.16/19.02 | | | | | | | | | | sub-proof #554.
% 133.16/19.02 | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | Case 2:
% 133.16/19.02 | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | (4081) ~ (all_54_5 = e3)
% 133.16/19.02 | | | | | | | | | | (4082) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 133.16/19.02 | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | BETA: splitting (4082) gives:
% 133.16/19.02 | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | Case 1:
% 133.16/19.02 | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | (4083) all_54_5 = e2
% 133.16/19.02 | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | COMBINE_EQS: (267), (4083) imply:
% 133.16/19.02 | | | | | | | | | | | (4084) all_8_2 = e2
% 133.16/19.02 | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | SIMP: (4084) implies:
% 133.16/19.02 | | | | | | | | | | | (4085) all_8_2 = e2
% 133.16/19.02 | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | REDUCE: (356), (4085) imply:
% 133.16/19.02 | | | | | | | | | | | (4086) ~ (all_52_9 = e2)
% 133.16/19.02 | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | REDUCE: (358), (4085) imply:
% 133.16/19.02 | | | | | | | | | | | (4087) ~ (all_52_13 = e2)
% 133.16/19.02 | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | BETA: splitting (82) gives:
% 133.16/19.02 | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | Case 1:
% 133.16/19.02 | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | (4088) ~ (all_34_2 = e3)
% 133.16/19.02 | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | REDUCE: (307), (4088) imply:
% 133.16/19.02 | | | | | | | | | | | | (4089) ~ (all_4_2 = e3)
% 133.16/19.02 | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | BETA: splitting (189) gives:
% 133.16/19.02 | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | Case 1:
% 133.16/19.02 | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | (4090) all_54_15 = e3
% 133.16/19.02 | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | REF_CLOSE: (245), (4089), (4090) are inconsistent by
% 133.16/19.02 | | | | | | | | | | | | | sub-proof #601.
% 133.16/19.02 | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | Case 2:
% 133.16/19.02 | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | (4091) ~ (all_54_15 = e3)
% 133.16/19.02 | | | | | | | | | | | | | (4092) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 133.16/19.02 | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | BETA: splitting (4092) gives:
% 133.16/19.02 | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | Case 1:
% 133.16/19.02 | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | (4093) all_54_15 = e2
% 133.16/19.02 | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | REF_CLOSE: (245), (4075), (4093) are inconsistent by
% 133.16/19.02 | | | | | | | | | | | | | | sub-proof #748.
% 133.16/19.02 | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | Case 2:
% 133.16/19.02 | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | (4094) ~ (all_54_15 = e2)
% 133.16/19.02 | | | | | | | | | | | | | | (4095) all_54_15 = e1 | all_54_15 = e0
% 133.16/19.02 | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | BETA: splitting (4095) gives:
% 133.16/19.02 | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | Case 1:
% 133.16/19.02 | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | (4096) all_54_15 = e1
% 133.16/19.02 | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | REF_CLOSE: (245), (371), (4096) are inconsistent by sub-proof
% 133.16/19.02 | | | | | | | | | | | | | | | #747.
% 133.16/19.02 | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | Case 2:
% 133.16/19.02 | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | (4097) all_54_15 = e0
% 133.16/19.02 | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | COMBINE_EQS: (245), (4097) imply:
% 133.16/19.02 | | | | | | | | | | | | | | | (4098) all_4_2 = e0
% 133.16/19.02 | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | SIMP: (4098) implies:
% 133.16/19.02 | | | | | | | | | | | | | | | (4099) all_4_2 = e0
% 133.16/19.02 | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | REDUCE: (4089), (4099) imply:
% 133.16/19.02 | | | | | | | | | | | | | | | (4100) ~ (e3 = e0)
% 133.16/19.02 | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | REDUCE: (4075), (4099) imply:
% 133.16/19.02 | | | | | | | | | | | | | | | (4101) ~ (e2 = e0)
% 133.16/19.02 | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | REDUCE: (371), (4099) imply:
% 133.16/19.02 | | | | | | | | | | | | | | | (4102) ~ (e1 = e0)
% 133.16/19.02 | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | REDUCE: (36), (4099) imply:
% 133.16/19.02 | | | | | | | | | | | | | | | (4103) op(e0, e0) = e0
% 133.16/19.02 | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.16/19.02 | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | Case 1:
% 133.16/19.02 | | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | | (4104) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.16/19.02 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.16/19.02 | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.16/19.02 | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.16/19.02 | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.16/19.02 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.16/19.02 | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.16/19.02 | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.16/19.02 | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.16/19.02 | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.16/19.02 | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.16/19.02 | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.16/19.02 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.16/19.02 | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.16/19.02 | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.16/19.02 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.16/19.02 | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.16/19.02 | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.16/19.02 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.16/19.02 | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.16/19.02 | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.16/19.02 | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.16/19.02 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.16/19.02 | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.16/19.02 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.16/19.02 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.16/19.02 | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.16/19.02 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.16/19.02 | | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | | BETA: splitting (4104) gives:
% 133.16/19.02 | | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | | Case 1:
% 133.16/19.02 | | | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | | | (4105) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.16/19.02 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.16/19.02 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.16/19.02 | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.16/19.02 | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.16/19.02 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.16/19.02 | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.16/19.02 | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.16/19.02 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.16/19.02 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.16/19.02 | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.16/19.02 | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.16/19.02 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.16/19.02 | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 133.16/19.02 | | | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (4071), (4105), (function-axioms) are
% 133.16/19.02 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #229.
% 133.16/19.02 | | | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | | Case 2:
% 133.16/19.02 | | | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | | | (4106) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.16/19.02 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.16/19.02 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.16/19.02 | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.16/19.02 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.16/19.02 | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.16/19.02 | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.16/19.02 | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.16/19.02 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.16/19.02 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.16/19.02 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.16/19.02 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.16/19.02 | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.16/19.02 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.16/19.02 | | | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | | | BETA: splitting (4106) gives:
% 133.16/19.02 | | | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | | | Case 1:
% 133.16/19.02 | | | | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | | | | (4107) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.16/19.02 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.16/19.02 | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3,
% 133.16/19.02 | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.16/19.02 | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 133.16/19.02 | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.16/19.02 | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 133.16/19.02 | | | | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | | | | ALPHA: (4107) implies:
% 133.16/19.02 | | | | | | | | | | | | | | | | | | (4108) ~ (all_56_31 = e0)
% 133.16/19.02 | | | | | | | | | | | | | | | | | | (4109) op(e0, e0) = all_56_31
% 133.16/19.02 | | | | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4103), (4108), (4109), (function-axioms) are
% 133.16/19.02 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #712.
% 133.16/19.02 | | | | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | | | Case 2:
% 133.16/19.02 | | | | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | | | | (4110) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.16/19.02 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.16/19.02 | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.16/19.02 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.16/19.02 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2,
% 133.16/19.02 | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.16/19.02 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 133.16/19.02 | | | | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | | | | ALPHA: (4110) implies:
% 133.16/19.02 | | | | | | | | | | | | | | | | | | (4111) op(e2, e2) = e3
% 133.16/19.02 | | | | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (4073), (4111), (function-axioms) are
% 133.16/19.02 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #228.
% 133.16/19.02 | | | | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | | | End of split
% 133.16/19.02 | | | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | | End of split
% 133.16/19.02 | | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | Case 2:
% 133.16/19.02 | | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | | (4112) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.16/19.02 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.16/19.02 | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.16/19.02 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.16/19.02 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.16/19.02 | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.16/19.02 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.16/19.02 | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.16/19.02 | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.16/19.02 | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.16/19.02 | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.16/19.02 | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.16/19.02 | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.16/19.02 | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.16/19.02 | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.16/19.02 | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.16/19.02 | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.16/19.02 | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.16/19.02 | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.16/19.02 | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.16/19.02 | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.16/19.02 | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.16/19.02 | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.16/19.02 | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.16/19.02 | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.16/19.02 | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.16/19.02 | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.16/19.02 | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.16/19.02 | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.16/19.02 | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.16/19.02 | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.16/19.02 | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.16/19.02 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.16/19.02 | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.16/19.02 | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.16/19.02 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.16/19.02 | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.16/19.02 | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.16/19.02 | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.16/19.02 | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.16/19.02 | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.16/19.02 | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.16/19.02 | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.16/19.02 | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.16/19.02 | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.16/19.02 | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.16/19.02 | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.16/19.02 | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.16/19.02 | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.16/19.02 | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.16/19.02 | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.16/19.02 | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.16/19.02 | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.16/19.02 | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.16/19.02 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.16/19.02 | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.16/19.02 | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.16/19.02 | | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (39), (164), (165), (372), (4077),
% 133.16/19.02 | | | | | | | | | | | | | | | | (4086), (4087), (4103), (4112), (function-axioms)
% 133.16/19.02 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #708.
% 133.16/19.02 | | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | End of split
% 133.16/19.02 | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | End of split
% 133.16/19.02 | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | End of split
% 133.16/19.02 | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | End of split
% 133.16/19.02 | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | Case 2:
% 133.16/19.02 | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | (4113) all_34_2 = e3
% 133.16/19.02 | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | COMBINE_EQS: (307), (4113) imply:
% 133.16/19.02 | | | | | | | | | | | | (4114) all_4_2 = e3
% 133.16/19.02 | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | SIMP: (4114) implies:
% 133.16/19.02 | | | | | | | | | | | | (4115) all_4_2 = e3
% 133.16/19.02 | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | REDUCE: (367), (4115) imply:
% 133.16/19.02 | | | | | | | | | | | | (4116) ~ (all_52_11 = e3)
% 133.16/19.02 | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | REDUCE: (368), (4115) imply:
% 133.16/19.02 | | | | | | | | | | | | (4117) ~ (all_52_12 = e3)
% 133.16/19.02 | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | REDUCE: (36), (4115) imply:
% 133.16/19.02 | | | | | | | | | | | | (4118) op(e0, e0) = e3
% 133.16/19.02 | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.16/19.02 | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | Case 1:
% 133.16/19.02 | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | (4119) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.16/19.02 | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.16/19.02 | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.16/19.02 | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.16/19.02 | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.16/19.02 | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.16/19.02 | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.16/19.02 | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.16/19.02 | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.16/19.02 | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.16/19.02 | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.16/19.02 | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.16/19.02 | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.16/19.02 | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.16/19.02 | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.16/19.02 | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.16/19.02 | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.16/19.02 | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.16/19.02 | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.16/19.02 | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.16/19.02 | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.16/19.02 | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.16/19.02 | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.16/19.02 | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.16/19.02 | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.16/19.02 | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.16/19.02 | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.16/19.02 | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.16/19.02 | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | BETA: splitting (4119) gives:
% 133.16/19.02 | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | Case 1:
% 133.16/19.02 | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | (4120) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.16/19.02 | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.16/19.02 | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.16/19.02 | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.16/19.02 | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.16/19.02 | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.16/19.02 | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.16/19.02 | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.16/19.02 | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.16/19.02 | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.16/19.02 | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.16/19.02 | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.16/19.02 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.16/19.02 | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 133.16/19.02 | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (4071), (4120), (function-axioms) are
% 133.16/19.02 | | | | | | | | | | | | | | inconsistent by sub-proof #229.
% 133.16/19.02 | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | Case 2:
% 133.16/19.02 | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | (4121) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.16/19.02 | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.16/19.02 | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.16/19.02 | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.16/19.02 | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.16/19.02 | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.16/19.02 | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.16/19.02 | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.16/19.02 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.16/19.02 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.16/19.02 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.16/19.02 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.16/19.02 | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.16/19.02 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.16/19.02 | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | BETA: splitting (4121) gives:
% 133.16/19.02 | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | Case 1:
% 133.16/19.02 | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | (4122) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.16/19.02 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.16/19.02 | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3,
% 133.16/19.02 | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.16/19.02 | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 133.16/19.02 | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.16/19.02 | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 133.16/19.02 | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | ALPHA: (4122) implies:
% 133.16/19.02 | | | | | | | | | | | | | | | (4123) op(e3, e0) = e3
% 133.16/19.02 | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | REF_CLOSE: (168), (4117), (4123), (function-axioms) are
% 133.16/19.02 | | | | | | | | | | | | | | | inconsistent by sub-proof #733.
% 133.16/19.02 | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | Case 2:
% 133.16/19.02 | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | (4124) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.16/19.02 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.16/19.02 | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.16/19.02 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.16/19.02 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2,
% 133.16/19.02 | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.16/19.02 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 133.16/19.02 | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | ALPHA: (4124) implies:
% 133.16/19.02 | | | | | | | | | | | | | | | (4125) op(e2, e2) = e3
% 133.16/19.02 | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | REF_CLOSE: (42), (4073), (4125), (function-axioms) are
% 133.16/19.02 | | | | | | | | | | | | | | | inconsistent by sub-proof #228.
% 133.16/19.02 | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | End of split
% 133.16/19.02 | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | End of split
% 133.16/19.02 | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | Case 2:
% 133.16/19.02 | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | (4126) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.16/19.02 | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.16/19.02 | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.16/19.02 | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.16/19.02 | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.16/19.02 | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.16/19.02 | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.16/19.02 | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.16/19.02 | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.16/19.02 | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.16/19.02 | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.16/19.02 | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.16/19.02 | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.16/19.02 | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.16/19.02 | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.16/19.02 | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.16/19.02 | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.16/19.02 | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.16/19.02 | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.16/19.02 | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.16/19.02 | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.16/19.02 | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.16/19.02 | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.16/19.02 | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.16/19.02 | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.16/19.02 | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.16/19.02 | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.16/19.02 | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.16/19.02 | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.16/19.02 | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.16/19.02 | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.16/19.02 | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.16/19.02 | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.16/19.02 | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.16/19.02 | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.16/19.02 | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.16/19.02 | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.16/19.02 | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.16/19.02 | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.16/19.02 | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.16/19.02 | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.16/19.02 | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.16/19.02 | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.16/19.02 | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.16/19.02 | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.16/19.02 | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.16/19.02 | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.16/19.02 | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.16/19.02 | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.16/19.02 | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.16/19.02 | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.16/19.02 | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.16/19.02 | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.16/19.02 | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.16/19.02 | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.16/19.02 | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.16/19.02 | | | | | | | | | | | | | & $i(all_56_29))))
% 133.16/19.02 | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | BETA: splitting (4126) gives:
% 133.16/19.02 | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | Case 1:
% 133.16/19.02 | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | (4127) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.16/19.02 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.16/19.02 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.16/19.02 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.16/19.02 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.16/19.02 | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.16/19.02 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.16/19.02 | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.16/19.02 | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.16/19.02 | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.16/19.02 | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.16/19.02 | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.16/19.02 | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.16/19.02 | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.16/19.02 | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | REF_CLOSE: (39), (165), (4077), (4086), (4127),
% 133.16/19.02 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.16/19.02 | | | | | | | | | | | | | | #769.
% 133.16/19.02 | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | Case 2:
% 133.16/19.02 | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | (4128) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.16/19.02 | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.16/19.02 | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 133.16/19.02 | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 133.16/19.02 | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.16/19.02 | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.16/19.02 | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.16/19.02 | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.16/19.02 | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.16/19.02 | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.16/19.02 | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.16/19.02 | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.16/19.02 | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.16/19.02 | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.16/19.02 | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.16/19.02 | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.16/19.02 | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.16/19.02 | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.16/19.02 | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.16/19.02 | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.16/19.02 | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.16/19.02 | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.16/19.02 | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.16/19.02 | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.16/19.02 | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.16/19.02 | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.16/19.02 | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.16/19.02 | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.16/19.02 | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.16/19.02 | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.16/19.02 | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.16/19.02 | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.16/19.02 | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.16/19.02 | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.16/19.02 | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.16/19.02 | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.16/19.02 | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.16/19.02 | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.16/19.02 | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.16/19.02 | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.16/19.02 | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.16/19.02 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.16/19.02 | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.16/19.02 | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.16/19.02 | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | BETA: splitting (4128) gives:
% 133.16/19.02 | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | Case 1:
% 133.16/19.02 | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | (4129) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.16/19.02 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.16/19.02 | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 133.16/19.02 | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.16/19.02 | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 133.16/19.02 | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.16/19.02 | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 133.16/19.02 | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | ALPHA: (4129) implies:
% 133.16/19.02 | | | | | | | | | | | | | | | (4130) op(e2, e0) = e2
% 133.16/19.02 | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | REF_CLOSE: (164), (4087), (4130), (function-axioms) are
% 133.16/19.02 | | | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 133.16/19.02 | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | Case 2:
% 133.16/19.02 | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | (4131) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.16/19.02 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.16/19.02 | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.16/19.02 | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.16/19.02 | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.16/19.02 | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.16/19.02 | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.16/19.02 | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.16/19.02 | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.16/19.02 | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.16/19.02 | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.16/19.02 | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.16/19.02 | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.16/19.02 | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.16/19.02 | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.16/19.02 | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.16/19.02 | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.16/19.02 | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.16/19.02 | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.16/19.02 | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.16/19.02 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.16/19.02 | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.16/19.02 | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.16/19.02 | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.16/19.02 | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.16/19.02 | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.16/19.02 | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.16/19.02 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.16/19.02 | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.16/19.02 | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.16/19.02 | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.16/19.02 | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.16/19.02 | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.16/19.02 | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.16/19.02 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.16/19.02 | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.16/19.02 | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.16/19.02 | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (42), (100), (157), (158), (159),
% 133.16/19.02 | | | | | | | | | | | | | | | (190), (199), (246), (267), (295), (354), (364),
% 133.16/19.02 | | | | | | | | | | | | | | | (372), (373), (4067), (4073), (4116), (4118),
% 133.16/19.02 | | | | | | | | | | | | | | | (4131), (function-axioms) are inconsistent by
% 133.16/19.02 | | | | | | | | | | | | | | | sub-proof #226.
% 133.16/19.02 | | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | | End of split
% 133.16/19.02 | | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | | End of split
% 133.16/19.02 | | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | | End of split
% 133.16/19.02 | | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | End of split
% 133.16/19.02 | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | Case 2:
% 133.16/19.02 | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | (4132) all_54_5 = e1 | all_54_5 = e0
% 133.16/19.02 | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | | REF_CLOSE: (267), (373), (4079), (4132) are inconsistent by
% 133.16/19.02 | | | | | | | | | | | sub-proof #624.
% 133.16/19.02 | | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | | End of split
% 133.16/19.02 | | | | | | | | | |
% 133.16/19.02 | | | | | | | | | End of split
% 133.16/19.02 | | | | | | | | |
% 133.16/19.02 | | | | | | | | Case 2:
% 133.16/19.02 | | | | | | | | |
% 133.16/19.02 | | | | | | | | | (4133) all_30_2 = e0
% 133.16/19.02 | | | | | | | | |
% 133.16/19.02 | | | | | | | | | COMBINE_EQS: (309), (4133) imply:
% 133.16/19.02 | | | | | | | | | (4134) all_8_2 = e0
% 133.16/19.02 | | | | | | | | |
% 133.16/19.02 | | | | | | | | | SIMP: (4134) implies:
% 133.16/19.02 | | | | | | | | | (4135) all_8_2 = e0
% 133.16/19.02 | | | | | | | | |
% 133.16/19.03 | | | | | | | | | COMBINE_EQS: (301), (4135) imply:
% 133.16/19.03 | | | | | | | | | (4136) all_42_2 = e0
% 133.16/19.03 | | | | | | | | |
% 133.16/19.03 | | | | | | | | | REDUCE: (352), (4135) imply:
% 133.16/19.03 | | | | | | | | | (4137) ~ (all_52_6 = e0)
% 133.16/19.03 | | | | | | | | |
% 133.16/19.03 | | | | | | | | | REDUCE: (354), (4135) imply:
% 133.16/19.03 | | | | | | | | | (4138) ~ (all_52_7 = e0)
% 133.16/19.03 | | | | | | | | |
% 133.16/19.03 | | | | | | | | | REDUCE: (356), (4135) imply:
% 133.16/19.03 | | | | | | | | | (4139) ~ (all_52_9 = e0)
% 133.16/19.03 | | | | | | | | |
% 133.16/19.03 | | | | | | | | | REDUCE: (4073), (4135) imply:
% 133.16/19.03 | | | | | | | | | (4140) ~ (e3 = e0)
% 133.16/19.03 | | | | | | | | |
% 133.16/19.03 | | | | | | | | | REDUCE: (373), (4135) imply:
% 133.16/19.03 | | | | | | | | | (4141) ~ (e1 = e0)
% 133.16/19.03 | | | | | | | | |
% 133.16/19.03 | | | | | | | | | BETA: splitting (223) gives:
% 133.16/19.03 | | | | | | | | |
% 133.16/19.03 | | | | | | | | | Case 1:
% 133.16/19.03 | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | (4142) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 133.16/19.03 | | | | | | | | | | & op(e2, e2) = e0)
% 133.16/19.03 | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | BETA: splitting (4142) gives:
% 133.16/19.03 | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | Case 1:
% 133.16/19.03 | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | (4143) all_57_2 = e0 & op(e2, e3) = e0
% 133.16/19.03 | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | REF_CLOSE: (167), (4066), (4143), (function-axioms) are
% 133.16/19.03 | | | | | | | | | | | inconsistent by sub-proof #225.
% 133.16/19.03 | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | Case 2:
% 133.16/19.03 | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | (4144) all_57_3 = e0 & op(e2, e2) = e0
% 133.16/19.03 | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | ALPHA: (4144) implies:
% 133.16/19.03 | | | | | | | | | | | (4145) all_57_3 = e0
% 133.16/19.03 | | | | | | | | | | | (4146) op(e2, e2) = e0
% 133.16/19.03 | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | BETA: splitting (82) gives:
% 133.16/19.03 | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | Case 1:
% 133.16/19.03 | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | (4147) ~ (all_34_2 = e3)
% 133.16/19.03 | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | REDUCE: (307), (4147) imply:
% 133.16/19.03 | | | | | | | | | | | | (4148) ~ (all_4_2 = e3)
% 133.16/19.03 | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | BETA: splitting (189) gives:
% 133.16/19.03 | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | Case 1:
% 133.16/19.03 | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | (4149) all_54_15 = e3
% 133.16/19.03 | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | COMBINE_EQS: (245), (4149) imply:
% 133.16/19.03 | | | | | | | | | | | | | (4150) all_4_2 = e3
% 133.16/19.03 | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | REDUCE: (4148), (4150) imply:
% 133.16/19.03 | | | | | | | | | | | | | (4151) $false
% 133.16/19.03 | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | CLOSE: (4151) is inconsistent.
% 133.16/19.03 | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | Case 2:
% 133.16/19.03 | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | (4152) ~ (all_54_15 = e3)
% 133.16/19.03 | | | | | | | | | | | | | (4153) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 133.16/19.03 | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | BETA: splitting (4153) gives:
% 133.16/19.03 | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | Case 1:
% 133.16/19.03 | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | (4154) all_54_15 = e2
% 133.16/19.03 | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | COMBINE_EQS: (245), (4154) imply:
% 133.16/19.03 | | | | | | | | | | | | | | (4155) all_4_2 = e2
% 133.16/19.03 | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | REDUCE: (4075), (4155) imply:
% 133.16/19.03 | | | | | | | | | | | | | | (4156) $false
% 133.16/19.03 | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | CLOSE: (4156) is inconsistent.
% 133.16/19.03 | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | Case 2:
% 133.16/19.03 | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | (4157) ~ (all_54_15 = e2)
% 133.16/19.03 | | | | | | | | | | | | | | (4158) all_54_15 = e1 | all_54_15 = e0
% 133.16/19.03 | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | BETA: splitting (4158) gives:
% 133.16/19.03 | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | Case 1:
% 133.16/19.03 | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | (4159) all_54_15 = e1
% 133.16/19.03 | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | COMBINE_EQS: (245), (4159) imply:
% 133.16/19.03 | | | | | | | | | | | | | | | (4160) all_4_2 = e1
% 133.16/19.03 | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | REDUCE: (371), (4160) imply:
% 133.16/19.03 | | | | | | | | | | | | | | | (4161) $false
% 133.16/19.03 | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | CLOSE: (4161) is inconsistent.
% 133.16/19.03 | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | Case 2:
% 133.16/19.03 | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | (4162) all_54_15 = e0
% 133.16/19.03 | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | COMBINE_EQS: (245), (4162) imply:
% 133.16/19.03 | | | | | | | | | | | | | | | (4163) all_4_2 = e0
% 133.16/19.03 | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | REDUCE: (4075), (4163) imply:
% 133.16/19.03 | | | | | | | | | | | | | | | (4164) ~ (e2 = e0)
% 133.16/19.03 | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | REDUCE: (36), (4163) imply:
% 133.16/19.03 | | | | | | | | | | | | | | | (4165) op(e0, e0) = e0
% 133.16/19.03 | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 133.16/19.03 | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | Case 1:
% 133.16/19.03 | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | | (4166) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 133.16/19.03 | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 133.16/19.03 | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | | BETA: splitting (4166) gives:
% 133.16/19.03 | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | | Case 1:
% 133.16/19.03 | | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | | | (4167) all_57_4 = e0 & op(e3, e1) = e0
% 133.16/19.03 | | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (4069), (4167), (function-axioms) are
% 133.16/19.03 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #224.
% 133.16/19.03 | | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | | Case 2:
% 133.16/19.03 | | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | | | (4168) all_57_5 = e0 & op(e2, e1) = e0
% 133.16/19.03 | | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (4139), (4168), (function-axioms) are
% 133.16/19.03 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #455.
% 133.16/19.03 | | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | | End of split
% 133.16/19.03 | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | Case 2:
% 133.16/19.03 | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | | (4169) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 133.16/19.03 | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 133.16/19.03 | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | | BETA: splitting (4169) gives:
% 133.16/19.03 | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | | Case 1:
% 133.16/19.03 | | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | | | (4170) all_57_8 = e0 & op(e1, e1) = e0
% 133.16/19.03 | | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | | | ALPHA: (4170) implies:
% 133.16/19.03 | | | | | | | | | | | | | | | | | (4171) op(e1, e1) = e0
% 133.16/19.03 | | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.16/19.03 | | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | | | Case 1:
% 133.16/19.03 | | | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | | | | (4172) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.16/19.03 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.16/19.03 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.16/19.03 | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.16/19.03 | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.16/19.03 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.16/19.03 | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.16/19.03 | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.16/19.03 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.16/19.03 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.16/19.03 | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.16/19.03 | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.16/19.03 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.16/19.03 | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.16/19.03 | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.16/19.03 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.16/19.03 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.16/19.03 | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.16/19.03 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.16/19.03 | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.16/19.03 | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.16/19.03 | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.16/19.03 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.16/19.03 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.16/19.03 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.16/19.03 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.16/19.03 | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.16/19.03 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.16/19.03 | | | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | | | | BETA: splitting (4172) gives:
% 133.16/19.03 | | | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | | | | Case 1:
% 133.16/19.03 | | | | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | (4173) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 133.16/19.03 | | | | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | BETA: splitting (4173) gives:
% 133.16/19.03 | | | | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | | (4174) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | | ALPHA: (4174) implies:
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | | (4175) op(e3, e3) = e2
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4071), (4175), (function-axioms) are
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495.
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | | (4176) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | | ALPHA: (4176) implies:
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | | (4177) op(e3, e3) = e1
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (39), (168), (169), (170), (206),
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | | (232), (245), (368), (371), (372), (4068), (4075),
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | | (4077), (4146), (4148), (4153), (4177),
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | | #594.
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.03 | | | | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | | | | Case 2:
% 133.16/19.03 | | | | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | (4178) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.16/19.03 | | | | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4146), (4165), (4178), (function-axioms) are
% 133.16/19.03 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #223.
% 133.16/19.03 | | | | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | | | | End of split
% 133.16/19.03 | | | | | | | | | | | | | | | | | |
% 133.16/19.03 | | | | | | | | | | | | | | | | | Case 2:
% 133.16/19.03 | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | (4179) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.03 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.26/19.03 | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.26/19.03 | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.26/19.03 | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.26/19.03 | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.26/19.03 | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.26/19.03 | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.26/19.03 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.26/19.03 | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.26/19.03 | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.26/19.03 | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.26/19.03 | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.26/19.03 | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.26/19.03 | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.26/19.03 | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.26/19.03 | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.26/19.03 | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.26/19.03 | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.26/19.03 | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.26/19.03 | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.26/19.03 | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.26/19.03 | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.26/19.03 | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.26/19.03 | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.26/19.03 | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.26/19.03 | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | BETA: splitting (4179) gives:
% 133.26/19.03 | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | (4180) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.26/19.03 | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | BETA: splitting (4180) gives:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | (4181) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | ALPHA: (4181) implies:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | (4182) op(e1, e1) = e3
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4171), (4182), (function-axioms) are
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753.
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | (4183) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2,
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | ALPHA: (4183) implies:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | (4184) op(e2, e2) = e1
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4146), (4184), (function-axioms) are
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675.
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.03 | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | (4185) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.26/19.03 | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (39), (372), (4165), (4185),
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | #596.
% 133.26/19.03 | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.03 | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | End of split
% 133.26/19.03 | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.03 | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | (4186) all_57_14 = e0 & op(e0, e1) = e0
% 133.26/19.03 | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | ALPHA: (4186) implies:
% 133.26/19.03 | | | | | | | | | | | | | | | | | (4187) all_57_14 = e0
% 133.26/19.03 | | | | | | | | | | | | | | | | | (4188) op(e0, e1) = e0
% 133.26/19.03 | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.26/19.03 | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.03 | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | (4189) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.26/19.03 | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.26/19.03 | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.03 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.03 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.26/19.03 | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | BETA: splitting (4189) gives:
% 133.26/19.03 | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | (4190) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 133.26/19.03 | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | BETA: splitting (4190) gives:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | (4191) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (168), (170),
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | (220), (221), (222), (232), (372), (4068), (4070),
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | (4187), (4188), (4191), (function-axioms) are
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #222.
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | (4192) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | ALPHA: (4192) implies:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | (4193) op(e3, e3) = e1
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | (4194) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4194) gives:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | (4195) all_57_12 = e1 & op(e0, e3) = e1
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4195) implies:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | (4196) all_57_12 = e1
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (235), (237),
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | (4193), (4196), (function-axioms) are inconsistent
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #583.
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | (4197) all_57_13 = e1 & op(e0, e2) = e1
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4197) implies:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | (4198) all_57_13 = e1
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | (4199) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4199) gives:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | (4200) all_57_12 = e2 & op(e0, e3) = e2
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4200) implies:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | (4201) all_57_12 = e2
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | (4202) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4202) gives:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (4203) all_57_12 = e3 & op(e0, e3) = e3
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4203) implies:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (4204) all_57_12 = e3
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4201), (4204) are inconsistent by sub-proof
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | #518.
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (4205) all_57_13 = e3 & op(e0, e2) = e3
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4205) implies:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (4206) all_57_13 = e3
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4198), (4206) imply:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (4207) e3 = e1
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (4207) imply:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (4208) $false
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4208) is inconsistent.
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | (4209) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4209) gives:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (4210) all_57_14 = e3 & op(e0, e1) = e3
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4187), (4210) are inconsistent by sub-proof
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | #661.
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (4211) all_57_15 = e3 & op(e0, e0) = e3
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4211) implies:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (4212) op(e0, e0) = e3
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4165), (4212), (function-axioms) are
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #715.
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | (4213) all_57_13 = e2 & op(e0, e2) = e2
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4213) implies:
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | (4214) all_57_13 = e2
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4198), (4214) are inconsistent by sub-proof
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | #567.
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | (4215) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4215) gives:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | (4216) all_57_14 = e2 & op(e0, e1) = e2
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4216) implies:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | (4217) op(e0, e1) = e2
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4188), (4217), (function-axioms) are
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #660.
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | (4218) all_57_15 = e2 & op(e0, e0) = e2
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4218) implies:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | (4219) op(e0, e0) = e2
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4165), (4219), (function-axioms) are
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #714.
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | (4220) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4220) gives:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | (4221) all_57_14 = e1 & op(e0, e1) = e1
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4221) implies:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | (4222) all_57_14 = e1
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4187), (4222) are inconsistent by sub-proof
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | #221.
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | (4223) all_57_15 = e1 & op(e0, e0) = e1
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4223) implies:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | (4224) op(e0, e0) = e1
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4165), (4224), (function-axioms) are
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #220.
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.04 | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | (4225) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.26/19.04 | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4146), (4165), (4225), (function-axioms) are
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #223.
% 133.26/19.04 | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.04 | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.04 | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | (4226) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.26/19.04 | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.26/19.04 | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.26/19.04 | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.26/19.04 | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.26/19.04 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.26/19.04 | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.26/19.04 | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.26/19.04 | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.26/19.04 | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.26/19.04 | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.26/19.04 | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.26/19.04 | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.26/19.04 | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.26/19.04 | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.26/19.04 | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.26/19.04 | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.26/19.04 | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.26/19.04 | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.26/19.04 | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | BETA: splitting (4226) gives:
% 133.26/19.04 | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | (4227) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.26/19.04 | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (4077), (4146), (4227),
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | #621.
% 133.26/19.04 | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | (4228) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.26/19.04 | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (39), (372), (4165), (4228),
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | #596.
% 133.26/19.04 | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.04 | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | End of split
% 133.26/19.04 | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | End of split
% 133.26/19.04 | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | End of split
% 133.26/19.04 | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | End of split
% 133.26/19.04 | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | End of split
% 133.26/19.04 | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | End of split
% 133.26/19.04 | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | Case 2:
% 133.26/19.04 | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | (4229) all_34_2 = e3
% 133.26/19.04 | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | COMBINE_EQS: (307), (4229) imply:
% 133.26/19.04 | | | | | | | | | | | | (4230) all_4_2 = e3
% 133.26/19.04 | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | SIMP: (4230) implies:
% 133.26/19.04 | | | | | | | | | | | | (4231) all_4_2 = e3
% 133.26/19.04 | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | REDUCE: (360), (4231) imply:
% 133.26/19.04 | | | | | | | | | | | | (4232) ~ (all_52_7 = e3)
% 133.26/19.04 | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | REDUCE: (367), (4231) imply:
% 133.26/19.04 | | | | | | | | | | | | (4233) ~ (all_52_11 = e3)
% 133.26/19.04 | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | REDUCE: (368), (4231) imply:
% 133.26/19.04 | | | | | | | | | | | | (4234) ~ (all_52_12 = e3)
% 133.26/19.04 | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | REDUCE: (370), (4231) imply:
% 133.26/19.04 | | | | | | | | | | | | (4235) ~ (all_52_14 = e3)
% 133.26/19.04 | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | REDUCE: (36), (4231) imply:
% 133.26/19.04 | | | | | | | | | | | | (4236) op(e0, e0) = e3
% 133.26/19.04 | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | BETA: splitting (94) gives:
% 133.26/19.04 | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | Case 1:
% 133.26/19.04 | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | (4237) ~ (all_42_2 = e0)
% 133.26/19.04 | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | REDUCE: (4136), (4237) imply:
% 133.26/19.04 | | | | | | | | | | | | | (4238) $false
% 133.26/19.04 | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | CLOSE: (4238) is inconsistent.
% 133.26/19.04 | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | Case 2:
% 133.26/19.04 | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | (4239) ( ~ (all_42_0 = e1) & op(e0, e2) = all_42_0 &
% 133.26/19.04 | | | | | | | | | | | | | $i(all_42_0)) | ( ~ (all_42_1 = e3) & op(e0, e0)
% 133.26/19.04 | | | | | | | | | | | | | = all_42_1 & $i(all_42_1))
% 133.26/19.04 | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | BETA: splitting (4239) gives:
% 133.26/19.04 | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | Case 1:
% 133.26/19.04 | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | (4240) ~ (all_42_0 = e1) & op(e0, e2) = all_42_0 &
% 133.26/19.04 | | | | | | | | | | | | | | $i(all_42_0)
% 133.26/19.04 | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | ALPHA: (4240) implies:
% 133.26/19.04 | | | | | | | | | | | | | | (4241) ~ (all_42_0 = e1)
% 133.26/19.04 | | | | | | | | | | | | | | (4242) op(e0, e2) = all_42_0
% 133.26/19.04 | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 133.26/19.04 | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | Case 1:
% 133.26/19.04 | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | (4243) all_57_15 = e0 & op(e0, e0) = e0
% 133.26/19.04 | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | ALPHA: (4243) implies:
% 133.26/19.04 | | | | | | | | | | | | | | | (4244) op(e0, e0) = e0
% 133.26/19.04 | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | REF_CLOSE: (7), (4236), (4244), (function-axioms) are
% 133.26/19.04 | | | | | | | | | | | | | | | inconsistent by sub-proof #715.
% 133.26/19.04 | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | Case 2:
% 133.26/19.04 | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | (4245) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 133.26/19.04 | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 133.26/19.04 | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 133.26/19.04 | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 133.26/19.04 | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 133.26/19.04 | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | ALPHA: (4245) implies:
% 133.26/19.04 | | | | | | | | | | | | | | | (4246) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 133.26/19.04 | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 133.26/19.04 | | | | | | | | | | | | | | | e1) = e0)
% 133.26/19.04 | | | | | | | | | | | | | | | (4247) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 133.26/19.04 | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 133.26/19.04 | | | | | | | | | | | | | | | e0) = e0)
% 133.26/19.04 | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | BETA: splitting (4247) gives:
% 133.26/19.04 | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | Case 1:
% 133.26/19.04 | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | (4248) all_57_9 = e0 & op(e3, e0) = e0
% 133.26/19.04 | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | REF_CLOSE: (168), (4070), (4248), (function-axioms) are
% 133.26/19.04 | | | | | | | | | | | | | | | | inconsistent by sub-proof #618.
% 133.26/19.04 | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | Case 2:
% 133.26/19.04 | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | (4249) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 133.26/19.04 | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 133.26/19.04 | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | BETA: splitting (4249) gives:
% 133.26/19.04 | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.04 | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | (4250) all_57_10 = e0 & op(e2, e0) = e0
% 133.26/19.04 | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | ALPHA: (4250) implies:
% 133.26/19.04 | | | | | | | | | | | | | | | | | (4251) all_57_10 = e0
% 133.26/19.04 | | | | | | | | | | | | | | | | | (4252) op(e2, e0) = e0
% 133.26/19.04 | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (224), (225), (226),
% 133.26/19.04 | | | | | | | | | | | | | | | | | (4145), (4146), (4251), (4252), (function-axioms)
% 133.26/19.04 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #446.
% 133.26/19.04 | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.04 | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | (4253) all_57_11 = e0 & op(e1, e0) = e0
% 133.26/19.04 | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | ALPHA: (4253) implies:
% 133.26/19.04 | | | | | | | | | | | | | | | | | (4254) op(e1, e0) = e0
% 133.26/19.04 | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7,
% 133.26/19.04 | | | | | | | | | | | | | | | | | all_42_0, e2, e0, simplifying with (158), (4242)
% 133.26/19.04 | | | | | | | | | | | | | | | | | gives:
% 133.26/19.04 | | | | | | | | | | | | | | | | | (4255) all_52_7 = all_42_0
% 133.26/19.04 | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 133.26/19.04 | | | | | | | | | | | | | | | | | e0, e0, e1, simplifying with (160), (4254) gives:
% 133.26/19.04 | | | | | | | | | | | | | | | | | (4256) all_52_14 = e0
% 133.26/19.04 | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (4255) imply:
% 133.26/19.04 | | | | | | | | | | | | | | | | | (4257) all_54_13 = all_42_0
% 133.26/19.04 | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | REDUCE: (4232), (4255) imply:
% 133.26/19.04 | | | | | | | | | | | | | | | | | (4258) ~ (all_42_0 = e3)
% 133.26/19.04 | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | REDUCE: (4138), (4255) imply:
% 133.26/19.04 | | | | | | | | | | | | | | | | | (4259) ~ (all_42_0 = e0)
% 133.26/19.04 | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | REDUCE: (366), (4256) imply:
% 133.26/19.04 | | | | | | | | | | | | | | | | | (4260) ~ (all_6_2 = e0)
% 133.26/19.04 | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | SIMP: (4260) implies:
% 133.26/19.04 | | | | | | | | | | | | | | | | | (4261) ~ (all_6_2 = e0)
% 133.26/19.04 | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 133.26/19.04 | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.04 | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | (4262) all_54_10 = e3
% 133.26/19.04 | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (4077), (4262) are inconsistent by
% 133.26/19.04 | | | | | | | | | | | | | | | | | | sub-proof #742.
% 133.26/19.04 | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.04 | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | (4263) ~ (all_54_10 = e3)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | (4264) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 133.26/19.04 | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 133.26/19.04 | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | (4265) all_54_13 = e3
% 133.26/19.04 | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4257), (4258), (4265) are inconsistent by
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | sub-proof #617.
% 133.26/19.04 | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | (4266) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 133.26/19.04 | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | BETA: splitting (4246) gives:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | (4267) all_57_12 = e0 & op(e0, e3) = e0
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | ALPHA: (4267) implies:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | (4268) op(e0, e3) = e0
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (4067), (4268), (function-axioms) are
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #219.
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | (4269) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4269) gives:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | (4270) all_57_13 = e0 & op(e0, e2) = e0
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4270) implies:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | (4271) op(e0, e2) = e0
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (4138), (4271), (function-axioms) are
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #545.
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | (4272) all_57_14 = e0 & op(e0, e1) = e0
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4272) implies:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | (4273) all_57_14 = e0
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | (4274) op(e0, e1) = e0
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4264) gives:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | (4275) all_54_10 = e2
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (372), (4275) are inconsistent by sub-proof
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | #741.
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | (4276) ~ (all_54_10 = e2)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | (4277) all_54_10 = e1 | all_54_10 = e0
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4277) gives:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | (4278) all_54_10 = e1
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (4278) imply:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | (4279) all_6_2 = e1
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4279) implies:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | (4280) all_6_2 = e1
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4077), (4280) imply:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | (4281) ~ (e3 = e1)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (4280) imply:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | (4282) ~ (e2 = e1)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (4280) imply:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | (4283) op(e1, e1) = e1
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | (4284) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4284) gives:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | (4285) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4285) gives:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (4286) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (168), (170),
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (220), (221), (222), (232), (372), (4068), (4070),
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (4273), (4274), (4286), (function-axioms) are
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #222.
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (4287) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4287) implies:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (4288) op(e3, e3) = e1
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4071), (4288), (function-axioms) are
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #717.
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | (4289) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (4146), (4234), (4289),
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | #622.
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | (4290) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4290) gives:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | (4291) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (39), (4146), (4283), (4291),
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | #508.
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | (4292) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4292) gives:
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (4293) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4293) implies:
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (4294) ~ (all_56_15 = e2)
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (4295) op(e0, e2) = all_56_15
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4241), (4242), (4257), (4259), (4266), (4294),
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (4295), (function-axioms) are inconsistent by
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #539.
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (4296) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (42), (100), (157), (158), (159),
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (190), (199), (246), (267), (295), (354), (364),
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (373), (4067), (4073), (4233), (4236),
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (4296), (function-axioms) are inconsistent by
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #226.
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | (4297) all_54_10 = e0
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (4261), (4297) are inconsistent by
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #506.
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.05 | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.05 | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | End of split
% 133.26/19.05 | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | End of split
% 133.26/19.05 | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | End of split
% 133.26/19.05 | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | End of split
% 133.26/19.05 | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | Case 2:
% 133.26/19.05 | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | (4298) ~ (all_42_1 = e3) & op(e0, e0) = all_42_1 &
% 133.26/19.05 | | | | | | | | | | | | | | $i(all_42_1)
% 133.26/19.05 | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | REF_CLOSE: (4236), (4298), (function-axioms) are inconsistent
% 133.26/19.05 | | | | | | | | | | | | | | by sub-proof #602.
% 133.26/19.05 | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | End of split
% 133.26/19.05 | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | End of split
% 133.26/19.05 | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | End of split
% 133.26/19.05 | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | End of split
% 133.26/19.05 | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | Case 2:
% 133.26/19.05 | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | (4299) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 133.26/19.05 | | | | | | | | | | e0 & op(e2, e0) = e0)
% 133.26/19.05 | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | BETA: splitting (4299) gives:
% 133.26/19.05 | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | Case 1:
% 133.26/19.05 | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | (4300) all_57_5 = e0 & op(e2, e1) = e0
% 133.26/19.05 | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | REF_CLOSE: (165), (4139), (4300), (function-axioms) are
% 133.26/19.05 | | | | | | | | | | | inconsistent by sub-proof #455.
% 133.26/19.05 | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | Case 2:
% 133.26/19.05 | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | (4301) all_57_10 = e0 & op(e2, e0) = e0
% 133.26/19.05 | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | ALPHA: (4301) implies:
% 133.26/19.05 | | | | | | | | | | | (4302) all_57_10 = e0
% 133.26/19.05 | | | | | | | | | | | (4303) op(e2, e0) = e0
% 133.26/19.05 | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | BETA: splitting (227) gives:
% 133.26/19.05 | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | Case 1:
% 133.26/19.05 | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | (4304) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 133.26/19.05 | | | | | | | | | | | | & op(e2, e2) = e0)
% 133.26/19.05 | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (224), (225),
% 133.26/19.05 | | | | | | | | | | | | (226), (4068), (4302), (4303), (4304),
% 133.26/19.05 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.26/19.05 | | | | | | | | | | | | #445.
% 133.26/19.05 | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | Case 2:
% 133.26/19.05 | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | (4305) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 133.26/19.05 | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 133.26/19.05 | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | REF_CLOSE: (158), (162), (4137), (4138), (4305),
% 133.26/19.05 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.26/19.05 | | | | | | | | | | | | #504.
% 133.26/19.05 | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | End of split
% 133.26/19.05 | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | End of split
% 133.26/19.05 | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | End of split
% 133.26/19.05 | | | | | | | | |
% 133.26/19.05 | | | | | | | | End of split
% 133.26/19.05 | | | | | | | |
% 133.26/19.05 | | | | | | | Case 2:
% 133.26/19.05 | | | | | | | |
% 133.26/19.05 | | | | | | | | (4306) all_28_2 = e3
% 133.26/19.05 | | | | | | | | (4307) ( ~ (all_28_0 = e2) & op(e3, e1) = all_28_0 &
% 133.26/19.05 | | | | | | | | $i(all_28_0)) | ( ~ (all_28_1 = e0) & op(e3, e3) =
% 133.26/19.05 | | | | | | | | all_28_1 & $i(all_28_1))
% 133.26/19.05 | | | | | | | |
% 133.26/19.05 | | | | | | | | COMBINE_EQS: (316), (4306) imply:
% 133.26/19.05 | | | | | | | | (4308) all_6_2 = e3
% 133.26/19.05 | | | | | | | |
% 133.26/19.05 | | | | | | | | SIMP: (4308) implies:
% 133.26/19.05 | | | | | | | | (4309) all_6_2 = e3
% 133.26/19.05 | | | | | | | |
% 133.26/19.05 | | | | | | | | REDUCE: (361), (4309) imply:
% 133.26/19.05 | | | | | | | | (4310) ~ (all_52_8 = e3)
% 133.26/19.05 | | | | | | | |
% 133.26/19.05 | | | | | | | | REDUCE: (362), (4309) imply:
% 133.26/19.05 | | | | | | | | (4311) ~ (all_52_9 = e3)
% 133.26/19.05 | | | | | | | |
% 133.26/19.05 | | | | | | | | REDUCE: (364), (4309) imply:
% 133.26/19.05 | | | | | | | | (4312) ~ (all_52_11 = e3)
% 133.26/19.05 | | | | | | | |
% 133.26/19.05 | | | | | | | | REDUCE: (39), (4309) imply:
% 133.26/19.05 | | | | | | | | (4313) op(e1, e1) = e3
% 133.26/19.05 | | | | | | | |
% 133.26/19.05 | | | | | | | | BETA: splitting (4307) gives:
% 133.26/19.05 | | | | | | | |
% 133.26/19.05 | | | | | | | | Case 1:
% 133.26/19.05 | | | | | | | | |
% 133.26/19.05 | | | | | | | | | (4314) ~ (all_28_0 = e2) & op(e3, e1) = all_28_0 &
% 133.26/19.05 | | | | | | | | | $i(all_28_0)
% 133.26/19.05 | | | | | | | | |
% 133.26/19.05 | | | | | | | | | ALPHA: (4314) implies:
% 133.26/19.05 | | | | | | | | | (4315) ~ (all_28_0 = e2)
% 133.26/19.05 | | | | | | | | | (4316) op(e3, e1) = all_28_0
% 133.26/19.05 | | | | | | | | |
% 133.26/19.05 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8,
% 133.26/19.05 | | | | | | | | | all_28_0, e1, e3, simplifying with (169), (4316)
% 133.26/19.05 | | | | | | | | | gives:
% 133.26/19.05 | | | | | | | | | (4317) all_52_8 = all_28_0
% 133.26/19.05 | | | | | | | | |
% 133.26/19.05 | | | | | | | | | COMBINE_EQS: (270), (4317) imply:
% 133.26/19.05 | | | | | | | | | (4318) all_54_2 = all_28_0
% 133.26/19.05 | | | | | | | | |
% 133.26/19.05 | | | | | | | | | REDUCE: (134), (4317) imply:
% 133.26/19.05 | | | | | | | | | (4319) ~ (all_52_4 = all_28_0)
% 133.26/19.05 | | | | | | | | |
% 133.26/19.05 | | | | | | | | | REDUCE: (123), (4317) imply:
% 133.26/19.05 | | | | | | | | | (4320) ~ (all_52_9 = all_28_0)
% 133.26/19.05 | | | | | | | | |
% 133.26/19.05 | | | | | | | | | SIMP: (4320) implies:
% 133.26/19.05 | | | | | | | | | (4321) ~ (all_52_9 = all_28_0)
% 133.26/19.05 | | | | | | | | |
% 133.26/19.05 | | | | | | | | | REDUCE: (121), (4317) imply:
% 133.26/19.05 | | | | | | | | | (4322) ~ (all_52_11 = all_28_0)
% 133.26/19.05 | | | | | | | | |
% 133.26/19.05 | | | | | | | | | SIMP: (4322) implies:
% 133.26/19.05 | | | | | | | | | (4323) ~ (all_52_11 = all_28_0)
% 133.26/19.05 | | | | | | | | |
% 133.26/19.05 | | | | | | | | | REDUCE: (120), (4317) imply:
% 133.26/19.05 | | | | | | | | | (4324) ~ (all_52_12 = all_28_0)
% 133.26/19.05 | | | | | | | | |
% 133.26/19.05 | | | | | | | | | SIMP: (4324) implies:
% 133.26/19.05 | | | | | | | | | (4325) ~ (all_52_12 = all_28_0)
% 133.26/19.05 | | | | | | | | |
% 133.26/19.05 | | | | | | | | | REDUCE: (4310), (4317) imply:
% 133.26/19.05 | | | | | | | | | (4326) ~ (all_28_0 = e3)
% 133.26/19.05 | | | | | | | | |
% 133.26/19.05 | | | | | | | | | REDUCE: (4069), (4317) imply:
% 133.26/19.05 | | | | | | | | | (4327) ~ (all_28_0 = e0)
% 133.26/19.05 | | | | | | | | |
% 133.26/19.05 | | | | | | | | | BETA: splitting (202) gives:
% 133.26/19.05 | | | | | | | | |
% 133.26/19.05 | | | | | | | | | Case 1:
% 133.26/19.05 | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | (4328) all_54_2 = e3
% 133.26/19.05 | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | COMBINE_EQS: (4318), (4328) imply:
% 133.26/19.05 | | | | | | | | | | (4329) all_28_0 = e3
% 133.26/19.05 | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | REDUCE: (4326), (4329) imply:
% 133.26/19.05 | | | | | | | | | | (4330) $false
% 133.26/19.05 | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | CLOSE: (4330) is inconsistent.
% 133.26/19.05 | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | Case 2:
% 133.26/19.05 | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | (4331) ~ (all_54_2 = e3)
% 133.26/19.05 | | | | | | | | | | (4332) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 133.26/19.05 | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | BETA: splitting (4332) gives:
% 133.26/19.05 | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | Case 1:
% 133.26/19.05 | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | (4333) all_54_2 = e2
% 133.26/19.05 | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | COMBINE_EQS: (4318), (4333) imply:
% 133.26/19.05 | | | | | | | | | | | (4334) all_28_0 = e2
% 133.26/19.05 | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | REDUCE: (4315), (4334) imply:
% 133.26/19.05 | | | | | | | | | | | (4335) $false
% 133.26/19.05 | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | CLOSE: (4335) is inconsistent.
% 133.26/19.05 | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | Case 2:
% 133.26/19.05 | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | (4336) ~ (all_54_2 = e2)
% 133.26/19.05 | | | | | | | | | | | (4337) all_54_2 = e1 | all_54_2 = e0
% 133.26/19.05 | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | BETA: splitting (4337) gives:
% 133.26/19.05 | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | Case 1:
% 133.26/19.05 | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | (4338) all_54_2 = e1
% 133.26/19.05 | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | COMBINE_EQS: (4318), (4338) imply:
% 133.26/19.05 | | | | | | | | | | | | (4339) all_28_0 = e1
% 133.26/19.05 | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | REDUCE: (4319), (4339) imply:
% 133.26/19.05 | | | | | | | | | | | | (4340) ~ (all_52_4 = e1)
% 133.26/19.05 | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | REDUCE: (4321), (4339) imply:
% 133.26/19.05 | | | | | | | | | | | | (4341) ~ (all_52_9 = e1)
% 133.26/19.05 | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | REDUCE: (4323), (4339) imply:
% 133.26/19.05 | | | | | | | | | | | | (4342) ~ (all_52_11 = e1)
% 133.26/19.05 | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | REDUCE: (4325), (4339) imply:
% 133.26/19.05 | | | | | | | | | | | | (4343) ~ (all_52_12 = e1)
% 133.26/19.05 | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | REDUCE: (4326), (4339) imply:
% 133.26/19.05 | | | | | | | | | | | | (4344) ~ (e3 = e1)
% 133.26/19.05 | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | REDUCE: (4315), (4339) imply:
% 133.26/19.05 | | | | | | | | | | | | (4345) ~ (e2 = e1)
% 133.26/19.05 | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | REDUCE: (4316), (4339) imply:
% 133.26/19.05 | | | | | | | | | | | | (4346) op(e3, e1) = e1
% 133.26/19.05 | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | BETA: splitting (220) gives:
% 133.26/19.05 | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | Case 1:
% 133.26/19.05 | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | (4347) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 133.26/19.05 | | | | | | | | | | | | | & op(e2, e1) = e1)
% 133.26/19.05 | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | BETA: splitting (4347) gives:
% 133.26/19.05 | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | Case 1:
% 133.26/19.05 | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | (4348) all_57_4 = e1 & op(e3, e1) = e1
% 133.26/19.05 | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | ALPHA: (4348) implies:
% 133.26/19.05 | | | | | | | | | | | | | | (4349) all_57_4 = e1
% 133.26/19.05 | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 133.26/19.05 | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | Case 1:
% 133.26/19.05 | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | (4350) ~ (all_30_2 = e0)
% 133.26/19.05 | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | REDUCE: (309), (4350) imply:
% 133.26/19.05 | | | | | | | | | | | | | | | (4351) ~ (all_8_2 = e0)
% 133.26/19.05 | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 133.26/19.05 | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | Case 1:
% 133.26/19.05 | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | (4352) all_54_5 = e3
% 133.26/19.05 | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | REF_CLOSE: (267), (4073), (4352) are inconsistent by
% 133.26/19.05 | | | | | | | | | | | | | | | | sub-proof #554.
% 133.26/19.05 | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | Case 2:
% 133.26/19.05 | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | (4353) ~ (all_54_5 = e3)
% 133.26/19.05 | | | | | | | | | | | | | | | | (4354) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 133.26/19.05 | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | BETA: splitting (4354) gives:
% 133.26/19.05 | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.05 | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | (4355) all_54_5 = e2
% 133.26/19.05 | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (4355) imply:
% 133.26/19.05 | | | | | | | | | | | | | | | | | (4356) all_8_2 = e2
% 133.26/19.05 | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | SIMP: (4356) implies:
% 133.26/19.05 | | | | | | | | | | | | | | | | | (4357) all_8_2 = e2
% 133.26/19.05 | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | REDUCE: (350), (4357) imply:
% 133.26/19.05 | | | | | | | | | | | | | | | | | (4358) ~ (all_52_4 = e2)
% 133.26/19.05 | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | REDUCE: (356), (4357) imply:
% 133.26/19.05 | | | | | | | | | | | | | | | | | (4359) ~ (all_52_9 = e2)
% 133.26/19.05 | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | REDUCE: (358), (4357) imply:
% 133.26/19.05 | | | | | | | | | | | | | | | | | (4360) ~ (all_52_13 = e2)
% 133.26/19.05 | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | REDUCE: (4073), (4357) imply:
% 133.26/19.05 | | | | | | | | | | | | | | | | | (4361) ~ (e3 = e2)
% 133.26/19.05 | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 133.26/19.05 | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.05 | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | (4362) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 133.26/19.05 | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 133.26/19.05 | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | BETA: splitting (4362) gives:
% 133.26/19.05 | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.05 | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | (4363) all_57_4 = e2 & op(e3, e1) = e2
% 133.26/19.05 | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4315), (4316), (4363), (function-axioms) are
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #218.
% 133.26/19.05 | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.05 | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | (4364) all_57_5 = e2 & op(e2, e1) = e2
% 133.26/19.05 | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | ALPHA: (4364) implies:
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | (4365) op(e2, e1) = e2
% 133.26/19.05 | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (4359), (4365), (function-axioms) are
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #770.
% 133.26/19.05 | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.05 | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.05 | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | (4366) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 133.26/19.05 | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | BETA: splitting (4366) gives:
% 133.26/19.05 | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.05 | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | (4367) all_57_8 = e2 & op(e1, e1) = e2
% 133.26/19.05 | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | ALPHA: (4367) implies:
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | (4368) op(e1, e1) = e2
% 133.26/19.05 | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (4368), (function-axioms) are
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 133.26/19.05 | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.05 | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | (4369) all_57_14 = e2 & op(e0, e1) = e2
% 133.26/19.05 | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | ALPHA: (4369) implies:
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | (4370) op(e0, e1) = e2
% 133.26/19.05 | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.26/19.05 | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | (4371) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4371) gives:
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | (4372) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4372) gives:
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | (4373) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4373) implies:
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | (4374) op(e3, e3) = e2
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4071), (4374), (function-axioms) are
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495.
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | (4375) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4375) implies:
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | (4376) op(e3, e3) = e1
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (236),
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | (238), (4068), (4349), (4376), (function-axioms)
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #667.
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | (4377) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4377) gives:
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | (4378) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3,
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (133), (168), (203), (271), (4068), (4340),
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | (4358), (4378), (function-axioms) are inconsistent
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #217.
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | (4379) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2,
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4379) implies:
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | (4380) op(e2, e2) = e3
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (4073), (4380), (function-axioms) are
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #228.
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | (4381) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.05 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4381) gives:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | (4382) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (4346), (4359), (4382), (function-axioms)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #348.
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | (4383) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4383) gives:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | (4384) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4384) implies:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | (4385) op(e2, e0) = e2
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (4360), (4385), (function-axioms) are
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | (4386) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4386) gives:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (4387) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4387) implies:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (4388) op(e1, e1) = e2
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (4388), (function-axioms) are
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (4389) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4389) implies:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (4390) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4390) gives:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | (4391) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27))
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4391) gives:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4392) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4392) implies:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4393) ~ (all_56_17 = e1)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4394) op(e3, e1) = all_56_17
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4346), (4393), (4394), (function-axioms) are
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #349.
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4395) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4395) implies:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4396) ~ (all_56_11 = e2)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4397) op(e0, e2) = e0
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4398) op(e2, e2) = all_56_11
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (158), (199), (267), (354), (373), (4073),
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4396), (4397), (4398), (function-axioms) are
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #227.
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | (4399) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4399) gives:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4400) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4400) implies:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4401) op(e1, e1) = e0
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4313), (4401), (function-axioms) are
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753.
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4402) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4402) implies:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4403) op(e0, e1) = e0
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4370), (4403), (function-axioms) are
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #660.
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.06 | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.06 | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | End of split
% 133.26/19.06 | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.06 | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | (4404) all_54_5 = e1 | all_54_5 = e0
% 133.26/19.06 | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (373), (4351), (4404) are inconsistent by
% 133.26/19.06 | | | | | | | | | | | | | | | | | sub-proof #624.
% 133.26/19.06 | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | End of split
% 133.26/19.06 | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | End of split
% 133.26/19.06 | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | Case 2:
% 133.26/19.06 | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | (4405) all_30_2 = e0
% 133.26/19.06 | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | COMBINE_EQS: (309), (4405) imply:
% 133.26/19.06 | | | | | | | | | | | | | | | (4406) all_8_2 = e0
% 133.26/19.06 | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | SIMP: (4406) implies:
% 133.26/19.06 | | | | | | | | | | | | | | | (4407) all_8_2 = e0
% 133.26/19.06 | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | REDUCE: (356), (4407) imply:
% 133.26/19.06 | | | | | | | | | | | | | | | (4408) ~ (all_52_9 = e0)
% 133.26/19.06 | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | REDUCE: (358), (4407) imply:
% 133.26/19.06 | | | | | | | | | | | | | | | (4409) ~ (all_52_13 = e0)
% 133.26/19.06 | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | REDUCE: (4073), (4407) imply:
% 133.26/19.06 | | | | | | | | | | | | | | | (4410) ~ (e3 = e0)
% 133.26/19.06 | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | REDUCE: (373), (4407) imply:
% 133.26/19.06 | | | | | | | | | | | | | | | (4411) ~ (e1 = e0)
% 133.26/19.06 | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | REDUCE: (42), (4407) imply:
% 133.26/19.06 | | | | | | | | | | | | | | | (4412) op(e2, e2) = e0
% 133.26/19.06 | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 133.26/19.06 | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | Case 1:
% 133.26/19.06 | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | (4413) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 133.26/19.06 | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 133.26/19.06 | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | BETA: splitting (4413) gives:
% 133.26/19.06 | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.06 | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | (4414) all_57_4 = e0 & op(e3, e1) = e0
% 133.26/19.06 | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | ALPHA: (4414) implies:
% 133.26/19.06 | | | | | | | | | | | | | | | | | (4415) op(e3, e1) = e0
% 133.26/19.06 | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4346), (4415), (function-axioms) are
% 133.26/19.06 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #343.
% 133.26/19.06 | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.06 | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | (4416) all_57_5 = e0 & op(e2, e1) = e0
% 133.26/19.06 | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (4408), (4416), (function-axioms) are
% 133.26/19.06 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #455.
% 133.26/19.06 | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | End of split
% 133.26/19.06 | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | Case 2:
% 133.26/19.06 | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | (4417) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 133.26/19.06 | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 133.26/19.06 | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | BETA: splitting (4417) gives:
% 133.26/19.06 | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.06 | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | (4418) all_57_8 = e0 & op(e1, e1) = e0
% 133.26/19.06 | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | ALPHA: (4418) implies:
% 133.26/19.06 | | | | | | | | | | | | | | | | | (4419) op(e1, e1) = e0
% 133.26/19.06 | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4313), (4419), (function-axioms) are
% 133.26/19.06 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753.
% 133.26/19.06 | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.06 | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | (4420) all_57_14 = e0 & op(e0, e1) = e0
% 133.26/19.06 | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | ALPHA: (4420) implies:
% 133.26/19.06 | | | | | | | | | | | | | | | | | (4421) all_57_14 = e0
% 133.26/19.06 | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 133.26/19.06 | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.06 | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | (4422) all_54_6 = e3
% 133.26/19.06 | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (4422) imply:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | (4423) all_52_9 = e3
% 133.26/19.06 | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | REDUCE: (4311), (4423) imply:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | (4424) $false
% 133.26/19.06 | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | CLOSE: (4424) is inconsistent.
% 133.26/19.06 | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.06 | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | (4425) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 133.26/19.06 | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | BETA: splitting (4425) gives:
% 133.26/19.06 | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | (4426) all_54_6 = e2
% 133.26/19.06 | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (4426) imply:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | (4427) all_52_9 = e2
% 133.26/19.06 | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | REDUCE: (118), (4427) imply:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | (4428) ~ (all_52_11 = e2)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | SIMP: (4428) implies:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | (4429) ~ (all_52_11 = e2)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | (4430) all_54_14 = e3
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (4430) imply:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | (4431) all_52_11 = e3
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | REDUCE: (4312), (4431) imply:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | (4432) $false
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | CLOSE: (4432) is inconsistent.
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | (4433) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4433) gives:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | (4434) all_54_14 = e2
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (4434) imply:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | (4435) all_52_11 = e2
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | REDUCE: (4429), (4435) imply:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | (4436) $false
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | CLOSE: (4436) is inconsistent.
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | (4437) all_54_14 = e1 | all_54_14 = e0
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4437) gives:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | (4438) all_54_14 = e1
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (4438) imply:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | (4439) all_52_11 = e1
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4342), (4439) imply:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | (4440) $false
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4440) is inconsistent.
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | (4441) all_54_14 = e0
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (4441) imply:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | (4442) all_52_11 = e0
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (4442) imply:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | (4443) ~ (all_52_7 = e0)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (367), (4442) imply:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | (4444) ~ (all_4_2 = e0)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | SIMP: (4444) implies:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | (4445) ~ (all_4_2 = e0)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (4442) imply:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | (4446) op(e0, e1) = e0
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (4447) all_54_15 = e3
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (4447) imply:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (4448) all_4_2 = e3
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (4448) imply:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (4449) all_34_2 = e3
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (4448) imply:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (4450) ~ (all_52_12 = e3)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (4448) imply:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (4451) ~ (all_52_13 = e3)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (4448) imply:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (4452) op(e0, e0) = e3
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | (4453) all_54_3 = e3
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (4450), (4453) are inconsistent by
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #216.
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | (4454) ~ (all_54_3 = e3)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | (4455) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4455) gives:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4456) all_54_3 = e2
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (4456) imply:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4457) all_52_12 = e2
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4457) implies:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4458) all_52_12 = e2
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (4458) imply:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4459) ~ (all_52_4 = e2)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (4458) imply:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4460) ~ (all_52_13 = e2)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4460) implies:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4461) ~ (all_52_13 = e2)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4450), (4458) imply:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4462) ~ (e3 = e2)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (4458) imply:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4463) op(e3, e0) = e2
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (4464) ~ (all_34_2 = e3)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4449), (4464) imply:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (4465) $false
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4465) is inconsistent.
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (4466) ( ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_34_0)) | ( ~ (all_34_1 = e1) & op(e3, e3)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_34_1 & $i(all_34_1))
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4466) gives:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4467) ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_34_0)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4467) implies:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4468) ~ (all_34_0 = e2)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4469) op(e3, e0) = all_34_0
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4463), (4468), (4469), (function-axioms) are
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #551.
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4470) ~ (all_34_1 = e1) & op(e3, e3) = all_34_1 &
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_34_1)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4470) implies:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4471) ~ (all_34_1 = e1)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4472) op(e3, e3) = all_34_1
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4473) all_54_7 = e3
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (4451), (4473) are inconsistent by
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #338.
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4474) ~ (all_54_7 = e3)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4475) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4475) gives:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4476) all_54_7 = e2
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (4461), (4476) are inconsistent by
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #337.
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4477) ~ (all_54_7 = e2)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4478) all_54_7 = e1 | all_54_7 = e0
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4478) gives:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4479) all_54_7 = e1
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (4479) imply:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4480) all_52_13 = e1
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4480) implies:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4481) all_52_13 = e1
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (4481) imply:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4482) ~ (all_52_14 = e1)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4482) implies:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4483) ~ (all_52_14 = e1)
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4484) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4484) gives:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4485) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4485) gives:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4486) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (168), (170),
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220), (221), (222), (232), (372), (4068), (4070),
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4421), (4446), (4486), (function-axioms) are
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #222.
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4487) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4487) implies:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4488) op(e3, e3) = e1
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4471), (4472), (4488), (function-axioms) are
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #626.
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4489) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (133), (168), (203), (271), (4068), (4340),
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4412), (4459), (4489), (function-axioms) are
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #215.
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4490) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4490) gives:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4491) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4491) gives:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4492) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4492) implies:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4493) ~ (all_56_17 = e1)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4494) op(e3, e1) = all_56_17
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4346), (4493), (4494), (function-axioms) are
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #349.
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4495) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2,
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4495) implies:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4496) op(e2, e2) = e1
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4412), (4496), (function-axioms) are
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675.
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4497) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4497) gives:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4498) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4498) implies:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4499) op(e2, e0) = e2
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (4461), (4499), (function-axioms) are
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4500) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4500) gives:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4501) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4501) implies:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4502) op(e1, e1) = e2
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (4502), (function-axioms) are
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4503) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4503) implies:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4504) op(e0, e0) = all_56_31
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4505) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4505) gives:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4506) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27))
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4506) gives:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4507) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4507) implies:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4508) ~ (all_56_17 = e1)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4509) op(e3, e1) = all_56_17
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4346), (4508), (4509), (function-axioms) are
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #349.
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4510) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4510) implies:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4511) op(e0, e2) = e0
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (4443), (4511), (function-axioms) are
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #545.
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4512) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4512) gives:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4513) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4513) implies:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4514) op(e1, e0) = e1
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (4483), (4514), (function-axioms) are
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #327.
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4515) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4515) implies:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4516) all_56_31 = e1
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4504), (4516) imply:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4517) op(e0, e0) = e1
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4452), (4517), (function-axioms) are
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #606.
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4518) all_54_7 = e0
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (4409), (4518) are inconsistent by
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #326.
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | (4519) all_54_3 = e1 | all_54_3 = e0
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (4070), (4343), (4519) are inconsistent by
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #321.
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | (4520) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (371), (4075), (4445), (4520) are
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #746.
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.07 | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.07 | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | (4521) all_54_6 = e1 | all_54_6 = e0
% 133.26/19.07 | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (4341), (4408), (4521) are inconsistent by
% 133.26/19.07 | | | | | | | | | | | | | | | | | | | sub-proof #479.
% 133.26/19.07 | | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.07 | | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | | End of split
% 133.26/19.07 | | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | | End of split
% 133.26/19.07 | | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | | End of split
% 133.26/19.07 | | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | End of split
% 133.26/19.07 | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | Case 2:
% 133.26/19.07 | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | (4522) all_57_5 = e1 & op(e2, e1) = e1
% 133.26/19.07 | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | ALPHA: (4522) implies:
% 133.26/19.07 | | | | | | | | | | | | | | (4523) all_57_5 = e1
% 133.26/19.07 | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (39), (219), (221), (372),
% 133.26/19.07 | | | | | | | | | | | | | | (4313), (4315), (4316), (4346), (4523),
% 133.26/19.07 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.26/19.07 | | | | | | | | | | | | | | #214.
% 133.26/19.07 | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | End of split
% 133.26/19.07 | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | Case 2:
% 133.26/19.07 | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | (4524) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 133.26/19.07 | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 133.26/19.07 | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | BETA: splitting (4524) gives:
% 133.26/19.07 | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | Case 1:
% 133.26/19.07 | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | (4525) all_57_8 = e1 & op(e1, e1) = e1
% 133.26/19.07 | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | ALPHA: (4525) implies:
% 133.26/19.07 | | | | | | | | | | | | | | (4526) op(e1, e1) = e1
% 133.26/19.07 | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (4313), (4526), (function-axioms) are
% 133.26/19.07 | | | | | | | | | | | | | | inconsistent by sub-proof #662.
% 133.26/19.07 | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | Case 2:
% 133.26/19.07 | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | (4527) all_57_14 = e1 & op(e0, e1) = e1
% 133.26/19.07 | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | ALPHA: (4527) implies:
% 133.26/19.07 | | | | | | | | | | | | | | (4528) all_57_14 = e1
% 133.26/19.07 | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (39), (219), (221), (372),
% 133.26/19.07 | | | | | | | | | | | | | | (4313), (4315), (4316), (4346), (4528),
% 133.26/19.07 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.26/19.07 | | | | | | | | | | | | | | #212.
% 133.26/19.07 | | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | | End of split
% 133.26/19.07 | | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | End of split
% 133.26/19.07 | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | Case 2:
% 133.26/19.07 | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | (4529) all_54_2 = e0
% 133.26/19.07 | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | COMBINE_EQS: (4318), (4529) imply:
% 133.26/19.07 | | | | | | | | | | | | (4530) all_28_0 = e0
% 133.26/19.07 | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | REDUCE: (4327), (4530) imply:
% 133.26/19.07 | | | | | | | | | | | | (4531) $false
% 133.26/19.07 | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | | CLOSE: (4531) is inconsistent.
% 133.26/19.07 | | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | | End of split
% 133.26/19.07 | | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | | End of split
% 133.26/19.07 | | | | | | | | | |
% 133.26/19.07 | | | | | | | | | End of split
% 133.26/19.07 | | | | | | | | |
% 133.26/19.07 | | | | | | | | Case 2:
% 133.26/19.07 | | | | | | | | |
% 133.26/19.07 | | | | | | | | | (4532) ~ (all_28_1 = e0) & op(e3, e3) = all_28_1 &
% 133.26/19.07 | | | | | | | | | $i(all_28_1)
% 133.26/19.07 | | | | | | | | |
% 133.26/19.07 | | | | | | | | | REF_CLOSE: (4071), (4532), (function-axioms) are inconsistent
% 133.26/19.07 | | | | | | | | | by sub-proof #211.
% 133.26/19.07 | | | | | | | | |
% 133.26/19.07 | | | | | | | | End of split
% 133.26/19.07 | | | | | | | |
% 133.26/19.07 | | | | | | | End of split
% 133.26/19.07 | | | | | | |
% 133.26/19.07 | | | | | | Case 2:
% 133.26/19.07 | | | | | | |
% 133.26/19.07 | | | | | | | (4533) all_20_2 = e2
% 133.26/19.07 | | | | | | |
% 133.26/19.07 | | | | | | | COMBINE_EQS: (318), (4533) imply:
% 133.26/19.08 | | | | | | | (4534) all_4_2 = e2
% 133.26/19.08 | | | | | | |
% 133.26/19.08 | | | | | | | SIMP: (4534) implies:
% 133.26/19.08 | | | | | | | (4535) all_4_2 = e2
% 133.26/19.08 | | | | | | |
% 133.26/19.08 | | | | | | | REDUCE: (349), (4535) imply:
% 133.26/19.08 | | | | | | | (4536) ~ (all_52_3 = e2)
% 133.26/19.08 | | | | | | |
% 133.26/19.08 | | | | | | | REDUCE: (368), (4535) imply:
% 133.26/19.08 | | | | | | | (4537) ~ (all_52_12 = e2)
% 133.26/19.08 | | | | | | |
% 133.26/19.08 | | | | | | | REDUCE: (369), (4535) imply:
% 133.26/19.08 | | | | | | | (4538) ~ (all_52_13 = e2)
% 133.26/19.08 | | | | | | |
% 133.26/19.08 | | | | | | | REDUCE: (36), (4535) imply:
% 133.26/19.08 | | | | | | | (4539) op(e0, e0) = e2
% 133.26/19.08 | | | | | | |
% 133.26/19.08 | | | | | | | BETA: splitting (67) gives:
% 133.26/19.08 | | | | | | |
% 133.26/19.08 | | | | | | | Case 1:
% 133.26/19.08 | | | | | | | |
% 133.26/19.08 | | | | | | | | (4540) ~ (all_24_2 = e0)
% 133.26/19.08 | | | | | | | |
% 133.26/19.08 | | | | | | | | REDUCE: (4065), (4540) imply:
% 133.26/19.08 | | | | | | | | (4541) $false
% 133.26/19.08 | | | | | | | |
% 133.26/19.08 | | | | | | | | CLOSE: (4541) is inconsistent.
% 133.26/19.08 | | | | | | | |
% 133.26/19.08 | | | | | | | Case 2:
% 133.26/19.08 | | | | | | | |
% 133.26/19.08 | | | | | | | | (4542) ( ~ (all_24_0 = e1) & op(e0, e3) = all_24_0 &
% 133.26/19.08 | | | | | | | | $i(all_24_0)) | ( ~ (all_24_1 = e2) & op(e0, e0) =
% 133.26/19.08 | | | | | | | | all_24_1 & $i(all_24_1))
% 133.26/19.08 | | | | | | | |
% 133.26/19.08 | | | | | | | | BETA: splitting (4542) gives:
% 133.26/19.08 | | | | | | | |
% 133.26/19.08 | | | | | | | | Case 1:
% 133.26/19.08 | | | | | | | | |
% 133.26/19.08 | | | | | | | | | (4543) ~ (all_24_0 = e1) & op(e0, e3) = all_24_0 &
% 133.26/19.08 | | | | | | | | | $i(all_24_0)
% 133.26/19.08 | | | | | | | | |
% 133.26/19.08 | | | | | | | | | ALPHA: (4543) implies:
% 133.26/19.08 | | | | | | | | | (4544) ~ (all_24_0 = e1)
% 133.26/19.08 | | | | | | | | | (4545) op(e0, e3) = all_24_0
% 133.26/19.08 | | | | | | | | |
% 133.26/19.08 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 133.26/19.08 | | | | | | | | | all_24_0, e3, e0, simplifying with (159), (4545)
% 133.26/19.08 | | | | | | | | | gives:
% 133.26/19.08 | | | | | | | | | (4546) all_52_3 = all_24_0
% 133.26/19.08 | | | | | | | | |
% 133.26/19.08 | | | | | | | | | COMBINE_EQS: (248), (4546) imply:
% 133.26/19.08 | | | | | | | | | (4547) all_54_12 = all_24_0
% 133.26/19.08 | | | | | | | | |
% 133.26/19.08 | | | | | | | | | REDUCE: (148), (4546) imply:
% 133.26/19.08 | | | | | | | | | (4548) ~ (all_52_1 = all_24_0)
% 133.26/19.08 | | | | | | | | |
% 133.26/19.08 | | | | | | | | | REDUCE: (144), (4546) imply:
% 133.26/19.08 | | | | | | | | | (4549) ~ (all_52_2 = all_24_0)
% 133.26/19.08 | | | | | | | | |
% 133.26/19.08 | | | | | | | | | REDUCE: (140), (4546) imply:
% 133.26/19.08 | | | | | | | | | (4550) ~ (all_52_7 = all_24_0)
% 133.26/19.08 | | | | | | | | |
% 133.26/19.08 | | | | | | | | | SIMP: (4550) implies:
% 133.26/19.08 | | | | | | | | | (4551) ~ (all_52_7 = all_24_0)
% 133.26/19.08 | | | | | | | | |
% 133.26/19.08 | | | | | | | | | REDUCE: (139), (4546) imply:
% 133.26/19.08 | | | | | | | | | (4552) ~ (all_52_11 = all_24_0)
% 133.26/19.08 | | | | | | | | |
% 133.26/19.08 | | | | | | | | | SIMP: (4552) implies:
% 133.26/19.08 | | | | | | | | | (4553) ~ (all_52_11 = all_24_0)
% 133.26/19.08 | | | | | | | | |
% 133.26/19.08 | | | | | | | | | REDUCE: (4536), (4546) imply:
% 133.26/19.08 | | | | | | | | | (4554) ~ (all_24_0 = e2)
% 133.26/19.08 | | | | | | | | |
% 133.26/19.08 | | | | | | | | | REDUCE: (4067), (4546) imply:
% 133.26/19.08 | | | | | | | | | (4555) ~ (all_24_0 = e0)
% 133.26/19.08 | | | | | | | | |
% 133.26/19.08 | | | | | | | | | BETA: splitting (192) gives:
% 133.26/19.08 | | | | | | | | |
% 133.26/19.08 | | | | | | | | | Case 1:
% 133.26/19.08 | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | (4556) all_54_12 = e3
% 133.26/19.08 | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | COMBINE_EQS: (4547), (4556) imply:
% 133.26/19.08 | | | | | | | | | | (4557) all_24_0 = e3
% 133.26/19.08 | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | REDUCE: (4548), (4557) imply:
% 133.26/19.08 | | | | | | | | | | (4558) ~ (all_52_1 = e3)
% 133.26/19.08 | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | REDUCE: (4549), (4557) imply:
% 133.26/19.08 | | | | | | | | | | (4559) ~ (all_52_2 = e3)
% 133.26/19.08 | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | REDUCE: (4551), (4557) imply:
% 133.26/19.08 | | | | | | | | | | (4560) ~ (all_52_7 = e3)
% 133.26/19.08 | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | REDUCE: (4553), (4557) imply:
% 133.26/19.08 | | | | | | | | | | (4561) ~ (all_52_11 = e3)
% 133.26/19.08 | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | BETA: splitting (237) gives:
% 133.26/19.08 | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | Case 1:
% 133.26/19.08 | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | (4562) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 133.26/19.08 | | | | | | | | | | | & op(e2, e3) = e3)
% 133.26/19.08 | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | REF_CLOSE: (7), (167), (4071), (4558), (4562),
% 133.26/19.08 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.26/19.08 | | | | | | | | | | | #210.
% 133.26/19.08 | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | Case 2:
% 133.26/19.08 | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | (4563) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 133.26/19.08 | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 133.26/19.08 | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | BETA: splitting (4563) gives:
% 133.26/19.08 | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | Case 1:
% 133.26/19.08 | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | (4564) all_57_6 = e3 & op(e1, e3) = e3
% 133.26/19.08 | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | REF_CLOSE: (163), (4559), (4564), (function-axioms) are
% 133.26/19.08 | | | | | | | | | | | | inconsistent by sub-proof #761.
% 133.26/19.08 | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | Case 2:
% 133.26/19.08 | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | (4565) all_57_12 = e3 & op(e0, e3) = e3
% 133.26/19.08 | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | ALPHA: (4565) implies:
% 133.26/19.08 | | | | | | | | | | | | (4566) all_57_12 = e3
% 133.26/19.08 | | | | | | | | | | | | (4567) op(e0, e3) = e3
% 133.26/19.08 | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | BETA: splitting (73) gives:
% 133.26/19.08 | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | Case 1:
% 133.26/19.08 | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | (4568) ~ (all_28_2 = e3)
% 133.26/19.08 | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | REDUCE: (316), (4568) imply:
% 133.26/19.08 | | | | | | | | | | | | | (4569) ~ (all_6_2 = e3)
% 133.26/19.08 | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.26/19.08 | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | Case 1:
% 133.26/19.08 | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | (4570) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.26/19.08 | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.26/19.08 | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.26/19.08 | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.26/19.08 | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.08 | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.26/19.08 | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.26/19.08 | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.26/19.08 | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.26/19.08 | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.26/19.08 | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.26/19.08 | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.08 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.26/19.08 | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.26/19.08 | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.26/19.08 | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.26/19.08 | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.26/19.08 | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.08 | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.08 | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.26/19.08 | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.26/19.08 | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.26/19.08 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.08 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.08 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.08 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.26/19.08 | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.08 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.26/19.08 | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | BETA: splitting (4570) gives:
% 133.26/19.08 | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | Case 1:
% 133.26/19.08 | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | (4571) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.26/19.08 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.26/19.08 | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.26/19.08 | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.26/19.08 | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.08 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.26/19.08 | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.26/19.08 | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.26/19.08 | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.26/19.08 | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.26/19.08 | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.26/19.08 | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.08 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.26/19.08 | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 133.26/19.08 | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (4071), (4571), (function-axioms) are
% 133.26/19.08 | | | | | | | | | | | | | | | inconsistent by sub-proof #229.
% 133.26/19.08 | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | Case 2:
% 133.26/19.08 | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | (4572) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.26/19.08 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.26/19.08 | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.26/19.08 | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.08 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.08 | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.26/19.08 | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.26/19.08 | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.26/19.08 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.08 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.08 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.08 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.26/19.08 | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.08 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.26/19.08 | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | BETA: splitting (4572) gives:
% 133.26/19.08 | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | Case 1:
% 133.26/19.08 | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | | (4573) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.26/19.08 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.26/19.08 | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3,
% 133.26/19.08 | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.26/19.08 | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 133.26/19.08 | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.26/19.08 | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 133.26/19.08 | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | | ALPHA: (4573) implies:
% 133.26/19.08 | | | | | | | | | | | | | | | | (4574) ~ (all_56_7 = e3)
% 133.26/19.08 | | | | | | | | | | | | | | | | (4575) op(e0, e3) = all_56_7
% 133.26/19.08 | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_56_7,
% 133.26/19.08 | | | | | | | | | | | | | | | | e3, e0, simplifying with (4567), (4575) gives:
% 133.26/19.08 | | | | | | | | | | | | | | | | (4576) all_56_7 = e3
% 133.26/19.08 | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | | REDUCE: (4574), (4576) imply:
% 133.26/19.08 | | | | | | | | | | | | | | | | (4577) $false
% 133.26/19.08 | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | | CLOSE: (4577) is inconsistent.
% 133.26/19.08 | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | Case 2:
% 133.26/19.08 | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | | (4578) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.26/19.08 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.26/19.08 | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.08 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.08 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2,
% 133.26/19.08 | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.08 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 133.26/19.08 | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | | ALPHA: (4578) implies:
% 133.26/19.08 | | | | | | | | | | | | | | | | (4579) op(e2, e2) = e3
% 133.26/19.08 | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | | REF_CLOSE: (42), (4073), (4579), (function-axioms) are
% 133.26/19.08 | | | | | | | | | | | | | | | | inconsistent by sub-proof #228.
% 133.26/19.08 | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | End of split
% 133.26/19.08 | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | End of split
% 133.26/19.08 | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | Case 2:
% 133.26/19.08 | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | (4580) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.26/19.08 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.08 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.08 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.08 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.26/19.08 | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.08 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.26/19.08 | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.26/19.08 | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.26/19.08 | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.26/19.08 | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.26/19.08 | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.26/19.08 | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.26/19.08 | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.26/19.08 | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.26/19.08 | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.26/19.08 | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.26/19.08 | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.26/19.08 | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.26/19.08 | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.26/19.08 | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.26/19.08 | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.26/19.08 | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.26/19.08 | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.26/19.08 | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.26/19.08 | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.26/19.08 | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.26/19.08 | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.26/19.08 | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.26/19.08 | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.26/19.08 | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.26/19.08 | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.08 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.26/19.08 | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.26/19.08 | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.08 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.26/19.08 | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.26/19.08 | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.26/19.08 | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.26/19.08 | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.26/19.08 | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.26/19.08 | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.26/19.08 | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.26/19.08 | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.26/19.08 | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.26/19.08 | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.26/19.08 | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.26/19.08 | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.26/19.08 | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.26/19.08 | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.26/19.08 | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.26/19.08 | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.26/19.08 | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.26/19.08 | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.08 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.26/19.08 | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.26/19.08 | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.26/19.08 | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | BETA: splitting (4580) gives:
% 133.26/19.08 | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | Case 1:
% 133.26/19.08 | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | (4581) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.26/19.08 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.08 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.08 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.08 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.26/19.08 | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.08 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.26/19.08 | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.26/19.08 | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.26/19.08 | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.26/19.08 | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.26/19.08 | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.26/19.08 | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.26/19.08 | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.26/19.08 | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | BETA: splitting (4581) gives:
% 133.26/19.08 | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | Case 1:
% 133.26/19.08 | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | | (4582) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.26/19.08 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.26/19.08 | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.08 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.08 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 133.26/19.08 | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.08 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 133.26/19.08 | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | | ALPHA: (4582) implies:
% 133.26/19.08 | | | | | | | | | | | | | | | | (4583) op(e1, e1) = e3
% 133.26/19.08 | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | | REF_CLOSE: (39), (4569), (4583), (function-axioms) are
% 133.26/19.08 | | | | | | | | | | | | | | | | inconsistent by sub-proof #771.
% 133.26/19.08 | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | Case 2:
% 133.26/19.08 | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | | (4584) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 =
% 133.26/19.08 | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.26/19.08 | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2,
% 133.26/19.08 | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.26/19.08 | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.26/19.08 | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.26/19.08 | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 133.26/19.08 | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | | ALPHA: (4584) implies:
% 133.26/19.08 | | | | | | | | | | | | | | | | (4585) op(e2, e2) = e1
% 133.26/19.08 | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, e1,
% 133.26/19.08 | | | | | | | | | | | | | | | | e2, e2, simplifying with (42), (4585) gives:
% 133.26/19.08 | | | | | | | | | | | | | | | | (4586) all_8_2 = e1
% 133.26/19.08 | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | | REDUCE: (373), (4586) imply:
% 133.26/19.08 | | | | | | | | | | | | | | | | (4587) $false
% 133.26/19.08 | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | | CLOSE: (4587) is inconsistent.
% 133.26/19.08 | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | End of split
% 133.26/19.08 | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | Case 2:
% 133.26/19.08 | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | (4588) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.26/19.08 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.26/19.08 | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 133.26/19.08 | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.08 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.08 | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.26/19.08 | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.26/19.08 | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.26/19.08 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.26/19.08 | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.26/19.08 | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.26/19.08 | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.26/19.08 | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.26/19.08 | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.26/19.08 | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.26/19.08 | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.26/19.08 | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.26/19.08 | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.26/19.08 | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.26/19.08 | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.26/19.08 | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.26/19.08 | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.26/19.08 | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.26/19.08 | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.26/19.08 | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.26/19.08 | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.26/19.08 | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.08 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.26/19.08 | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.26/19.08 | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.26/19.08 | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.26/19.08 | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.26/19.08 | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.26/19.08 | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.08 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.08 | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.26/19.08 | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.26/19.08 | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.26/19.08 | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.26/19.08 | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.26/19.08 | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.08 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.26/19.08 | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.26/19.08 | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.26/19.08 | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | BETA: splitting (4588) gives:
% 133.26/19.08 | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | Case 1:
% 133.26/19.08 | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | | (4589) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.26/19.08 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.26/19.08 | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 133.26/19.08 | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.26/19.08 | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 133.26/19.08 | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.26/19.08 | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 133.26/19.08 | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | | ALPHA: (4589) implies:
% 133.26/19.08 | | | | | | | | | | | | | | | | (4590) op(e2, e0) = e2
% 133.26/19.08 | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | | REF_CLOSE: (164), (4538), (4590), (function-axioms) are
% 133.26/19.08 | | | | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 133.26/19.08 | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | Case 2:
% 133.26/19.08 | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | | (4591) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.26/19.08 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.26/19.08 | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.26/19.08 | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.26/19.08 | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.26/19.08 | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.26/19.08 | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.26/19.08 | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.26/19.08 | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.26/19.08 | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.26/19.08 | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.26/19.08 | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.26/19.08 | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.26/19.08 | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.26/19.08 | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.26/19.08 | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.26/19.08 | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.26/19.08 | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.26/19.08 | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.26/19.08 | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.08 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.26/19.08 | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.26/19.08 | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.26/19.08 | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.26/19.08 | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.26/19.08 | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.26/19.08 | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.08 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.08 | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.26/19.08 | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.26/19.08 | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.26/19.08 | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.26/19.08 | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.26/19.08 | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.08 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.26/19.08 | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.26/19.08 | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.26/19.08 | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | | BETA: splitting (4591) gives:
% 133.26/19.08 | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.08 | | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | | | (4592) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.26/19.08 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 133.26/19.08 | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.26/19.08 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.08 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 133.26/19.08 | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.26/19.08 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 133.26/19.08 | | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | | | ALPHA: (4592) implies:
% 133.26/19.08 | | | | | | | | | | | | | | | | | (4593) op(e1, e1) = e2
% 133.26/19.08 | | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (4593), (function-axioms) are
% 133.26/19.08 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 133.26/19.08 | | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.08 | | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | | | (4594) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.26/19.08 | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.26/19.08 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 133.26/19.08 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.26/19.08 | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 133.26/19.08 | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.26/19.08 | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.08 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 133.26/19.08 | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 133.26/19.08 | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.26/19.08 | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.26/19.08 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.26/19.08 | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.26/19.08 | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.26/19.08 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 133.26/19.08 | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.26/19.08 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.26/19.08 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.26/19.08 | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.08 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.08 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 133.26/19.08 | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 133.26/19.08 | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 133.26/19.08 | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 133.26/19.08 | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 133.26/19.08 | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.26/19.08 | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 133.26/19.08 | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 133.26/19.08 | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 133.26/19.08 | | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | | | ALPHA: (4594) implies:
% 133.26/19.08 | | | | | | | | | | | | | | | | | (4595) op(e0, e0) = all_56_31
% 133.26/19.08 | | | | | | | | | | | | | | | | | (4596) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.26/19.08 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.08 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.08 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.08 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 133.26/19.08 | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 133.26/19.08 | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 133.26/19.08 | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 133.26/19.08 | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 133.26/19.08 | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 133.26/19.08 | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 133.26/19.08 | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 133.26/19.08 | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 133.26/19.08 | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.26/19.08 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.26/19.08 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 133.26/19.08 | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.26/19.08 | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.08 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 133.26/19.08 | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 133.26/19.08 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.26/19.08 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 133.26/19.08 | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 133.26/19.08 | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 133.26/19.08 | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 133.26/19.08 | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.26/19.08 | | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (157), (158),
% 133.26/19.08 | | | | | | | | | | | | | | | | | (199), (208), (209), (211), (267), (354), (373),
% 133.26/19.08 | | | | | | | | | | | | | | | | | (4073), (4539), (4561), (4566), (4567), (4595),
% 133.26/19.08 | | | | | | | | | | | | | | | | | (4596), (function-axioms) are inconsistent by
% 133.26/19.08 | | | | | | | | | | | | | | | | | sub-proof #208.
% 133.26/19.08 | | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | | End of split
% 133.26/19.08 | | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | | End of split
% 133.26/19.08 | | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | | End of split
% 133.26/19.08 | | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | End of split
% 133.26/19.08 | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | Case 2:
% 133.26/19.08 | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | (4597) all_28_2 = e3
% 133.26/19.08 | | | | | | | | | | | | | (4598) ( ~ (all_28_0 = e2) & op(e3, e1) = all_28_0 &
% 133.26/19.08 | | | | | | | | | | | | | $i(all_28_0)) | ( ~ (all_28_1 = e0) & op(e3, e3)
% 133.26/19.08 | | | | | | | | | | | | | = all_28_1 & $i(all_28_1))
% 133.26/19.08 | | | | | | | | | | | | |
% 133.26/19.08 | | | | | | | | | | | | | COMBINE_EQS: (316), (4597) imply:
% 133.26/19.09 | | | | | | | | | | | | | (4599) all_6_2 = e3
% 133.26/19.09 | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | SIMP: (4599) implies:
% 133.26/19.09 | | | | | | | | | | | | | (4600) all_6_2 = e3
% 133.26/19.09 | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | REDUCE: (359), (4600) imply:
% 133.26/19.09 | | | | | | | | | | | | | (4601) ~ (all_52_6 = e3)
% 133.26/19.09 | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | BETA: splitting (4598) gives:
% 133.26/19.09 | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | (4602) ~ (all_28_0 = e2) & op(e3, e1) = all_28_0 &
% 133.26/19.09 | | | | | | | | | | | | | | $i(all_28_0)
% 133.26/19.09 | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | ALPHA: (4602) implies:
% 133.26/19.09 | | | | | | | | | | | | | | (4603) ~ (all_28_0 = e2)
% 133.26/19.09 | | | | | | | | | | | | | | (4604) op(e3, e1) = all_28_0
% 133.26/19.09 | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 133.26/19.09 | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | (4605) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 133.26/19.09 | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 133.26/19.09 | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | BETA: splitting (4605) gives:
% 133.26/19.09 | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | (4606) all_57_1 = e3 & op(e3, e2) = e3
% 133.26/19.09 | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | ALPHA: (4606) implies:
% 133.26/19.09 | | | | | | | | | | | | | | | | (4607) all_57_1 = e3
% 133.26/19.09 | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (168), (208),
% 133.26/19.09 | | | | | | | | | | | | | | | | (209), (211), (236), (4071), (4537), (4539),
% 133.26/19.09 | | | | | | | | | | | | | | | | (4561), (4566), (4603), (4604), (4607),
% 133.26/19.09 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.26/19.09 | | | | | | | | | | | | | | | | #206.
% 133.26/19.09 | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | Case 2:
% 133.26/19.09 | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | (4608) all_57_3 = e3 & op(e2, e2) = e3
% 133.26/19.09 | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | ALPHA: (4608) implies:
% 133.26/19.09 | | | | | | | | | | | | | | | | (4609) op(e2, e2) = e3
% 133.26/19.09 | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | REF_CLOSE: (42), (4073), (4609), (function-axioms) are
% 133.26/19.09 | | | | | | | | | | | | | | | | inconsistent by sub-proof #228.
% 133.26/19.09 | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | End of split
% 133.26/19.09 | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | Case 2:
% 133.26/19.09 | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | (4610) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 133.26/19.09 | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 133.26/19.09 | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (4560), (4601), (4610),
% 133.26/19.09 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.26/19.09 | | | | | | | | | | | | | | | #555.
% 133.26/19.09 | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | End of split
% 133.26/19.09 | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | Case 2:
% 133.26/19.09 | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | (4611) ~ (all_28_1 = e0) & op(e3, e3) = all_28_1 &
% 133.26/19.09 | | | | | | | | | | | | | | $i(all_28_1)
% 133.26/19.09 | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | REF_CLOSE: (4071), (4611), (function-axioms) are inconsistent
% 133.26/19.09 | | | | | | | | | | | | | | by sub-proof #211.
% 133.26/19.09 | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | End of split
% 133.26/19.09 | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | End of split
% 133.26/19.09 | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | End of split
% 133.26/19.09 | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | End of split
% 133.26/19.09 | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | Case 2:
% 133.26/19.09 | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | (4612) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 133.26/19.09 | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | REF_CLOSE: (4544), (4547), (4554), (4555), (4612) are
% 133.26/19.09 | | | | | | | | | | inconsistent by sub-proof #205.
% 133.26/19.09 | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | End of split
% 133.26/19.09 | | | | | | | | |
% 133.26/19.09 | | | | | | | | Case 2:
% 133.26/19.09 | | | | | | | | |
% 133.26/19.09 | | | | | | | | | (4613) ~ (all_24_1 = e2) & op(e0, e0) = all_24_1 &
% 133.26/19.09 | | | | | | | | | $i(all_24_1)
% 133.26/19.09 | | | | | | | | |
% 133.26/19.09 | | | | | | | | | REF_CLOSE: (4539), (4613), (function-axioms) are inconsistent
% 133.26/19.09 | | | | | | | | | by sub-proof #204.
% 133.26/19.09 | | | | | | | | |
% 133.26/19.09 | | | | | | | | End of split
% 133.26/19.09 | | | | | | | |
% 133.26/19.09 | | | | | | | End of split
% 133.26/19.09 | | | | | | |
% 133.26/19.09 | | | | | | End of split
% 133.26/19.09 | | | | | |
% 133.26/19.09 | | | | | Case 2:
% 133.26/19.09 | | | | | |
% 133.26/19.09 | | | | | | (4614) all_14_2 = e3
% 133.26/19.09 | | | | | | (4615) ( ~ (all_14_0 = e1) & op(e3, e2) = all_14_0 &
% 133.26/19.09 | | | | | | $i(all_14_0)) | ( ~ (all_14_1 = e0) & op(e3, e3) =
% 133.26/19.09 | | | | | | all_14_1 & $i(all_14_1))
% 133.26/19.09 | | | | | |
% 133.26/19.09 | | | | | | COMBINE_EQS: (329), (4614) imply:
% 133.26/19.09 | | | | | | (4616) all_8_2 = e3
% 133.26/19.09 | | | | | |
% 133.26/19.09 | | | | | | REDUCE: (347), (4616) imply:
% 133.26/19.09 | | | | | | (4617) ~ (all_52_1 = e3)
% 133.26/19.09 | | | | | |
% 133.26/19.09 | | | | | | REDUCE: (350), (4616) imply:
% 133.26/19.09 | | | | | | (4618) ~ (all_52_4 = e3)
% 133.26/19.09 | | | | | |
% 133.26/19.09 | | | | | | REDUCE: (352), (4616) imply:
% 133.26/19.09 | | | | | | (4619) ~ (all_52_6 = e3)
% 133.26/19.09 | | | | | |
% 133.26/19.09 | | | | | | REDUCE: (354), (4616) imply:
% 133.26/19.09 | | | | | | (4620) ~ (all_52_7 = e3)
% 133.26/19.09 | | | | | |
% 133.26/19.09 | | | | | | REDUCE: (356), (4616) imply:
% 133.26/19.09 | | | | | | (4621) ~ (all_52_9 = e3)
% 133.26/19.09 | | | | | |
% 133.26/19.09 | | | | | | REDUCE: (358), (4616) imply:
% 133.26/19.09 | | | | | | (4622) ~ (all_52_13 = e3)
% 133.26/19.09 | | | | | |
% 133.26/19.09 | | | | | | BETA: splitting (4615) gives:
% 133.26/19.09 | | | | | |
% 133.26/19.09 | | | | | | Case 1:
% 133.26/19.09 | | | | | | |
% 133.26/19.09 | | | | | | | (4623) ~ (all_14_0 = e1) & op(e3, e2) = all_14_0 &
% 133.26/19.09 | | | | | | | $i(all_14_0)
% 133.26/19.09 | | | | | | |
% 133.26/19.09 | | | | | | | ALPHA: (4623) implies:
% 133.26/19.09 | | | | | | | (4624) ~ (all_14_0 = e1)
% 133.26/19.09 | | | | | | | (4625) op(e3, e2) = all_14_0
% 133.26/19.09 | | | | | | |
% 133.26/19.09 | | | | | | | BETA: splitting (230) gives:
% 133.26/19.09 | | | | | | |
% 133.26/19.09 | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | |
% 133.26/19.09 | | | | | | | | (4626) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 &
% 133.26/19.09 | | | | | | | | op(e2, e2) = e3)
% 133.26/19.09 | | | | | | | |
% 133.26/19.09 | | | | | | | | BETA: splitting (4626) gives:
% 133.26/19.09 | | | | | | | |
% 133.26/19.09 | | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | | |
% 133.26/19.09 | | | | | | | | | (4627) all_57_1 = e3 & op(e3, e2) = e3
% 133.26/19.09 | | | | | | | | |
% 133.26/19.09 | | | | | | | | | ALPHA: (4627) implies:
% 133.26/19.09 | | | | | | | | | (4628) op(e3, e2) = e3
% 133.26/19.09 | | | | | | | | |
% 133.26/19.09 | | | | | | | | | REF_CLOSE: (170), (4618), (4628), (function-axioms) are
% 133.26/19.09 | | | | | | | | | inconsistent by sub-proof #738.
% 133.26/19.09 | | | | | | | | |
% 133.26/19.09 | | | | | | | | Case 2:
% 133.26/19.09 | | | | | | | | |
% 133.26/19.09 | | | | | | | | | (4629) all_57_3 = e3 & op(e2, e2) = e3
% 133.26/19.09 | | | | | | | | |
% 133.26/19.09 | | | | | | | | | ALPHA: (4629) implies:
% 133.26/19.09 | | | | | | | | | (4630) all_57_3 = e3
% 133.26/19.09 | | | | | | | | | (4631) op(e2, e2) = e3
% 133.26/19.09 | | | | | | | | |
% 133.26/19.09 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4,
% 133.26/19.09 | | | | | | | | | all_14_0, e2, e3, simplifying with (170), (4625)
% 133.26/19.09 | | | | | | | | | gives:
% 133.26/19.09 | | | | | | | | | (4632) all_52_4 = all_14_0
% 133.26/19.09 | | | | | | | | |
% 133.26/19.09 | | | | | | | | | COMBINE_EQS: (271), (4632) imply:
% 133.26/19.09 | | | | | | | | | (4633) all_54_1 = all_14_0
% 133.26/19.09 | | | | | | | | |
% 133.26/19.09 | | | | | | | | | REDUCE: (136), (4632) imply:
% 133.26/19.09 | | | | | | | | | (4634) ~ (all_52_6 = all_14_0)
% 133.26/19.09 | | | | | | | | |
% 133.26/19.09 | | | | | | | | | SIMP: (4634) implies:
% 133.26/19.09 | | | | | | | | | (4635) ~ (all_52_6 = all_14_0)
% 133.26/19.09 | | | | | | | | |
% 133.26/19.09 | | | | | | | | | REDUCE: (134), (4632) imply:
% 133.26/19.09 | | | | | | | | | (4636) ~ (all_52_8 = all_14_0)
% 133.26/19.09 | | | | | | | | |
% 133.26/19.09 | | | | | | | | | SIMP: (4636) implies:
% 133.26/19.09 | | | | | | | | | (4637) ~ (all_52_8 = all_14_0)
% 133.26/19.09 | | | | | | | | |
% 133.26/19.09 | | | | | | | | | REDUCE: (133), (4632) imply:
% 133.26/19.09 | | | | | | | | | (4638) ~ (all_52_12 = all_14_0)
% 133.26/19.09 | | | | | | | | |
% 133.26/19.09 | | | | | | | | | SIMP: (4638) implies:
% 133.26/19.09 | | | | | | | | | (4639) ~ (all_52_12 = all_14_0)
% 133.26/19.09 | | | | | | | | |
% 133.26/19.09 | | | | | | | | | REDUCE: (4618), (4632) imply:
% 133.26/19.09 | | | | | | | | | (4640) ~ (all_14_0 = e3)
% 133.26/19.09 | | | | | | | | |
% 133.26/19.09 | | | | | | | | | REDUCE: (4068), (4632) imply:
% 133.26/19.09 | | | | | | | | | (4641) ~ (all_14_0 = e0)
% 133.26/19.09 | | | | | | | | |
% 133.26/19.09 | | | | | | | | | BETA: splitting (203) gives:
% 133.26/19.09 | | | | | | | | |
% 133.26/19.09 | | | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | (4642) all_54_1 = e3
% 133.26/19.09 | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | COMBINE_EQS: (4633), (4642) imply:
% 133.26/19.09 | | | | | | | | | | (4643) all_14_0 = e3
% 133.26/19.09 | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | SIMP: (4643) implies:
% 133.26/19.09 | | | | | | | | | | (4644) all_14_0 = e3
% 133.26/19.09 | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | REDUCE: (4640), (4644) imply:
% 133.26/19.09 | | | | | | | | | | (4645) $false
% 133.26/19.09 | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | CLOSE: (4645) is inconsistent.
% 133.26/19.09 | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | Case 2:
% 133.26/19.09 | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | (4646) ~ (all_54_1 = e3)
% 133.26/19.09 | | | | | | | | | | (4647) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 133.26/19.09 | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | BETA: splitting (4647) gives:
% 133.26/19.09 | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | (4648) all_54_1 = e2
% 133.26/19.09 | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | COMBINE_EQS: (4633), (4648) imply:
% 133.26/19.09 | | | | | | | | | | | (4649) all_14_0 = e2
% 133.26/19.09 | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | SIMP: (4649) implies:
% 133.26/19.09 | | | | | | | | | | | (4650) all_14_0 = e2
% 133.26/19.09 | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | REDUCE: (4635), (4650) imply:
% 133.26/19.09 | | | | | | | | | | | (4651) ~ (all_52_6 = e2)
% 133.26/19.09 | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | REDUCE: (4637), (4650) imply:
% 133.26/19.09 | | | | | | | | | | | (4652) ~ (all_52_8 = e2)
% 133.26/19.09 | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | REDUCE: (4639), (4650) imply:
% 133.26/19.09 | | | | | | | | | | | (4653) ~ (all_52_12 = e2)
% 133.26/19.09 | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | REDUCE: (4640), (4650) imply:
% 133.26/19.09 | | | | | | | | | | | (4654) ~ (e3 = e2)
% 133.26/19.09 | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | BETA: splitting (229) gives:
% 133.26/19.09 | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | (4655) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 133.26/19.09 | | | | | | | | | | | | & op(e2, e2) = e2)
% 133.26/19.09 | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | BETA: splitting (4655) gives:
% 133.26/19.09 | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | (4656) all_57_1 = e2 & op(e3, e2) = e2
% 133.26/19.09 | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | ALPHA: (4656) implies:
% 133.26/19.09 | | | | | | | | | | | | | (4657) all_57_1 = e2
% 133.26/19.09 | | | | | | | | | | | | | (4658) op(e3, e2) = e2
% 133.26/19.09 | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | BETA: splitting (61) gives:
% 133.26/19.09 | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | (4659) ~ (all_20_2 = e2)
% 133.26/19.09 | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | REDUCE: (318), (4659) imply:
% 133.26/19.09 | | | | | | | | | | | | | | (4660) ~ (all_4_2 = e2)
% 133.26/19.09 | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 133.26/19.09 | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | (4661) ~ (all_28_2 = e3)
% 133.26/19.09 | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | REDUCE: (316), (4661) imply:
% 133.26/19.09 | | | | | | | | | | | | | | | (4662) ~ (all_6_2 = e3)
% 133.26/19.09 | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 133.26/19.09 | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | (4663) ~ (all_34_2 = e3)
% 133.26/19.09 | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | REDUCE: (307), (4663) imply:
% 133.26/19.09 | | | | | | | | | | | | | | | | (4664) ~ (all_4_2 = e3)
% 133.26/19.09 | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 133.26/19.09 | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | (4665) all_54_15 = e3
% 133.26/19.09 | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (4664), (4665) are inconsistent by
% 133.26/19.09 | | | | | | | | | | | | | | | | | sub-proof #601.
% 133.26/19.09 | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.09 | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | (4666) ~ (all_54_15 = e3)
% 133.26/19.09 | | | | | | | | | | | | | | | | | (4667) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 133.26/19.09 | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | BETA: splitting (4667) gives:
% 133.26/19.09 | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | (4668) all_54_15 = e2
% 133.26/19.09 | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (4660), (4668) are inconsistent by
% 133.26/19.09 | | | | | | | | | | | | | | | | | | sub-proof #748.
% 133.26/19.09 | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.09 | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | (4669) ~ (all_54_15 = e2)
% 133.26/19.09 | | | | | | | | | | | | | | | | | | (4670) all_54_15 = e1 | all_54_15 = e0
% 133.26/19.09 | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | BETA: splitting (4670) gives:
% 133.26/19.09 | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | (4671) all_54_15 = e1
% 133.26/19.09 | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (371), (4671) are inconsistent by sub-proof
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | #747.
% 133.26/19.09 | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | (4672) all_54_15 = e0
% 133.26/19.09 | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (4672) imply:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | (4673) all_4_2 = e0
% 133.26/19.09 | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | SIMP: (4673) implies:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | (4674) all_4_2 = e0
% 133.26/19.09 | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | REDUCE: (4664), (4674) imply:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | (4675) ~ (e3 = e0)
% 133.26/19.09 | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | REDUCE: (4660), (4674) imply:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | (4676) ~ (e2 = e0)
% 133.26/19.09 | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | REDUCE: (371), (4674) imply:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | (4677) ~ (e1 = e0)
% 133.26/19.09 | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | REDUCE: (36), (4674) imply:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | (4678) op(e0, e0) = e0
% 133.26/19.09 | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | (4679) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4679) gives:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | (4680) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (4071), (4680), (function-axioms) are
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #229.
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | (4681) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4681) gives:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | (4682) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3,
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4682) implies:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | (4683) ~ (all_56_31 = e0)
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | (4684) op(e0, e0) = all_56_31
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4678), (4683), (4684), (function-axioms) are
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #712.
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | (4685) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2,
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4685) implies:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | (4686) ~ (all_56_17 = e1)
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | (4687) op(e2, e3) = e2
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | (4688) op(e3, e1) = all_56_17
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | (4689) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (167), (4066), (4631), (4689),
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | #203.
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | (4690) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4690) gives:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | (4691) all_57_5 = e0 & op(e2, e1) = e0
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4691) implies:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | (4692) all_57_5 = e0
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | (4693) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4693) gives:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (4694) all_57_4 = e2 & op(e3, e1) = e2
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (4652), (4694), (function-axioms) are
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #442.
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (4695) all_57_5 = e2 & op(e2, e1) = e2
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4695) implies:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (4696) all_57_5 = e2
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4692), (4696) are inconsistent by sub-proof
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | #372.
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | (4697) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4697) gives:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (4698) all_57_8 = e2 & op(e1, e1) = e2
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4698) implies:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (4699) op(e1, e1) = e2
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (4699), (function-axioms) are
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (4700) all_57_14 = e2 & op(e0, e1) = e2
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4700) implies:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (4701) all_57_14 = e2
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4702) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4702) gives:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4703) all_57_4 = e3 & op(e3, e1) = e3
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4703) implies:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4704) op(e3, e1) = e3
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4705) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (168), (169), (170), (232), (4068),
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4070), (4657), (4704), (4705), (function-axioms)
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #202.
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4706) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4706) gives:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4707) all_57_4 = e1 & op(e3, e1) = e1
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4707) implies:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4708) op(e3, e1) = e1
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4686), (4688), (4708), (function-axioms) are
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #349.
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4709) all_57_9 = e1 & op(e3, e0) = e1
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4709) implies:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4710) all_57_9 = e1
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4711) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4711) gives:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4712) all_57_12 = e3 & op(e0, e3) = e3
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4712) implies:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4713) all_57_12 = e3
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4714) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (4622), (4710), (4714),
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #331.
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4715) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4715) gives:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4716) all_57_11 = e3 & op(e1, e0) = e3
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4716) implies:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4717) all_57_11 = e3
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4718) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4718) gives:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4719) all_57_9 = e2 & op(e3, e0) = e2
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (4653), (4719), (function-axioms) are
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #460.
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4720) all_57_10 = e2 & op(e2, e0) = e2
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4720) implies:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4721) all_57_10 = e2
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4722) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (4631), (4687), (4722),
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #292.
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4723) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (4692), (4721), (4723) are inconsistent
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #364.
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4724) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4724) gives:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4725) all_57_11 = e2 & op(e1, e0) = e2
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4725) implies:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4726) all_57_11 = e2
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (227), (228),
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230), (4619), (4630), (4657), (4717), (4726),
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #201.
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4727) all_57_15 = e2 & op(e0, e0) = e2
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4727) implies:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4728) all_57_15 = e2
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (208), (209), (4701),
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4713), (4728) are inconsistent by sub-proof #434.
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4729) all_57_15 = e3 & op(e0, e0) = e3
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4729) implies:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4730) all_57_15 = e3
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4731) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4731) gives:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4732) all_57_12 = e1 & op(e0, e3) = e1
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4713), (4732) are inconsistent by sub-proof
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #490.
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4733) all_57_13 = e1 & op(e0, e2) = e1
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4733) implies:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4734) all_57_13 = e1
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4735) all_57_15 = e0 & op(e0, e0) = e0
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4730), (4735) are inconsistent by sub-proof
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #406.
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4736) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4736) implies:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4737) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4737) gives:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4738) all_57_12 = e0 & op(e0, e3) = e0
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4713), (4738) are inconsistent by sub-proof
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #436.
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4739) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (4701), (4734), (4739) are inconsistent
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #579.
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4740) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4740) gives:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4741) all_57_14 = e1 & op(e0, e1) = e1
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4741) implies:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4742) all_57_14 = e1
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4701), (4742) are inconsistent by sub-proof
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #560.
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4743) all_57_15 = e1 & op(e0, e0) = e1
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4743) implies:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4744) all_57_15 = e1
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4730), (4744) imply:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4745) e3 = e1
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4745) implies:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4746) e3 = e1
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (4746) imply:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4747) $false
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4747) is inconsistent.
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4748) all_57_13 = e3 & op(e0, e2) = e3
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (4620), (4748), (function-axioms) are
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #556.
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4749) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4749) gives:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4750) all_57_14 = e3 & op(e0, e1) = e3
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4750) implies:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4751) all_57_14 = e3
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4701), (4751) imply:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4752) e3 = e2
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4630), (4752) imply:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4753) all_57_3 = e2
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (227), (228),
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230), (4619), (4657), (4753), (function-axioms)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #463.
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4754) all_57_15 = e3 & op(e0, e0) = e3
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4754) implies:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4755) op(e0, e0) = e3
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4678), (4755), (function-axioms) are
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #715.
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4756) all_57_5 = e3 & op(e2, e1) = e3
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (4621), (4756), (function-axioms) are
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547.
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4757) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4757) gives:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4758) all_57_8 = e3 & op(e1, e1) = e3
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4758) implies:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4759) op(e1, e1) = e3
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (4662), (4759), (function-axioms) are
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #771.
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4760) all_57_14 = e3 & op(e0, e1) = e3
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4760) implies:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4761) all_57_14 = e3
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4701), (4761) imply:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4762) e3 = e2
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4762) implies:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4763) e3 = e2
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4630), (4763) imply:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4764) all_57_3 = e2
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (227), (228),
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230), (4619), (4657), (4764), (function-axioms)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #463.
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | (4765) all_57_10 = e0 & op(e2, e0) = e0
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4765) implies:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | (4766) op(e2, e0) = e0
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | (4767) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (168), (4653), (4766), (4767),
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | #200.
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | (4768) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4768) gives:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (4769) all_57_11 = e2 & op(e1, e0) = e2
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4769) implies:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (4770) all_57_11 = e2
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (4771) op(e1, e0) = e2
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4772) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4772) gives:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4773) all_57_9 = e1 & op(e3, e0) = e1
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4773) implies:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4774) all_57_9 = e1
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4775) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4775) gives:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4776) all_57_9 = e3 & op(e3, e0) = e3
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4774), (4776) are inconsistent by sub-proof
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #345.
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4777) all_57_10 = e3 & op(e2, e0) = e3
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (4622), (4777), (function-axioms) are
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749.
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4778) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4778) gives:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4779) all_57_11 = e3 & op(e1, e0) = e3
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4779) implies:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4780) all_57_11 = e3
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (227), (228),
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230), (4619), (4630), (4657), (4770), (4780),
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #201.
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4781) all_57_15 = e3 & op(e0, e0) = e3
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4781) implies:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4782) op(e0, e0) = e3
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4678), (4782), (function-axioms) are
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #715.
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4783) all_57_10 = e1 & op(e2, e0) = e1
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4783) implies:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4784) op(e2, e0) = e1
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4766), (4784), (function-axioms) are
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #695.
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4785) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4785) gives:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4786) all_57_11 = e1 & op(e1, e0) = e1
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4786) implies:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4787) op(e1, e0) = e1
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4771), (4787), (function-axioms) are
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #720.
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4788) all_57_15 = e1 & op(e0, e0) = e1
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4788) implies:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4789) op(e0, e0) = e1
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4678), (4789), (function-axioms) are
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #220.
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (4790) all_57_15 = e2 & op(e0, e0) = e2
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4790) implies:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (4791) op(e0, e0) = e2
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4678), (4791), (function-axioms) are
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #714.
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | (4792) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4792) gives:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | (4793) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (4631), (4662), (4793),
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | #324.
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | (4794) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4794) gives:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | (4795) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4795) implies:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | (4796) op(e2, e2) = e0
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4631), (4796), (function-axioms) are
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641.
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | (4797) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (39), (372), (4678), (4797),
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | #709.
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | Case 2:
% 133.26/19.10 | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | (4798) all_34_2 = e3
% 133.26/19.10 | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (4798) imply:
% 133.26/19.10 | | | | | | | | | | | | | | | | (4799) all_4_2 = e3
% 133.26/19.10 | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | SIMP: (4799) implies:
% 133.26/19.10 | | | | | | | | | | | | | | | | (4800) all_4_2 = e3
% 133.26/19.10 | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | REDUCE: (368), (4800) imply:
% 133.26/19.10 | | | | | | | | | | | | | | | | (4801) ~ (all_52_12 = e3)
% 133.26/19.10 | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | REDUCE: (370), (4800) imply:
% 133.26/19.10 | | | | | | | | | | | | | | | | (4802) ~ (all_52_14 = e3)
% 133.26/19.10 | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 133.26/19.10 | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.10 | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | (4803) all_54_3 = e3
% 133.26/19.10 | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (4803) imply:
% 133.26/19.10 | | | | | | | | | | | | | | | | | (4804) all_52_12 = e3
% 133.26/19.10 | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | REDUCE: (4801), (4804) imply:
% 133.26/19.10 | | | | | | | | | | | | | | | | | (4805) $false
% 133.26/19.10 | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | CLOSE: (4805) is inconsistent.
% 133.26/19.10 | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.10 | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | (4806) ~ (all_54_3 = e3)
% 133.26/19.10 | | | | | | | | | | | | | | | | | (4807) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 133.26/19.10 | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 133.26/19.10 | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.10 | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | (4808) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 133.26/19.10 | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 133.26/19.10 | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | BETA: splitting (4808) gives:
% 133.26/19.10 | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | (4809) all_57_6 = e3 & op(e1, e3) = e3
% 133.26/19.10 | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | ALPHA: (4809) implies:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | (4810) all_57_6 = e3
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | (4811) op(e1, e3) = e3
% 133.26/19.10 | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | (4812) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4812) gives:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | (4813) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4813) gives:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | (4814) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4814) implies:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | (4815) op(e3, e3) = e2
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4071), (4815), (function-axioms) are
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495.
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | (4816) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4816) implies:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | (4817) op(e3, e1) = e3
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | (4818) op(e3, e3) = e1
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (168), (169), (170), (232), (4068),
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | (4070), (4817), (4818), (function-axioms) are
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #599.
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | (4819) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (4658), (4801), (4819), (function-axioms)
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #198.
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.10 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | (4820) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4820) gives:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | (4821) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4821) gives:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | (4822) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4822) implies:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | (4823) op(e1, e1) = e3
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (4662), (4823), (function-axioms) are
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #771.
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | (4824) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2,
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4824) implies:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | (4825) ~ (all_56_5 = e3)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | (4826) op(e1, e3) = all_56_5
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4811), (4825), (4826), (function-axioms) are
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #724.
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | (4827) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4827) gives:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | (4828) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4828) implies:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | (4829) op(e2, e2) = e0
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4631), (4829), (function-axioms) are
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641.
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | (4830) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4830) gives:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | (4831) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4831) implies:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | (4832) op(e1, e1) = e2
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (4832), (function-axioms) are
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | (4833) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4833) implies:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | (4834) op(e0, e0) = all_56_31
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | (4835) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4807) gives:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | (4836) all_54_3 = e2
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (4836) imply:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | (4837) all_52_12 = e2
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4653), (4837) imply:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | (4838) $false
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4838) is inconsistent.
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | (4839) all_54_3 = e1 | all_54_3 = e0
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | (4840) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4840) gives:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (4841) all_57_6 = e2 & op(e1, e3) = e2
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4841) implies:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (4842) all_57_6 = e2
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4810), (4842) imply:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (4843) e3 = e2
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4630), (4843) imply:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (4844) all_57_3 = e2
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (227), (228),
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (230), (4619), (4657), (4844), (function-axioms)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #463.
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (4845) all_57_7 = e2 & op(e1, e2) = e2
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (4651), (4845), (function-axioms) are
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #515.
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | (4846) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4846) gives:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (4847) all_57_8 = e2 & op(e1, e1) = e2
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4847) implies:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (4848) op(e1, e1) = e2
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (4848), (function-axioms) are
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (4849) all_57_11 = e2 & op(e1, e0) = e2
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4849) implies:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (4850) all_57_11 = e2
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (4851) op(e1, e0) = e2
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4852) all_57_15 = e0 & op(e0, e0) = e0
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4852) implies:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4853) op(e0, e0) = e0
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (4834), (4835), (4853),
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | #710.
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4854) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4854) implies:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4855) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4855) gives:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4856) all_57_9 = e0 & op(e3, e0) = e0
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4856) implies:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4857) op(e3, e0) = e0
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (208), (212),
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (214), (4622), (4811), (4834), (4835), (4850),
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4851), (4857), (function-axioms) are inconsistent
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #632.
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4858) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4858) gives:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4859) all_57_10 = e0 & op(e2, e0) = e0
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4859) implies:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4860) op(e2, e0) = e0
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4839) gives:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4861) all_54_3 = e1
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (4861) imply:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4862) all_52_12 = e1
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (4862) imply:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4863) ~ (all_52_14 = e1)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4863) implies:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4864) ~ (all_52_14 = e1)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e3,
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (163), (4811) gives:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4865) all_52_2 = e3
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e0, e2, simplifying with (164), (4860) gives:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4866) all_52_13 = e0
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4835) gives:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4867) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27))
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4867) gives:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4868) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4868) implies:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4869) ~ (all_56_9 = e2)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4870) op(e3, e2) = all_56_9
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4658), (4869), (4870), (function-axioms) are
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #199.
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4871) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4871) implies:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4872) ~ (all_56_27 = e0)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4873) op(e2, e0) = all_56_27
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4860), (4872), (4873), (function-axioms) are
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #275.
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4874) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4874) gives:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4875) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4875) implies:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4876) op(e1, e0) = e1
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (4864), (4876), (function-axioms) are
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #327.
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4877) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4877) implies:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4878) ~ (all_56_5 = e3)
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4879) op(e1, e3) = all_56_5
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4811), (4878), (4879), (function-axioms) are
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #724.
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4880) all_54_3 = e0
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (4880) imply:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4881) all_52_12 = e0
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4070), (4881) imply:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4882) $false
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4882) is inconsistent.
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4883) all_57_11 = e0 & op(e1, e0) = e0
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4883) implies:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4884) all_57_11 = e0
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4850), (4884) are inconsistent by sub-proof
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #638.
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.11 | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | (4885) all_57_7 = e3 & op(e1, e2) = e3
% 133.26/19.11 | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | ALPHA: (4885) implies:
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | (4886) op(e1, e2) = e3
% 133.26/19.11 | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (4619), (4886), (function-axioms) are
% 133.26/19.11 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #654.
% 133.26/19.11 | | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.11 | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.11 | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | (4887) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 133.26/19.11 | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 133.26/19.11 | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (160), (4662), (4802), (4887),
% 133.26/19.11 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.26/19.11 | | | | | | | | | | | | | | | | | | #653.
% 133.26/19.11 | | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | | End of split
% 133.26/19.11 | | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | | End of split
% 133.26/19.11 | | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | End of split
% 133.26/19.11 | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | Case 2:
% 133.26/19.11 | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | (4888) all_28_2 = e3
% 133.26/19.11 | | | | | | | | | | | | | | | (4889) ( ~ (all_28_0 = e2) & op(e3, e1) = all_28_0 &
% 133.26/19.11 | | | | | | | | | | | | | | | $i(all_28_0)) | ( ~ (all_28_1 = e0) & op(e3, e3)
% 133.26/19.11 | | | | | | | | | | | | | | | = all_28_1 & $i(all_28_1))
% 133.26/19.11 | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | COMBINE_EQS: (316), (4888) imply:
% 133.26/19.11 | | | | | | | | | | | | | | | (4890) all_6_2 = e3
% 133.26/19.11 | | | | | | | | | | | | | | |
% 133.26/19.11 | | | | | | | | | | | | | | | SIMP: (4890) implies:
% 133.26/19.12 | | | | | | | | | | | | | | | (4891) all_6_2 = e3
% 133.26/19.12 | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | REDUCE: (348), (4891) imply:
% 133.26/19.12 | | | | | | | | | | | | | | | (4892) ~ (all_52_2 = e3)
% 133.26/19.12 | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | REDUCE: (361), (4891) imply:
% 133.26/19.12 | | | | | | | | | | | | | | | (4893) ~ (all_52_8 = e3)
% 133.26/19.12 | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | REDUCE: (364), (4891) imply:
% 133.26/19.12 | | | | | | | | | | | | | | | (4894) ~ (all_52_11 = e3)
% 133.26/19.12 | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | REDUCE: (366), (4891) imply:
% 133.26/19.12 | | | | | | | | | | | | | | | (4895) ~ (all_52_14 = e3)
% 133.26/19.12 | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | REDUCE: (39), (4891) imply:
% 133.26/19.12 | | | | | | | | | | | | | | | (4896) op(e1, e1) = e3
% 133.26/19.12 | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 133.26/19.12 | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | Case 1:
% 133.26/19.12 | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | (4897) all_54_2 = e3
% 133.26/19.12 | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (4897) imply:
% 133.26/19.12 | | | | | | | | | | | | | | | | (4898) all_52_8 = e3
% 133.26/19.12 | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | REDUCE: (4893), (4898) imply:
% 133.26/19.12 | | | | | | | | | | | | | | | | (4899) $false
% 133.26/19.12 | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | CLOSE: (4899) is inconsistent.
% 133.26/19.12 | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | Case 2:
% 133.26/19.12 | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | (4900) ~ (all_54_2 = e3)
% 133.26/19.12 | | | | | | | | | | | | | | | | (4901) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 133.26/19.12 | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | BETA: splitting (4889) gives:
% 133.26/19.12 | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.12 | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | (4902) ~ (all_28_0 = e2) & op(e3, e1) = all_28_0 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | $i(all_28_0)
% 133.26/19.12 | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | ALPHA: (4902) implies:
% 133.26/19.12 | | | | | | | | | | | | | | | | | (4903) ~ (all_28_0 = e2)
% 133.26/19.12 | | | | | | | | | | | | | | | | | (4904) op(e3, e1) = all_28_0
% 133.26/19.12 | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | BETA: splitting (4901) gives:
% 133.26/19.12 | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.12 | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | (4905) all_54_2 = e2
% 133.26/19.12 | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (4905) imply:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | (4906) all_52_8 = e2
% 133.26/19.12 | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | REDUCE: (4652), (4906) imply:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | (4907) $false
% 133.26/19.12 | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | CLOSE: (4907) is inconsistent.
% 133.26/19.12 | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.12 | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | (4908) ~ (all_54_2 = e2)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | (4909) all_54_2 = e1 | all_54_2 = e0
% 133.26/19.12 | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | BETA: splitting (4909) gives:
% 133.26/19.12 | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | (4910) all_54_2 = e1
% 133.26/19.12 | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (4910) imply:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | (4911) all_52_8 = e1
% 133.26/19.12 | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | REDUCE: (121), (4911) imply:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | (4912) ~ (all_52_11 = e1)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | SIMP: (4912) implies:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | (4913) ~ (all_52_11 = e1)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | REDUCE: (120), (4911) imply:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | (4914) ~ (all_52_12 = e1)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | SIMP: (4914) implies:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | (4915) ~ (all_52_12 = e1)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | REDUCE: (4893), (4911) imply:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | (4916) ~ (e3 = e1)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | REDUCE: (4652), (4911) imply:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | (4917) ~ (e2 = e1)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | REDUCE: (169), (4911) imply:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | (4918) op(e3, e1) = e1
% 133.26/19.12 | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | (4919) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4919) gives:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | (4920) all_57_4 = e1 & op(e3, e1) = e1
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4920) implies:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | (4921) all_57_4 = e1
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | (4922) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (167), (4071), (4617), (4922),
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | #210.
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | (4923) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4923) gives:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | (4924) all_57_6 = e3 & op(e1, e3) = e3
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (4892), (4924), (function-axioms) are
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #761.
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | (4925) all_57_12 = e3 & op(e0, e3) = e3
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4925) implies:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | (4926) all_57_12 = e3
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | (4927) op(e0, e3) = e3
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | (4928) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4928) gives:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | (4929) all_57_12 = e2 & op(e0, e3) = e2
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4929) implies:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | (4930) all_57_12 = e2
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4926), (4930) imply:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | (4931) e3 = e2
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4630), (4931) imply:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | (4932) all_57_3 = e2
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (227), (228),
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | (230), (4619), (4657), (4932), (function-axioms)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #463.
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | (4933) all_57_13 = e2 & op(e0, e2) = e2
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4933) implies:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | (4934) all_57_13 = e2
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (227), (228), (4630),
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | (4657), (4934) are inconsistent by sub-proof #301.
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | (4935) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4935) gives:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | (4936) all_57_14 = e2 & op(e0, e1) = e2
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4936) implies:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | (4937) all_57_14 = e2
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (4938) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (170), (4071), (4618), (4938),
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | #197.
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (4939) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4939) gives:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4940) all_57_4 = e3 & op(e3, e1) = e3
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4940) implies:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4941) op(e3, e1) = e3
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (120), (169), (201), (269), (4070), (4653),
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4915), (4941), (function-axioms) are inconsistent
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #319.
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4942) all_57_9 = e3 & op(e3, e0) = e3
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4942) implies:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4943) all_57_9 = e3
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4944) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4944) gives:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4945) all_57_12 = e1 & op(e0, e3) = e1
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4926), (4945) are inconsistent by sub-proof
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #490.
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4946) all_57_13 = e1 & op(e0, e2) = e1
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4946) implies:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4947) all_57_13 = e1
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4948) all_57_15 = e0 & op(e0, e0) = e0
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4948) implies:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4949) op(e0, e0) = e0
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4950) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4950) gives:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4951) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4951) gives:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4952) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4952) implies:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4953) op(e3, e3) = e2
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (234),
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (4618), (4657), (4943), (4953),
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #237.
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4954) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4954) implies:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4955) op(e3, e3) = e1
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (236),
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (4068), (4921), (4955), (function-axioms)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #667.
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4956) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4956) gives:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4957) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3,
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4957) implies:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4958) ~ (all_56_7 = e3)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4959) op(e0, e3) = all_56_7
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4927), (4958), (4959), (function-axioms) are
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #209.
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4960) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2,
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4960) implies:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4961) ~ (all_56_17 = e1)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4962) op(e3, e1) = all_56_17
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4918), (4961), (4962), (function-axioms) are
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #349.
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4963) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4963) gives:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4964) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4964) gives:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4965) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4965) implies:
% 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4966) ~ (all_56_17 = e1)
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4967) op(e3, e1) = all_56_17
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4918), (4966), (4967), (function-axioms) are
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #349.
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4968) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 =
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2,
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4968) implies:
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4969) op(e2, e2) = e1
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4631), (4969), (function-axioms) are
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #325.
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4970) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4970) gives:
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4971) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4971) implies:
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4972) op(e2, e2) = e0
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4631), (4972), (function-axioms) are
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641.
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4973) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4973) gives:
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4974) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4974) implies:
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4975) op(e1, e1) = e2
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (4975), (function-axioms) are
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4976) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4976) implies:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4977) op(e0, e0) = all_56_31
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4978) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (210), (227), (228),
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4630), (4657), (4896), (4926), (4949), (4977),
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4978), (function-axioms) are inconsistent by
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #300.
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4979) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4979) implies:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4980) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (4926), (4937), (4947), (4980) are
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #285.
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4981) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4981) gives:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4982) all_57_14 = e1 & op(e0, e1) = e1
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4982) implies:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4983) all_57_14 = e1
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (39), (219), (221), (372),
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4896), (4903), (4904), (4918), (4983),
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #212.
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4984) all_57_15 = e1 & op(e0, e0) = e1
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4984) implies:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4985) op(e0, e0) = e1
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (371), (4985), (function-axioms) are
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #354.
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | (4986) all_57_15 = e2 & op(e0, e0) = e2
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4986) implies:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | (4987) op(e0, e0) = e2
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (4988) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4988) gives:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4989) all_57_0 = e3 & op(e3, e3) = e3
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4989) implies:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4990) op(e3, e3) = e3
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4071), (4990), (function-axioms) are
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #773.
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4991) all_57_1 = e3 & op(e3, e2) = e3
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4991) implies:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4992) all_57_1 = e3
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (168), (208),
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (211), (236), (4071), (4653), (4894),
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4903), (4904), (4926), (4987), (4992),
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | #206.
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (4993) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4993) gives:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4994) all_57_4 = e3 & op(e3, e1) = e3
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4994) implies:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4995) op(e3, e1) = e3
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (120), (169), (201), (269), (4070), (4653),
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4915), (4995), (function-axioms) are inconsistent
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #319.
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4996) all_57_9 = e3 & op(e3, e0) = e3
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4996) implies:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4997) all_57_9 = e3
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4998) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4998) gives:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4999) all_57_12 = e1 & op(e0, e3) = e1
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4999) implies:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5000) all_57_12 = e1
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4926), (5000) imply:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5001) e3 = e1
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4997), (5001) imply:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5002) all_57_9 = e1
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (160), (164), (214), (4622), (4895),
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4987), (5002), (function-axioms) are inconsistent
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #329.
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5003) all_57_13 = e1 & op(e0, e2) = e1
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5003) implies:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5004) all_57_13 = e1
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5005) all_57_15 = e0 & op(e0, e0) = e0
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5005) implies:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5006) op(e0, e0) = e0
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4987), (5006), (function-axioms) are
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #714.
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5007) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5007) implies:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5008) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5008) gives:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5009) all_57_12 = e0 & op(e0, e3) = e0
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5009) implies:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5010) op(e0, e3) = e0
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (4067), (5010), (function-axioms) are
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #219.
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5011) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5011) gives:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5012) all_57_13 = e0 & op(e0, e2) = e0
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5012) implies:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5013) all_57_13 = e0
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5004), (5013) are inconsistent by sub-proof
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #681.
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5014) all_57_14 = e0 & op(e0, e1) = e0
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5014) implies:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5015) op(e0, e1) = e0
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5016) all_54_3 = e3
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (5016) imply:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5017) all_52_12 = e3
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (5017) imply:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5018) ~ (all_4_2 = e3)
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5018) implies:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5019) ~ (all_4_2 = e3)
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5020) all_54_15 = e3
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (5019), (5020) are inconsistent by
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #601.
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5021) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (190), (245), (246), (367), (371), (4660),
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4894), (4913), (5015), (5021), (function-axioms)
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #232.
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5022) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (4070), (4653), (4915), (5022) are
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #320.
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5023) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5023) gives:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5024) all_57_14 = e1 & op(e0, e1) = e1
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5024) implies:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5025) all_57_14 = e1
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (39), (219), (221), (372),
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4896), (4903), (4904), (4918), (5025),
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #212.
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5026) all_57_15 = e1 & op(e0, e0) = e1
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5026) implies:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5027) op(e0, e0) = e1
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4987), (5027), (function-axioms) are
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #636.
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | (5028) all_57_5 = e1 & op(e2, e1) = e1
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5028) implies:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | (5029) all_57_5 = e1
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (39), (219), (221), (372),
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | (4896), (4903), (4904), (4918), (5029),
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | #214.
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | (5030) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | BETA: splitting (5030) gives:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | (5031) all_57_8 = e1 & op(e1, e1) = e1
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5031) implies:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | (5032) op(e1, e1) = e1
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (4896), (5032), (function-axioms) are
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #662.
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | (5033) all_57_14 = e1 & op(e0, e1) = e1
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5033) implies:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | (5034) all_57_14 = e1
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (39), (219), (221), (372),
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | (4896), (4903), (4904), (4918), (5034),
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | #212.
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.13 | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | (5035) all_54_2 = e0
% 133.56/19.13 | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (5035) imply:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | (5036) all_52_8 = e0
% 133.56/19.13 | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | REDUCE: (4069), (5036) imply:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | (5037) $false
% 133.56/19.13 | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | CLOSE: (5037) is inconsistent.
% 133.56/19.13 | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.13 | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | End of split
% 133.56/19.13 | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.13 | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | (5038) ~ (all_28_1 = e0) & op(e3, e3) = all_28_1 &
% 133.56/19.13 | | | | | | | | | | | | | | | | | $i(all_28_1)
% 133.56/19.13 | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | REF_CLOSE: (4071), (5038), (function-axioms) are inconsistent
% 133.56/19.13 | | | | | | | | | | | | | | | | | by sub-proof #211.
% 133.56/19.13 | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | End of split
% 133.56/19.13 | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | End of split
% 133.56/19.13 | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | End of split
% 133.56/19.13 | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | Case 2:
% 133.56/19.13 | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | (5039) all_20_2 = e2
% 133.56/19.13 | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | COMBINE_EQS: (318), (5039) imply:
% 133.56/19.13 | | | | | | | | | | | | | | (5040) all_4_2 = e2
% 133.56/19.13 | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | SIMP: (5040) implies:
% 133.56/19.13 | | | | | | | | | | | | | | (5041) all_4_2 = e2
% 133.56/19.13 | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | COMBINE_EQS: (331), (5041) imply:
% 133.56/19.13 | | | | | | | | | | | | | | (5042) all_26_2 = e2
% 133.56/19.13 | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | REDUCE: (369), (5041) imply:
% 133.56/19.13 | | | | | | | | | | | | | | (5043) ~ (all_52_13 = e2)
% 133.56/19.13 | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | REDUCE: (36), (5041) imply:
% 133.56/19.13 | | | | | | | | | | | | | | (5044) op(e0, e0) = e2
% 133.56/19.13 | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 133.56/19.13 | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | Case 1:
% 133.56/19.13 | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | (5045) ~ (all_24_2 = e0)
% 133.56/19.13 | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | REDUCE: (4065), (5045) imply:
% 133.56/19.13 | | | | | | | | | | | | | | | (5046) $false
% 133.56/19.13 | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | CLOSE: (5046) is inconsistent.
% 133.56/19.13 | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | Case 2:
% 133.56/19.13 | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | (5047) ( ~ (all_24_0 = e1) & op(e0, e3) = all_24_0 &
% 133.56/19.13 | | | | | | | | | | | | | | | $i(all_24_0)) | ( ~ (all_24_1 = e2) & op(e0, e0)
% 133.56/19.13 | | | | | | | | | | | | | | | = all_24_1 & $i(all_24_1))
% 133.56/19.13 | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 133.56/19.13 | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | Case 1:
% 133.56/19.13 | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | (5048) ~ (all_26_2 = e2)
% 133.56/19.13 | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | REDUCE: (5042), (5048) imply:
% 133.56/19.13 | | | | | | | | | | | | | | | | (5049) $false
% 133.56/19.13 | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | CLOSE: (5049) is inconsistent.
% 133.56/19.13 | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | Case 2:
% 133.56/19.13 | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | (5050) ( ~ (all_26_0 = e1) & op(e2, e0) = all_26_0 &
% 133.56/19.13 | | | | | | | | | | | | | | | | $i(all_26_0)) | ( ~ (all_26_1 = e3) & op(e2, e2)
% 133.56/19.13 | | | | | | | | | | | | | | | | = all_26_1 & $i(all_26_1))
% 133.56/19.13 | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | BETA: splitting (5047) gives:
% 133.56/19.13 | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.13 | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | (5051) ~ (all_24_0 = e1) & op(e0, e3) = all_24_0 &
% 133.56/19.13 | | | | | | | | | | | | | | | | | $i(all_24_0)
% 133.56/19.13 | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | ALPHA: (5051) implies:
% 133.56/19.13 | | | | | | | | | | | | | | | | | (5052) ~ (all_24_0 = e1)
% 133.56/19.13 | | | | | | | | | | | | | | | | | (5053) op(e0, e3) = all_24_0
% 133.56/19.13 | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | BETA: splitting (5050) gives:
% 133.56/19.13 | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.13 | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | (5054) ~ (all_26_0 = e1) & op(e2, e0) = all_26_0 &
% 133.56/19.13 | | | | | | | | | | | | | | | | | | $i(all_26_0)
% 133.56/19.13 | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | ALPHA: (5054) implies:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | (5055) ~ (all_26_0 = e1)
% 133.56/19.13 | | | | | | | | | | | | | | | | | | (5056) op(e2, e0) = all_26_0
% 133.56/19.13 | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 133.56/19.13 | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | (5057) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 133.56/19.13 | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | BETA: splitting (5057) gives:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | (5058) all_57_6 = e2 & op(e1, e3) = e2
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | ALPHA: (5058) implies:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | (5059) all_57_6 = e2
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | (5060) op(e1, e3) = e2
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | (5061) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5061) gives:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | (5062) all_57_4 = e2 & op(e3, e1) = e2
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (4652), (5062), (function-axioms) are
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #442.
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | (5063) all_57_5 = e2 & op(e2, e1) = e2
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5063) implies:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | (5064) all_57_5 = e2
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | (5065) op(e2, e1) = e2
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | (5066) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (167), (4066), (4631), (5066),
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | #203.
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | (5067) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5067) gives:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | (5068) all_57_5 = e0 & op(e2, e1) = e0
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5064), (5068) are inconsistent by sub-proof
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | #277.
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | (5069) all_57_10 = e0 & op(e2, e0) = e0
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5069) implies:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | (5070) all_57_10 = e0
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | (5071) op(e2, e0) = e0
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | (5072) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5072) gives:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (5073) all_57_0 = e3 & op(e3, e3) = e3
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5073) implies:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (5074) op(e3, e3) = e3
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4071), (5074), (function-axioms) are
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #773.
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (5075) all_57_2 = e3 & op(e2, e3) = e3
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5075) implies:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (5076) all_57_2 = e3
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (224), (4630), (5064), (5070),
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (5076) are inconsistent by sub-proof #369.
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | (5077) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5077) gives:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (5078) all_57_6 = e3 & op(e1, e3) = e3
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5078) implies:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (5079) all_57_6 = e3
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5059), (5079) imply:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (5080) e3 = e2
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5080) implies:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (5081) e3 = e2
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4630), (5081) imply:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (5082) all_57_3 = e2
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (227), (228),
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (230), (4619), (4657), (5082), (function-axioms)
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #463.
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (5083) all_57_12 = e3 & op(e0, e3) = e3
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5083) implies:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (5084) all_57_12 = e3
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (5085) op(e0, e3) = e3
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5086) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5086) gives:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5087) all_57_2 = e1 & op(e2, e3) = e1
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5087) implies:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5088) all_57_2 = e1
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5089) op(e2, e3) = e1
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e3,
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (159), (5085) gives:
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5090) all_52_3 = e3
% 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_24_0, e3, e0, simplifying with (159), (5053)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5091) all_52_3 = all_24_0
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e2,
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (163), (5060) gives:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5092) all_52_2 = e2
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e0, e2, simplifying with (164), (5071) gives:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5093) all_52_13 = e0
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_26_0, e0, e2, simplifying with (164), (5056)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5094) all_52_13 = all_26_0
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2,
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (165), (5065) gives:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5095) all_52_9 = e2
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e1,
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e2, simplifying with (167), (5089) gives:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5096) all_52_1 = e1
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5090), (5091) imply:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5097) all_24_0 = e3
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5097) implies:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5098) all_24_0 = e3
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5093), (5094) imply:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5099) all_26_0 = e0
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (5095), (5096) imply:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5100) ~ (e2 = e1)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (5095) imply:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5101) ~ (all_52_11 = e2)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5101) implies:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5102) ~ (all_52_11 = e2)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (5095) imply:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5103) ~ (all_6_2 = e2)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4622), (5093) imply:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5104) ~ (e3 = e0)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5043), (5093) imply:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5105) ~ (e2 = e0)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5055), (5099) imply:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5106) ~ (e1 = e0)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5107) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5107) gives:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5108) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5108) gives:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5109) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5109) implies:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5110) op(e3, e3) = e2
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (231), (5059), (5084), (5088),
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5110), (function-axioms) are inconsistent by
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #392.
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5111) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (231), (235), (5084),
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5088), (5089), (5111), (function-axioms) are
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #195.
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5112) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4658), (5085), (5112), (function-axioms) are
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #194.
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5113) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5113) gives:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5114) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5114) gives:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5115) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5115) implies:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5116) op(e1, e3) = e1
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (5060), (5116), (function-axioms) are
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #517.
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5117) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2,
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5117) implies:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5118) op(e2, e2) = e1
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4631), (5118), (function-axioms) are
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #325.
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5119) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (39), (91), (157), (190), (246),
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332), (364), (372), (4631), (5044), (5071),
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5102), (5119), (function-axioms) are inconsistent
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #265.
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5120) all_57_3 = e1 & op(e2, e2) = e1
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5120) implies:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5121) op(e2, e2) = e1
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4631), (5121), (function-axioms) are
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #325.
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5122) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5122) gives:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5123) all_57_5 = e1 & op(e2, e1) = e1
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5064), (5123) are inconsistent by sub-proof
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #500.
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5124) all_57_10 = e1 & op(e2, e0) = e1
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5124) implies:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5125) op(e2, e0) = e1
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5055), (5056), (5125), (function-axioms) are
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #336.
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | (5126) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (158), (208),
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | (209), (211), (372), (4620), (5044), (5126),
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | #262.
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | (5127) all_57_7 = e2 & op(e1, e2) = e2
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (4651), (5127), (function-axioms) are
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #515.
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.14 | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | (5128) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (164), (208),
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | (212), (214), (372), (4622), (5044), (5128),
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.56/19.14 | | | | | | | | | | | | | | | | | | | #268.
% 133.56/19.14 | | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.14 | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.14 | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | (5129) ~ (all_26_1 = e3) & op(e2, e2) = all_26_1 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | | $i(all_26_1)
% 133.56/19.14 | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | ALPHA: (5129) implies:
% 133.56/19.14 | | | | | | | | | | | | | | | | | | (5130) ~ (all_26_1 = e3)
% 133.56/19.14 | | | | | | | | | | | | | | | | | | (5131) op(e2, e2) = all_26_1
% 133.56/19.14 | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4631), (5130), (5131), (function-axioms) are
% 133.56/19.14 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #334.
% 133.56/19.14 | | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | End of split
% 133.56/19.14 | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.14 | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | (5132) ~ (all_24_1 = e2) & op(e0, e0) = all_24_1 &
% 133.56/19.14 | | | | | | | | | | | | | | | | | $i(all_24_1)
% 133.56/19.14 | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | | REF_CLOSE: (5044), (5132), (function-axioms) are inconsistent
% 133.56/19.14 | | | | | | | | | | | | | | | | | by sub-proof #204.
% 133.56/19.14 | | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | End of split
% 133.56/19.14 | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | End of split
% 133.56/19.14 | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | End of split
% 133.56/19.14 | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | End of split
% 133.56/19.14 | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | Case 2:
% 133.56/19.14 | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | (5133) all_57_3 = e2 & op(e2, e2) = e2
% 133.56/19.14 | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | REF_CLOSE: (9), (4630), (5133) are inconsistent by sub-proof
% 133.56/19.14 | | | | | | | | | | | | | #375.
% 133.56/19.14 | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | End of split
% 133.56/19.14 | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | Case 2:
% 133.56/19.14 | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | (5134) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 133.56/19.14 | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 133.56/19.14 | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | BETA: splitting (5134) gives:
% 133.56/19.14 | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | Case 1:
% 133.56/19.14 | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | (5135) all_57_7 = e2 & op(e1, e2) = e2
% 133.56/19.14 | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | REF_CLOSE: (162), (4651), (5135), (function-axioms) are
% 133.56/19.14 | | | | | | | | | | | | | inconsistent by sub-proof #515.
% 133.56/19.14 | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | Case 2:
% 133.56/19.14 | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | (5136) all_57_13 = e2 & op(e0, e2) = e2
% 133.56/19.14 | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (168), (169), (227),
% 133.56/19.14 | | | | | | | | | | | | | (228), (236), (4071), (4630), (4652), (4653),
% 133.56/19.14 | | | | | | | | | | | | | (5136), (function-axioms) are inconsistent by
% 133.56/19.14 | | | | | | | | | | | | | sub-proof #193.
% 133.56/19.14 | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | End of split
% 133.56/19.14 | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | End of split
% 133.56/19.14 | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | Case 2:
% 133.56/19.14 | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | (5137) all_54_1 = e1 | all_54_1 = e0
% 133.56/19.14 | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | REF_CLOSE: (4624), (4633), (4641), (5137) are inconsistent by
% 133.56/19.14 | | | | | | | | | | | sub-proof #192.
% 133.56/19.14 | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | End of split
% 133.56/19.14 | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | End of split
% 133.56/19.14 | | | | | | | | |
% 133.56/19.14 | | | | | | | | End of split
% 133.56/19.14 | | | | | | | |
% 133.56/19.14 | | | | | | | Case 2:
% 133.56/19.14 | | | | | | | |
% 133.56/19.14 | | | | | | | | (5138) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 &
% 133.56/19.14 | | | | | | | | op(e0, e2) = e3)
% 133.56/19.14 | | | | | | | |
% 133.56/19.14 | | | | | | | | REF_CLOSE: (158), (162), (4619), (4620), (5138),
% 133.56/19.14 | | | | | | | | (function-axioms) are inconsistent by sub-proof #555.
% 133.56/19.14 | | | | | | | |
% 133.56/19.14 | | | | | | | End of split
% 133.56/19.14 | | | | | | |
% 133.56/19.14 | | | | | | Case 2:
% 133.56/19.14 | | | | | | |
% 133.56/19.14 | | | | | | | (5139) ~ (all_14_1 = e0) & op(e3, e3) = all_14_1 &
% 133.56/19.14 | | | | | | | $i(all_14_1)
% 133.56/19.14 | | | | | | |
% 133.56/19.14 | | | | | | | REF_CLOSE: (4071), (5139), (function-axioms) are inconsistent by
% 133.56/19.14 | | | | | | | sub-proof #191.
% 133.56/19.14 | | | | | | |
% 133.56/19.14 | | | | | | End of split
% 133.56/19.14 | | | | | |
% 133.56/19.14 | | | | | End of split
% 133.56/19.14 | | | | |
% 133.56/19.14 | | | | End of split
% 133.56/19.14 | | | |
% 133.56/19.14 | | | Case 2:
% 133.56/19.14 | | | |
% 133.56/19.14 | | | | (5140) all_8_2 = e1
% 133.56/19.14 | | | | (5141) ( ~ (all_8_0 = e0) & op(e1, e2) = all_8_0 & $i(all_8_0)) | ( ~
% 133.56/19.14 | | | | (all_8_1 = e3) & op(e1, e1) = all_8_1 & $i(all_8_1))
% 133.56/19.14 | | | |
% 133.56/19.14 | | | | COMBINE_EQS: (291), (5140) imply:
% 133.56/19.14 | | | | (5142) all_48_2 = e1
% 133.56/19.14 | | | |
% 133.56/19.14 | | | | REDUCE: (347), (5140) imply:
% 133.56/19.14 | | | | (5143) ~ (all_52_1 = e1)
% 133.56/19.14 | | | |
% 133.56/19.14 | | | | REDUCE: (350), (5140) imply:
% 133.56/19.14 | | | | (5144) ~ (all_52_4 = e1)
% 133.56/19.14 | | | |
% 133.56/19.14 | | | | REDUCE: (352), (5140) imply:
% 133.56/19.14 | | | | (5145) ~ (all_52_6 = e1)
% 133.56/19.14 | | | |
% 133.56/19.14 | | | | REDUCE: (354), (5140) imply:
% 133.56/19.14 | | | | (5146) ~ (all_52_7 = e1)
% 133.56/19.14 | | | |
% 133.56/19.14 | | | | REDUCE: (356), (5140) imply:
% 133.56/19.14 | | | | (5147) ~ (all_52_9 = e1)
% 133.56/19.14 | | | |
% 133.56/19.14 | | | | REDUCE: (358), (5140) imply:
% 133.56/19.14 | | | | (5148) ~ (all_52_13 = e1)
% 133.56/19.14 | | | |
% 133.56/19.14 | | | | BETA: splitting (224) gives:
% 133.56/19.14 | | | |
% 133.56/19.14 | | | | Case 1:
% 133.56/19.14 | | | | |
% 133.56/19.14 | | | | | (5149) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2,
% 133.56/19.14 | | | | | e2) = e1)
% 133.56/19.14 | | | | |
% 133.56/19.14 | | | | | BETA: splitting (5149) gives:
% 133.56/19.14 | | | | |
% 133.56/19.14 | | | | | Case 1:
% 133.56/19.14 | | | | | |
% 133.56/19.14 | | | | | | (5150) all_57_2 = e1 & op(e2, e3) = e1
% 133.56/19.14 | | | | | |
% 133.56/19.14 | | | | | | REF_CLOSE: (167), (5143), (5150), (function-axioms) are inconsistent
% 133.56/19.14 | | | | | | by sub-proof #676.
% 133.56/19.14 | | | | | |
% 133.56/19.14 | | | | | Case 2:
% 133.56/19.14 | | | | | |
% 133.56/19.14 | | | | | | (5151) all_57_3 = e1 & op(e2, e2) = e1
% 133.56/19.14 | | | | | |
% 133.56/19.14 | | | | | | ALPHA: (5151) implies:
% 133.56/19.14 | | | | | | (5152) all_57_3 = e1
% 133.56/19.14 | | | | | | (5153) op(e2, e2) = e1
% 133.56/19.14 | | | | | |
% 133.56/19.14 | | | | | | BETA: splitting (46) gives:
% 133.56/19.14 | | | | | |
% 133.56/19.14 | | | | | | Case 1:
% 133.56/19.14 | | | | | | |
% 133.56/19.14 | | | | | | | (5154) ~ (all_10_2 = e0)
% 133.56/19.14 | | | | | | |
% 133.56/19.14 | | | | | | | BETA: splitting (55) gives:
% 133.56/19.14 | | | | | | |
% 133.56/19.14 | | | | | | | Case 1:
% 133.56/19.14 | | | | | | | |
% 133.56/19.14 | | | | | | | | (5155) ~ (all_16_2 = e2)
% 133.56/19.14 | | | | | | | |
% 133.56/19.14 | | | | | | | | REDUCE: (327), (5155) imply:
% 133.56/19.14 | | | | | | | | (5156) ~ (all_10_2 = e2)
% 133.56/19.14 | | | | | | | |
% 133.56/19.14 | | | | | | | | BETA: splitting (61) gives:
% 133.56/19.14 | | | | | | | |
% 133.56/19.14 | | | | | | | | Case 1:
% 133.56/19.14 | | | | | | | | |
% 133.56/19.14 | | | | | | | | | (5157) ~ (all_20_2 = e2)
% 133.56/19.14 | | | | | | | | |
% 133.56/19.14 | | | | | | | | | REDUCE: (318), (5157) imply:
% 133.56/19.14 | | | | | | | | | (5158) ~ (all_4_2 = e2)
% 133.56/19.14 | | | | | | | | |
% 133.56/19.14 | | | | | | | | | BETA: splitting (73) gives:
% 133.56/19.14 | | | | | | | | |
% 133.56/19.14 | | | | | | | | | Case 1:
% 133.56/19.14 | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | (5159) ~ (all_28_2 = e3)
% 133.56/19.14 | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | REDUCE: (316), (5159) imply:
% 133.56/19.14 | | | | | | | | | | (5160) ~ (all_6_2 = e3)
% 133.56/19.14 | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | BETA: splitting (79) gives:
% 133.56/19.14 | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | Case 1:
% 133.56/19.14 | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | (5161) ~ (all_32_2 = e1)
% 133.56/19.14 | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | REDUCE: (312), (5161) imply:
% 133.56/19.14 | | | | | | | | | | | (5162) ~ (all_10_2 = e1)
% 133.56/19.14 | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | BETA: splitting (204) gives:
% 133.56/19.14 | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | Case 1:
% 133.56/19.14 | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | (5163) all_54_0 = e3
% 133.56/19.14 | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | COMBINE_EQS: (278), (5163) imply:
% 133.56/19.14 | | | | | | | | | | | | (5164) all_10_2 = e3
% 133.56/19.14 | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | REDUCE: (342), (5164) imply:
% 133.56/19.14 | | | | | | | | | | | | (5165) ~ (all_52_4 = e3)
% 133.56/19.14 | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | REDUCE: (344), (5164) imply:
% 133.56/19.14 | | | | | | | | | | | | (5166) ~ (all_52_8 = e3)
% 133.56/19.14 | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | REDUCE: (346), (5164) imply:
% 133.56/19.14 | | | | | | | | | | | | (5167) ~ (all_52_12 = e3)
% 133.56/19.14 | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | REDUCE: (45), (5164) imply:
% 133.56/19.14 | | | | | | | | | | | | (5168) op(e3, e3) = e3
% 133.56/19.14 | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | BETA: splitting (82) gives:
% 133.56/19.14 | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | Case 1:
% 133.56/19.14 | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | (5169) ~ (all_34_2 = e3)
% 133.56/19.14 | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | REDUCE: (307), (5169) imply:
% 133.56/19.14 | | | | | | | | | | | | | (5170) ~ (all_4_2 = e3)
% 133.56/19.14 | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | BETA: splitting (189) gives:
% 133.56/19.14 | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | Case 1:
% 133.56/19.14 | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | (5171) all_54_15 = e3
% 133.56/19.14 | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | COMBINE_EQS: (245), (5171) imply:
% 133.56/19.14 | | | | | | | | | | | | | | (5172) all_4_2 = e3
% 133.56/19.14 | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | REDUCE: (5170), (5172) imply:
% 133.56/19.14 | | | | | | | | | | | | | | (5173) $false
% 133.56/19.14 | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | CLOSE: (5173) is inconsistent.
% 133.56/19.14 | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | Case 2:
% 133.56/19.14 | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | (5174) ~ (all_54_15 = e3)
% 133.56/19.14 | | | | | | | | | | | | | | (5175) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 133.56/19.14 | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | BETA: splitting (5175) gives:
% 133.56/19.14 | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | Case 1:
% 133.56/19.14 | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | (5176) all_54_15 = e2
% 133.56/19.14 | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | COMBINE_EQS: (245), (5176) imply:
% 133.56/19.14 | | | | | | | | | | | | | | | (5177) all_4_2 = e2
% 133.56/19.14 | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | REDUCE: (5158), (5177) imply:
% 133.56/19.14 | | | | | | | | | | | | | | | (5178) $false
% 133.56/19.14 | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | CLOSE: (5178) is inconsistent.
% 133.56/19.14 | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | Case 2:
% 133.56/19.14 | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | (5179) ~ (all_54_15 = e2)
% 133.56/19.14 | | | | | | | | | | | | | | | (5180) all_54_15 = e1 | all_54_15 = e0
% 133.56/19.14 | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | BETA: splitting (5180) gives:
% 133.56/19.14 | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | Case 1:
% 133.56/19.14 | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | (5181) all_54_15 = e1
% 133.56/19.14 | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (5181) imply:
% 133.56/19.14 | | | | | | | | | | | | | | | | (5182) all_4_2 = e1
% 133.56/19.14 | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | REDUCE: (371), (5182) imply:
% 133.56/19.14 | | | | | | | | | | | | | | | | (5183) $false
% 133.56/19.14 | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | CLOSE: (5183) is inconsistent.
% 133.56/19.14 | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | Case 2:
% 133.56/19.14 | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | (5184) all_54_15 = e0
% 133.56/19.14 | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (5184) imply:
% 133.56/19.14 | | | | | | | | | | | | | | | | (5185) all_4_2 = e0
% 133.56/19.14 | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | REDUCE: (369), (5185) imply:
% 133.56/19.14 | | | | | | | | | | | | | | | | (5186) ~ (all_52_13 = e0)
% 133.56/19.14 | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | REDUCE: (5170), (5185) imply:
% 133.56/19.14 | | | | | | | | | | | | | | | | (5187) ~ (e3 = e0)
% 133.56/19.14 | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | REDUCE: (5158), (5185) imply:
% 133.56/19.14 | | | | | | | | | | | | | | | | (5188) ~ (e2 = e0)
% 133.56/19.14 | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | REDUCE: (371), (5185) imply:
% 133.56/19.14 | | | | | | | | | | | | | | | | (5189) ~ (e1 = e0)
% 133.56/19.14 | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | REDUCE: (36), (5185) imply:
% 133.56/19.14 | | | | | | | | | | | | | | | | (5190) op(e0, e0) = e0
% 133.56/19.14 | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.56/19.14 | | | | | | | | | | | | | | | |
% 133.56/19.14 | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.14 | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | (5191) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.56/19.15 | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.56/19.15 | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.56/19.15 | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.56/19.15 | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.56/19.15 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.56/19.15 | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.56/19.15 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.56/19.15 | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (45), (168), (204), (278), (5153), (5154),
% 133.56/19.15 | | | | | | | | | | | | | | | | | (5156), (5162), (5167), (5168), (5191),
% 133.56/19.15 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.56/19.15 | | | | | | | | | | | | | | | | | #189.
% 133.56/19.15 | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.15 | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | (5192) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.56/19.15 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.56/19.15 | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.56/19.15 | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.56/19.15 | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.56/19.15 | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.56/19.15 | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.56/19.15 | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.56/19.15 | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.56/19.15 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.56/19.15 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.56/19.15 | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.56/19.15 | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.56/19.15 | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.56/19.15 | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.56/19.15 | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.56/19.15 | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.56/19.15 | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.56/19.15 | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.56/19.15 | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.56/19.15 | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.56/19.15 | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.56/19.15 | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.56/19.15 | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.56/19.15 | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.56/19.15 | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.56/19.15 | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.56/19.15 | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.56/19.15 | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.56/19.15 | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.56/19.15 | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.56/19.15 | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.56/19.15 | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | BETA: splitting (5192) gives:
% 133.56/19.15 | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.15 | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | (5193) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.56/19.15 | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.56/19.15 | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.56/19.15 | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.56/19.15 | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | BETA: splitting (5193) gives:
% 133.56/19.15 | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.15 | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | (5194) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | ALPHA: (5194) implies:
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | (5195) op(e1, e1) = e3
% 133.56/19.15 | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (5160), (5195), (function-axioms) are
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #771.
% 133.56/19.15 | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.15 | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | (5196) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2,
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | ALPHA: (5196) implies:
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | (5197) ~ (all_56_21 = e1)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | (5198) ~ (all_56_5 = e3)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | (5199) op(e1, e0) = all_56_29
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | (5200) op(e1, e1) = all_56_21
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | (5201) op(e1, e3) = all_56_5
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | (5202) op(e2, e1) = e2
% 133.56/19.15 | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (103), (110), (117), (160), (165), (194),
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | (197), (218), (259), (334), (362), (5142), (5148),
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | (5160), (5186), (5197), (5198), (5199), (5200),
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | (5201), (5202), (function-axioms) are inconsistent
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | by sub-proof #185.
% 133.56/19.15 | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.15 | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.15 | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | (5203) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 133.56/19.15 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.56/19.15 | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.56/19.15 | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.56/19.15 | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.56/19.15 | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.56/19.15 | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.56/19.15 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.56/19.15 | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.56/19.15 | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.56/19.15 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.56/19.15 | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.56/19.15 | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.56/19.15 | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (39), (372), (5153), (5190),
% 133.56/19.15 | | | | | | | | | | | | | | | | | | (5203), (function-axioms) are inconsistent by
% 133.56/19.15 | | | | | | | | | | | | | | | | | | sub-proof #184.
% 133.56/19.15 | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | End of split
% 133.56/19.15 | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | End of split
% 133.56/19.15 | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | End of split
% 133.56/19.15 | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | End of split
% 133.56/19.15 | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | End of split
% 133.56/19.15 | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | Case 2:
% 133.56/19.15 | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | (5204) all_34_2 = e3
% 133.56/19.15 | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | COMBINE_EQS: (307), (5204) imply:
% 133.56/19.15 | | | | | | | | | | | | | (5205) all_4_2 = e3
% 133.56/19.15 | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | SIMP: (5205) implies:
% 133.56/19.15 | | | | | | | | | | | | | (5206) all_4_2 = e3
% 133.56/19.15 | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | REDUCE: (360), (5206) imply:
% 133.56/19.15 | | | | | | | | | | | | | (5207) ~ (all_52_7 = e3)
% 133.56/19.15 | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | REDUCE: (367), (5206) imply:
% 133.56/19.15 | | | | | | | | | | | | | (5208) ~ (all_52_11 = e3)
% 133.56/19.15 | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | REDUCE: (36), (5206) imply:
% 133.56/19.15 | | | | | | | | | | | | | (5209) op(e0, e0) = e3
% 133.56/19.15 | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | BETA: splitting (222) gives:
% 133.56/19.15 | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | Case 1:
% 133.56/19.15 | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | (5210) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 133.56/19.15 | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 133.56/19.15 | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | BETA: splitting (5210) gives:
% 133.56/19.15 | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | Case 1:
% 133.56/19.15 | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | (5211) all_57_4 = e3 & op(e3, e1) = e3
% 133.56/19.15 | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | ALPHA: (5211) implies:
% 133.56/19.15 | | | | | | | | | | | | | | | (5212) op(e3, e1) = e3
% 133.56/19.15 | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | REF_CLOSE: (169), (5166), (5212), (function-axioms) are
% 133.56/19.15 | | | | | | | | | | | | | | | inconsistent by sub-proof #705.
% 133.56/19.15 | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | Case 2:
% 133.56/19.15 | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | (5213) all_57_5 = e3 & op(e2, e1) = e3
% 133.56/19.15 | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | ALPHA: (5213) implies:
% 133.56/19.15 | | | | | | | | | | | | | | | (5214) op(e2, e1) = e3
% 133.56/19.15 | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 133.56/19.15 | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | Case 1:
% 133.56/19.15 | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | (5215) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 133.56/19.15 | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 133.56/19.15 | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (170), (5153), (5165), (5215),
% 133.56/19.15 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.56/19.15 | | | | | | | | | | | | | | | | #183.
% 133.56/19.15 | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | Case 2:
% 133.56/19.15 | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | (5216) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 133.56/19.15 | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 133.56/19.15 | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | BETA: splitting (5216) gives:
% 133.56/19.15 | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.15 | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | (5217) all_57_7 = e3 & op(e1, e2) = e3
% 133.56/19.15 | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | ALPHA: (5217) implies:
% 133.56/19.15 | | | | | | | | | | | | | | | | | (5218) op(e1, e2) = e3
% 133.56/19.15 | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e3,
% 133.56/19.15 | | | | | | | | | | | | | | | | | e2, e1, simplifying with (162), (5218) gives:
% 133.56/19.15 | | | | | | | | | | | | | | | | | (5219) all_52_6 = e3
% 133.56/19.15 | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e3,
% 133.56/19.15 | | | | | | | | | | | | | | | | | e1, e2, simplifying with (165), (5214) gives:
% 133.56/19.15 | | | | | | | | | | | | | | | | | (5220) all_52_9 = e3
% 133.56/19.15 | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | REDUCE: (362), (5220) imply:
% 133.56/19.15 | | | | | | | | | | | | | | | | | (5221) ~ (all_6_2 = e3)
% 133.56/19.15 | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 133.56/19.15 | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.15 | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | (5222) ~ (all_48_2 = e1)
% 133.56/19.15 | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | REDUCE: (5142), (5222) imply:
% 133.56/19.15 | | | | | | | | | | | | | | | | | | (5223) $false
% 133.56/19.15 | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | CLOSE: (5223) is inconsistent.
% 133.56/19.15 | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.15 | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | (5224) ( ~ (all_48_0 = e3) & op(e1, e2) = all_48_0 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | $i(all_48_0)) | ( ~ (all_48_1 = e0) & op(e1, e1)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | = all_48_1 & $i(all_48_1))
% 133.56/19.15 | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | BETA: splitting (5224) gives:
% 133.56/19.15 | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.15 | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | (5225) ~ (all_48_0 = e3) & op(e1, e2) = all_48_0 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | $i(all_48_0)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | ALPHA: (5225) implies:
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | (5226) ~ (all_48_0 = e3)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | (5227) op(e1, e2) = all_48_0
% 133.56/19.15 | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5218), (5226), (5227), (function-axioms) are
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #188.
% 133.56/19.15 | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.15 | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | (5228) ~ (all_48_1 = e0) & op(e1, e1) = all_48_1 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | $i(all_48_1)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | ALPHA: (5228) implies:
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | (5229) ~ (all_48_1 = e0)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | (5230) op(e1, e1) = all_48_1
% 133.56/19.15 | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.56/19.15 | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | (5231) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (45), (168), (204), (278), (5153), (5154),
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | (5156), (5162), (5167), (5168), (5231),
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | #189.
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | (5232) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | BETA: splitting (5232) gives:
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | (5233) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5233) gives:
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | (5234) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5234) implies:
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | (5235) op(e1, e1) = e3
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (5160), (5235), (function-axioms) are
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #771.
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | (5236) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2,
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5236) implies:
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | (5237) op(e2, e1) = e2
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, e2, e1,
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | e2, simplifying with (5214), (5237) gives:
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | (5238) e3 = e2
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (5238) imply:
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | (5239) $false
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5239) is inconsistent.
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | (5240) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5240) gives:
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | (5241) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5241) implies:
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | (5242) op(e2, e2) = e0
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5153), (5242), (function-axioms) are
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675.
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | (5243) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5243) gives:
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | (5244) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5244) implies:
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | (5245) op(e1, e1) = e2
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (5245), (function-axioms) are
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | (5246) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5246) implies:
% 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | (5247) op(e0, e0) = all_56_31
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | (5248) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | all_56_31, e0, e0, simplifying with (5209), (5247)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | gives:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | (5249) all_56_31 = e3
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | all_48_1, e1, e1, simplifying with (39), (5230)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | gives:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | (5250) all_48_1 = all_6_2
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5229), (5250) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | (5251) ~ (all_6_2 = e0)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | (5252) all_54_10 = e3
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (5160), (5252) are inconsistent by
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #742.
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | (5253) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5253) gives:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | (5254) all_54_10 = e2
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (372), (5254) are inconsistent by sub-proof
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | #741.
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | (5255) all_54_10 = e1 | all_54_10 = e0
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5255) gives:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (5256) all_54_10 = e1
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (5256) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (5257) all_6_2 = e1
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5257) implies:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (5258) all_6_2 = e1
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (5258) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (5259) ~ (all_52_14 = e1)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (5258) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (5260) op(e1, e1) = e1
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5248) gives:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5261) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27))
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5261) gives:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5262) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5262) implies:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5263) ~ (all_56_1 = e3)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5264) op(e3, e3) = all_56_1
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5168), (5263), (5264), (function-axioms) are
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #766.
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5265) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5265) implies:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5266) all_56_31 = e2
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5249), (5266) are inconsistent by sub-proof
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #532.
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5267) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (5259), (5260), (5267), (function-axioms)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #182.
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (5268) all_54_10 = e0
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (5251), (5268) are inconsistent by
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #506.
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.16 | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.16 | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | End of split
% 133.56/19.16 | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.16 | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | (5269) all_57_13 = e3 & op(e0, e2) = e3
% 133.56/19.16 | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (5207), (5269), (function-axioms) are
% 133.56/19.16 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #556.
% 133.56/19.16 | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | End of split
% 133.56/19.16 | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | End of split
% 133.56/19.16 | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | End of split
% 133.56/19.16 | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | Case 2:
% 133.56/19.16 | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | (5270) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 133.56/19.16 | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 133.56/19.16 | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | REF_CLOSE: (39), (157), (5160), (5208), (5270),
% 133.56/19.16 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.56/19.16 | | | | | | | | | | | | | | #651.
% 133.56/19.16 | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | End of split
% 133.56/19.16 | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | End of split
% 133.56/19.16 | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | Case 2:
% 133.56/19.16 | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | (5271) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 133.56/19.16 | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | REF_CLOSE: (278), (5154), (5156), (5162), (5271) are
% 133.56/19.16 | | | | | | | | | | | | inconsistent by sub-proof #777.
% 133.56/19.16 | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | End of split
% 133.56/19.16 | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | Case 2:
% 133.56/19.16 | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | (5272) all_32_2 = e1
% 133.56/19.16 | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | COMBINE_EQS: (312), (5272) imply:
% 133.56/19.16 | | | | | | | | | | | (5273) all_10_2 = e1
% 133.56/19.16 | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | COMBINE_EQS: (280), (5273) imply:
% 133.56/19.16 | | | | | | | | | | | (5274) all_50_2 = e1
% 133.56/19.16 | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | REDUCE: (346), (5273) imply:
% 133.56/19.16 | | | | | | | | | | | (5275) ~ (all_52_12 = e1)
% 133.56/19.16 | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | REDUCE: (5156), (5273) imply:
% 133.56/19.16 | | | | | | | | | | | (5276) ~ (e2 = e1)
% 133.56/19.16 | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | REDUCE: (45), (5273) imply:
% 133.56/19.16 | | | | | | | | | | | (5277) op(e3, e3) = e1
% 133.56/19.16 | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | BETA: splitting (212) gives:
% 133.56/19.16 | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | Case 1:
% 133.56/19.16 | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | (5278) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 133.56/19.16 | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 133.56/19.16 | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | REF_CLOSE: (164), (168), (5148), (5275), (5278),
% 133.56/19.16 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.56/19.16 | | | | | | | | | | | | #179.
% 133.56/19.16 | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | Case 2:
% 133.56/19.16 | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | (5279) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 133.56/19.16 | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 133.56/19.16 | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | BETA: splitting (5279) gives:
% 133.56/19.16 | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | Case 1:
% 133.56/19.16 | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | (5280) all_57_11 = e1 & op(e1, e0) = e1
% 133.56/19.16 | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | ALPHA: (5280) implies:
% 133.56/19.16 | | | | | | | | | | | | | (5281) all_57_11 = e1
% 133.56/19.16 | | | | | | | | | | | | | (5282) op(e1, e0) = e1
% 133.56/19.16 | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | BETA: splitting (209) gives:
% 133.56/19.16 | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | Case 1:
% 133.56/19.16 | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | (5283) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 133.56/19.16 | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 133.56/19.16 | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (231), (235),
% 133.56/19.16 | | | | | | | | | | | | | | (237), (5146), (5277), (5283), (function-axioms)
% 133.56/19.16 | | | | | | | | | | | | | | are inconsistent by sub-proof #177.
% 133.56/19.16 | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | Case 2:
% 133.56/19.16 | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | (5284) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 133.56/19.16 | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 133.56/19.16 | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | BETA: splitting (5284) gives:
% 133.56/19.16 | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | Case 1:
% 133.56/19.16 | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | (5285) all_57_14 = e1 & op(e0, e1) = e1
% 133.56/19.16 | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | ALPHA: (5285) implies:
% 133.56/19.16 | | | | | | | | | | | | | | | (5286) all_57_14 = e1
% 133.56/19.16 | | | | | | | | | | | | | | | (5287) op(e0, e1) = e1
% 133.56/19.16 | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 133.56/19.16 | | | | | | | | | | | | | | | e1, e1, e0, simplifying with (157), (5287) gives:
% 133.56/19.16 | | | | | | | | | | | | | | | (5288) all_52_11 = e1
% 133.56/19.16 | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 133.56/19.16 | | | | | | | | | | | | | | | e1, e0, e1, simplifying with (160), (5282) gives:
% 133.56/19.16 | | | | | | | | | | | | | | | (5289) all_52_14 = e1
% 133.56/19.16 | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | REDUCE: (141), (5289) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | (5290) ~ (all_52_2 = e1)
% 133.56/19.16 | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | REDUCE: (139), (5288) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | (5291) ~ (all_52_3 = e1)
% 133.56/19.16 | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | REDUCE: (366), (5289) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | (5292) ~ (all_6_2 = e1)
% 133.56/19.16 | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | SIMP: (5292) implies:
% 133.56/19.16 | | | | | | | | | | | | | | | (5293) ~ (all_6_2 = e1)
% 133.56/19.16 | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | REDUCE: (370), (5289) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | (5294) ~ (all_4_2 = e1)
% 133.56/19.16 | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 133.56/19.16 | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | Case 1:
% 133.56/19.16 | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | (5295) all_54_10 = e3
% 133.56/19.16 | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (5295) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | | (5296) all_6_2 = e3
% 133.56/19.16 | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | REDUCE: (5160), (5296) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | | (5297) $false
% 133.56/19.16 | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | CLOSE: (5297) is inconsistent.
% 133.56/19.16 | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | Case 2:
% 133.56/19.16 | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | (5298) ~ (all_54_10 = e3)
% 133.56/19.16 | | | | | | | | | | | | | | | | (5299) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 133.56/19.16 | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | BETA: splitting (5299) gives:
% 133.56/19.16 | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.16 | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | (5300) all_54_10 = e2
% 133.56/19.16 | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (5300) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | | | (5301) all_6_2 = e2
% 133.56/19.16 | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | REDUCE: (372), (5301) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | | | (5302) $false
% 133.56/19.16 | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | CLOSE: (5302) is inconsistent.
% 133.56/19.16 | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.16 | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | (5303) ~ (all_54_10 = e2)
% 133.56/19.16 | | | | | | | | | | | | | | | | | (5304) all_54_10 = e1 | all_54_10 = e0
% 133.56/19.16 | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | BETA: splitting (5304) gives:
% 133.56/19.16 | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.16 | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | (5305) all_54_10 = e1
% 133.56/19.16 | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (5305) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | (5306) all_6_2 = e1
% 133.56/19.16 | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | REDUCE: (5293), (5306) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | (5307) $false
% 133.56/19.16 | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | CLOSE: (5307) is inconsistent.
% 133.56/19.16 | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.16 | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | (5308) all_54_10 = e0
% 133.56/19.16 | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (5308) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | (5309) all_6_2 = e0
% 133.56/19.16 | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (295), (5309) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | (5310) all_46_2 = e0
% 133.56/19.16 | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | REDUCE: (348), (5309) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | (5311) ~ (all_52_2 = e0)
% 133.56/19.16 | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | REDUCE: (359), (5309) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | (5312) ~ (all_52_6 = e0)
% 133.56/19.16 | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | REDUCE: (5160), (5309) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | (5313) ~ (e3 = e0)
% 133.56/19.16 | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | REDUCE: (5293), (5309) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | (5314) ~ (e1 = e0)
% 133.56/19.16 | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | REDUCE: (39), (5309) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | (5315) op(e1, e1) = e0
% 133.56/19.16 | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 133.56/19.16 | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | (5316) ~ (all_48_2 = e1)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | REDUCE: (5142), (5316) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | (5317) $false
% 133.56/19.16 | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | CLOSE: (5317) is inconsistent.
% 133.56/19.16 | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | (5318) ( ~ (all_48_0 = e3) & op(e1, e2) = all_48_0 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | $i(all_48_0)) | ( ~ (all_48_1 = e0) & op(e1, e1)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | = all_48_1 & $i(all_48_1))
% 133.56/19.16 | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | (5319) ~ (all_50_2 = e1)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | REDUCE: (5274), (5319) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | (5320) $false
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | CLOSE: (5320) is inconsistent.
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | (5321) ( ~ (all_50_0 = e2) & op(e1, e3) = all_50_0 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | $i(all_50_0)) | ( ~ (all_50_1 = e0) & op(e1, e1)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | = all_50_1 & $i(all_50_1))
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | BETA: splitting (5321) gives:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | (5322) ~ (all_50_0 = e2) & op(e1, e3) = all_50_0 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | $i(all_50_0)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5322) implies:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | (5323) ~ (all_50_0 = e2)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | (5324) op(e1, e3) = all_50_0
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5318) gives:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | (5325) ~ (all_48_0 = e3) & op(e1, e2) = all_48_0 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | $i(all_48_0)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5325) implies:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | (5326) ~ (all_48_0 = e3)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | (5327) op(e1, e2) = all_48_0
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6,
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | all_48_0, e2, e1, simplifying with (162), (5327)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | gives:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | (5328) all_52_6 = all_48_0
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2,
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | all_50_0, e3, e1, simplifying with (163), (5324)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | gives:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | (5329) all_52_2 = all_50_0
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (5328) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | (5330) all_54_9 = all_48_0
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (5329) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | (5331) all_54_8 = all_50_0
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (5329) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | (5332) ~ (all_52_3 = all_50_0)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | SIMP: (5332) implies:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | (5333) ~ (all_52_3 = all_50_0)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (5328), (5329) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | (5334) ~ (all_50_0 = all_48_0)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5290), (5329) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | (5335) ~ (all_50_0 = e1)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5311), (5329) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | (5336) ~ (all_50_0 = e0)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (5328) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | (5337) ~ (all_52_4 = all_48_0)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5145), (5328) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | (5338) ~ (all_48_0 = e1)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5312), (5328) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | (5339) ~ (all_48_0 = e0)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | (5340) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5340) gives:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | (5341) all_57_6 = e3 & op(e1, e3) = e3
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5341) implies:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | (5342) all_57_6 = e3
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | (5343) all_54_9 = e3
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5326), (5330), (5343) are inconsistent by
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #176.
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | (5344) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (5345) all_54_8 = e3
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5331), (5345) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (5346) all_50_0 = e3
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5346) implies:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (5347) all_50_0 = e3
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5333), (5347) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (5348) ~ (all_52_3 = e3)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5334), (5347) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (5349) ~ (all_48_0 = e3)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5324), (5347) imply:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (5350) op(e1, e3) = e3
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5351) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (5153), (5277), (5350), (5351),
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | #174.
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5352) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5352) gives:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5353) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5353) gives:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5354) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5354) implies:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5355) op(e1, e1) = e3
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5315), (5355), (function-axioms) are
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753.
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5356) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2,
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5356) implies:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5357) ~ (all_56_5 = e3)
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5358) op(e1, e3) = all_56_5
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5350), (5357), (5358), (function-axioms) are
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #724.
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5359) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5359) gives:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5360) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5360) implies:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5361) op(e2, e2) = e0
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5153), (5361), (function-axioms) are
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675.
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5362) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5362) gives:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5363) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5363) implies:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5364) op(e1, e1) = e2
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (5364), (function-axioms) are
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5365) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5365) implies:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5366) op(e0, e0) = all_56_31
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5367) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5368) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5368) gives:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5369) all_57_6 = e2 & op(e1, e3) = e2
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5369) implies:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5370) op(e1, e3) = e2
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5323), (5324), (5370), (function-axioms) are
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #735.
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5371) all_57_7 = e2 & op(e1, e2) = e2
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5371) implies:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5372) all_57_7 = e2
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5344) gives:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5373) all_54_9 = e2
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5330), (5373) imply:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5374) all_48_0 = e2
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5337), (5374) imply:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5375) ~ (all_52_4 = e2)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5326), (5374) imply:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5376) ~ (e3 = e2)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5377) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5377) gives:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5378) all_57_12 = e2 & op(e0, e3) = e2
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5378) implies:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5379) all_57_12 = e2
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5380) op(e0, e3) = e2
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5381) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5381) gives:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5382) all_57_0 = e0 & op(e3, e3) = e0
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5382) implies:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5383) op(e3, e3) = e0
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5277), (5383), (function-axioms) are
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #717.
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5384) all_57_2 = e0 & op(e2, e3) = e0
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5384) implies:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5385) op(e2, e3) = e0
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31, e0, e0, simplifying with (36), (5366)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5386) all_56_31 = all_4_2
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e2,
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (159), (5380) gives:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5387) all_52_3 = e2
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e0,
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e2, simplifying with (167), (5385) gives:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5388) all_52_1 = e0
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (5387), (5388) imply:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5389) ~ (e2 = e0)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (349), (5387) imply:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5390) ~ (all_4_2 = e2)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5367) gives:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5391) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27))
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5391) gives:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5392) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5392) implies:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5393) all_56_31 = e3
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5394) ~ (all_56_25 = e0)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5395) op(e0, e3) = e0
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5396) op(e3, e0) = all_56_25
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5397) op(e3, e2) = all_56_9
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5398) op(e3, e3) = all_56_1
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5386), (5393) imply:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5399) all_4_2 = e3
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (5399) imply:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5400) all_34_2 = e3
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (5399) imply:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5401) ~ (all_52_7 = e3)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5402) ~ (all_34_2 = e3)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5400), (5402) imply:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5403) $false
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5403) is inconsistent.
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5404) ( ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_34_0)) | ( ~ (all_34_1 = e1) & op(e3, e3)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_34_1 & $i(all_34_1))
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5405) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (159), (168), (170), (232), (236),
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5153), (5277), (5291), (5348), (5375), (5394),
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5395), (5396), (5397), (5398), (5404), (5405),
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #173.
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5406) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5406) gives:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5407) all_57_7 = e3 & op(e1, e2) = e3
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (39), (217), (372), (5282), (5323),
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5324), (5407), (function-axioms) are inconsistent
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #171.
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5408) all_57_13 = e3 & op(e0, e2) = e3
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (5401), (5408), (function-axioms) are
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #556.
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5409) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5158), (5386), (5409) are inconsistent by
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #765.
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5410) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5410) gives:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5411) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5411) implies:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5412) ~ (all_56_31 = e0)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5413) ~ (all_56_23 = e1)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5414) op(e0, e1) = all_56_23
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5386), (5412) imply:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5415) ~ (all_4_2 = e0)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5416) all_54_15 = e3
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (5416) imply:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5417) all_4_2 = e3
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5417) implies:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5418) all_4_2 = e3
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (5418) imply:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5419) op(e0, e0) = e3
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5420) ~ (all_46_2 = e0)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5310), (5420) imply:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5421) $false
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5421) is inconsistent.
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5422) ( ~ (all_46_0 = e2) & op(e0, e1) = all_46_0 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_46_0)) | ( ~ (all_46_1 = e3) & op(e0, e0)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_46_1 & $i(all_46_1))
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5422) gives:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5423) ~ (all_46_0 = e2) & op(e0, e1) = all_46_0 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_46_0)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5423) implies:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5424) op(e0, e1) = all_46_0
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23, e1, e0, simplifying with (5287), (5414)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5425) all_56_23 = e1
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_46_0,
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23, e1, e0, simplifying with (5414), (5424)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5426) all_56_23 = all_46_0
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5425), (5426) imply:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5427) all_46_0 = e1
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5413), (5425) imply:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5428) $false
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5428) is inconsistent.
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5429) ~ (all_46_1 = e3) & op(e0, e0) = all_46_1 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_46_1)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5419), (5429), (function-axioms) are inconsistent
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #758.
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5430) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (371), (5158), (5415), (5430) are
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #746.
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5431) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5431) implies:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5432) ~ (all_56_5 = e3)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5433) op(e1, e3) = all_56_5
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5350), (5432), (5433), (function-axioms) are
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #724.
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5434) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5434) gives:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5435) all_57_6 = e0 & op(e1, e3) = e0
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5435) implies:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5436) all_57_6 = e0
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5342), (5436) are inconsistent by sub-proof
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #588.
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5437) all_57_12 = e0 & op(e0, e3) = e0
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5437) implies:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5438) all_57_12 = e0
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5379), (5438) are inconsistent by sub-proof
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #682.
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5439) all_57_13 = e2 & op(e0, e2) = e2
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5439) implies:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5440) all_57_13 = e2
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5441) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5441) gives:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5442) all_57_1 = e0 & op(e3, e2) = e0
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5442) implies:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5443) all_57_1 = e0
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5444) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5444) gives:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5445) all_57_1 = e3 & op(e3, e2) = e3
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5443), (5445) are inconsistent by sub-proof
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #376.
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5446) all_57_3 = e3 & op(e2, e2) = e3
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5446) implies:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5447) all_57_3 = e3
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (227), (228), (5372),
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5440), (5447) are inconsistent by sub-proof #287.
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5448) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5448) gives:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5449) all_57_7 = e3 & op(e1, e2) = e3
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (39), (217), (372), (5282), (5323),
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5324), (5449), (function-axioms) are inconsistent
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #171.
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5450) all_57_13 = e3 & op(e0, e2) = e3
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5450) implies:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5451) all_57_13 = e3
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5440), (5451) are inconsistent by sub-proof
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #408.
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5452) all_57_3 = e0 & op(e2, e2) = e0
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5452) implies:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5453) op(e2, e2) = e0
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5153), (5453), (function-axioms) are
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675.
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5454) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (162), (5312), (5440), (5454),
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #170.
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5455) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5455) gives:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5456) all_57_14 = e2 & op(e0, e1) = e2
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5286), (5456) are inconsistent by sub-proof
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #213.
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5457) all_57_15 = e2 & op(e0, e0) = e2
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5457) implies:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5458) op(e0, e0) = e2
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (5158), (5366), (5458), (function-axioms)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #427.
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5459) all_54_9 = e1 | all_54_9 = e0
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (5145), (5312), (5459) are inconsistent by
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #168.
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5460) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (39), (372), (5282), (5460),
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #172.
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (5461) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (5290), (5311), (5323), (5331), (5461) are
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #473.
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (5462) all_57_7 = e3 & op(e1, e2) = e3
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (39), (217), (372), (5282), (5323),
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (5324), (5462), (function-axioms) are inconsistent
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #171.
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | (5463) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5463) gives:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (5464) all_57_8 = e3 & op(e1, e1) = e3
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5464) implies:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (5465) op(e1, e1) = e3
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5315), (5465), (function-axioms) are
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753.
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (5466) all_57_11 = e3 & op(e1, e0) = e3
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5466) implies:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (5467) all_57_11 = e3
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5281), (5467) are inconsistent by sub-proof
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | #167.
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | (5468) ~ (all_48_1 = e0) & op(e1, e1) = all_48_1 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | $i(all_48_1)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5468) implies:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | (5469) ~ (all_48_1 = e0)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | (5470) op(e1, e1) = all_48_1
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_48_1,
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | e1, e1, simplifying with (5315), (5470) gives:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | (5471) all_48_1 = e0
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5469), (5471) imply:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | (5472) $false
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5472) is inconsistent.
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | (5473) ~ (all_50_1 = e0) & op(e1, e1) = all_50_1 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | $i(all_50_1)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5315), (5473), (function-axioms) are inconsistent
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | by sub-proof #719.
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.18 | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.18 | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | End of split
% 133.56/19.18 | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | End of split
% 133.56/19.18 | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | End of split
% 133.56/19.18 | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | Case 2:
% 133.56/19.18 | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | (5474) all_57_15 = e1 & op(e0, e0) = e1
% 133.56/19.18 | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | ALPHA: (5474) implies:
% 133.56/19.18 | | | | | | | | | | | | | | | (5475) op(e0, e0) = e1
% 133.56/19.18 | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | REF_CLOSE: (36), (371), (5475), (function-axioms) are
% 133.56/19.18 | | | | | | | | | | | | | | | inconsistent by sub-proof #354.
% 133.56/19.18 | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | End of split
% 133.56/19.18 | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | End of split
% 133.56/19.18 | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | Case 2:
% 133.56/19.18 | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | (5476) all_57_15 = e1 & op(e0, e0) = e1
% 133.56/19.18 | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | ALPHA: (5476) implies:
% 133.56/19.18 | | | | | | | | | | | | | (5477) op(e0, e0) = e1
% 133.56/19.18 | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | REF_CLOSE: (36), (371), (5477), (function-axioms) are
% 133.56/19.18 | | | | | | | | | | | | | inconsistent by sub-proof #354.
% 133.56/19.18 | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | End of split
% 133.56/19.18 | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | End of split
% 133.56/19.18 | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | End of split
% 133.56/19.18 | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | Case 2:
% 133.56/19.18 | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | (5478) all_28_2 = e3
% 133.56/19.18 | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | COMBINE_EQS: (316), (5478) imply:
% 133.56/19.18 | | | | | | | | | | (5479) all_6_2 = e3
% 133.56/19.18 | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | REDUCE: (359), (5479) imply:
% 133.56/19.18 | | | | | | | | | | (5480) ~ (all_52_6 = e3)
% 133.56/19.18 | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | REDUCE: (361), (5479) imply:
% 133.56/19.18 | | | | | | | | | | (5481) ~ (all_52_8 = e3)
% 133.56/19.18 | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | REDUCE: (362), (5479) imply:
% 133.56/19.18 | | | | | | | | | | (5482) ~ (all_52_9 = e3)
% 133.56/19.18 | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | REDUCE: (39), (5479) imply:
% 133.56/19.18 | | | | | | | | | | (5483) op(e1, e1) = e3
% 133.56/19.18 | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | BETA: splitting (5141) gives:
% 133.56/19.18 | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | Case 1:
% 133.56/19.18 | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | (5484) ~ (all_8_0 = e0) & op(e1, e2) = all_8_0 &
% 133.56/19.18 | | | | | | | | | | | $i(all_8_0)
% 133.56/19.18 | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | ALPHA: (5484) implies:
% 133.56/19.18 | | | | | | | | | | | (5485) ~ (all_8_0 = e0)
% 133.56/19.18 | | | | | | | | | | | (5486) op(e1, e2) = all_8_0
% 133.56/19.18 | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6,
% 133.56/19.18 | | | | | | | | | | | all_8_0, e2, e1, simplifying with (162), (5486)
% 133.56/19.18 | | | | | | | | | | | gives:
% 133.56/19.18 | | | | | | | | | | | (5487) all_52_6 = all_8_0
% 133.56/19.18 | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | COMBINE_EQS: (257), (5487) imply:
% 133.56/19.18 | | | | | | | | | | | (5488) all_54_9 = all_8_0
% 133.56/19.18 | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | REDUCE: (136), (5487) imply:
% 133.56/19.18 | | | | | | | | | | | (5489) ~ (all_52_4 = all_8_0)
% 133.56/19.18 | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | REDUCE: (5480), (5487) imply:
% 133.56/19.18 | | | | | | | | | | | (5490) ~ (all_8_0 = e3)
% 133.56/19.18 | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | REDUCE: (5145), (5487) imply:
% 133.56/19.18 | | | | | | | | | | | (5491) ~ (all_8_0 = e1)
% 133.56/19.18 | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | BETA: splitting (195) gives:
% 133.56/19.18 | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | Case 1:
% 133.56/19.18 | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | (5492) all_54_9 = e3
% 133.56/19.18 | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | COMBINE_EQS: (5488), (5492) imply:
% 133.56/19.18 | | | | | | | | | | | | (5493) all_8_0 = e3
% 133.56/19.18 | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | REDUCE: (5490), (5493) imply:
% 133.56/19.18 | | | | | | | | | | | | (5494) $false
% 133.56/19.18 | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | CLOSE: (5494) is inconsistent.
% 133.56/19.18 | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | Case 2:
% 133.56/19.18 | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | (5495) ~ (all_54_9 = e3)
% 133.56/19.18 | | | | | | | | | | | | (5496) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 133.56/19.18 | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | BETA: splitting (5496) gives:
% 133.56/19.18 | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | Case 1:
% 133.56/19.18 | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | (5497) all_54_9 = e2
% 133.56/19.18 | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | COMBINE_EQS: (5488), (5497) imply:
% 133.56/19.18 | | | | | | | | | | | | | (5498) all_8_0 = e2
% 133.56/19.18 | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | REDUCE: (5489), (5498) imply:
% 133.56/19.18 | | | | | | | | | | | | | (5499) ~ (all_52_4 = e2)
% 133.56/19.18 | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | REDUCE: (5490), (5498) imply:
% 133.56/19.18 | | | | | | | | | | | | | (5500) ~ (e3 = e2)
% 133.56/19.18 | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | REDUCE: (5486), (5498) imply:
% 133.56/19.18 | | | | | | | | | | | | | (5501) op(e1, e2) = e2
% 133.56/19.18 | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | BETA: splitting (79) gives:
% 133.56/19.18 | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | Case 1:
% 133.56/19.18 | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | (5502) ~ (all_32_2 = e1)
% 133.56/19.18 | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | REDUCE: (312), (5502) imply:
% 133.56/19.18 | | | | | | | | | | | | | | (5503) ~ (all_10_2 = e1)
% 133.56/19.18 | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 133.56/19.18 | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | Case 1:
% 133.56/19.18 | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | (5504) all_54_0 = e3
% 133.56/19.18 | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | COMBINE_EQS: (278), (5504) imply:
% 133.56/19.18 | | | | | | | | | | | | | | | (5505) all_10_2 = e3
% 133.56/19.18 | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | REDUCE: (336), (5505) imply:
% 133.56/19.18 | | | | | | | | | | | | | | | (5506) ~ (all_52_1 = e3)
% 133.56/19.18 | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | REDUCE: (342), (5505) imply:
% 133.56/19.18 | | | | | | | | | | | | | | | (5507) ~ (all_52_4 = e3)
% 133.56/19.18 | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | REDUCE: (346), (5505) imply:
% 133.56/19.18 | | | | | | | | | | | | | | | (5508) ~ (all_52_12 = e3)
% 133.56/19.18 | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | REDUCE: (45), (5505) imply:
% 133.56/19.18 | | | | | | | | | | | | | | | (5509) op(e3, e3) = e3
% 133.56/19.18 | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 133.56/19.18 | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | Case 1:
% 133.56/19.18 | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | (5510) all_54_1 = e3
% 133.56/19.18 | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (5510) imply:
% 133.56/19.18 | | | | | | | | | | | | | | | | (5511) all_52_4 = e3
% 133.56/19.18 | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | REDUCE: (5507), (5511) imply:
% 133.56/19.18 | | | | | | | | | | | | | | | | (5512) $false
% 133.56/19.18 | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | CLOSE: (5512) is inconsistent.
% 133.56/19.18 | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | Case 2:
% 133.56/19.18 | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | (5513) ~ (all_54_1 = e3)
% 133.56/19.18 | | | | | | | | | | | | | | | | (5514) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 133.56/19.18 | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | BETA: splitting (5514) gives:
% 133.56/19.18 | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.18 | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | (5515) all_54_1 = e2
% 133.56/19.18 | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (5515) imply:
% 133.56/19.18 | | | | | | | | | | | | | | | | | (5516) all_52_4 = e2
% 133.56/19.18 | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | REDUCE: (5499), (5516) imply:
% 133.56/19.18 | | | | | | | | | | | | | | | | | (5517) $false
% 133.56/19.18 | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | CLOSE: (5517) is inconsistent.
% 133.56/19.18 | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.18 | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | (5518) all_54_1 = e1 | all_54_1 = e0
% 133.56/19.18 | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | BETA: splitting (5518) gives:
% 133.56/19.18 | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.18 | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | (5519) all_54_1 = e1
% 133.56/19.18 | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (5519) imply:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | (5520) all_52_4 = e1
% 133.56/19.18 | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | REDUCE: (5144), (5520) imply:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | (5521) $false
% 133.56/19.18 | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | CLOSE: (5521) is inconsistent.
% 133.56/19.18 | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.18 | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | (5522) all_54_1 = e0
% 133.56/19.18 | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (5522) imply:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | (5523) all_52_4 = e0
% 133.56/19.18 | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | REDUCE: (135), (5523) imply:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | (5524) ~ (all_52_7 = e0)
% 133.56/19.18 | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | SIMP: (5524) implies:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | (5525) ~ (all_52_7 = e0)
% 133.56/19.18 | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | REDUCE: (5507), (5523) imply:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | (5526) ~ (e3 = e0)
% 133.56/19.18 | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | REDUCE: (5144), (5523) imply:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | (5527) ~ (e1 = e0)
% 133.56/19.18 | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 133.56/19.18 | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | (5528) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (167), (5153), (5506), (5528),
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | #166.
% 133.56/19.18 | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | (5529) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | BETA: splitting (5529) gives:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | (5530) all_57_5 = e3 & op(e2, e1) = e3
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (5482), (5530), (function-axioms) are
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547.
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | (5531) all_57_10 = e3 & op(e2, e0) = e3
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | ALPHA: (5531) implies:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | (5532) op(e2, e0) = e3
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | (5533) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (45), (168), (204), (278), (5153), (5154),
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | (5156), (5503), (5508), (5509), (5533),
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | #189.
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | (5534) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5534) gives:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | (5535) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5535) gives:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | (5536) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5536) implies:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | (5537) ~ (all_56_1 = e3)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | (5538) op(e3, e3) = all_56_1
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5509), (5537), (5538), (function-axioms) are
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #766.
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | (5539) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2,
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5539) implies:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | (5540) ~ (all_56_13 = e2)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | (5541) op(e1, e2) = all_56_13
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5501), (5540), (5541), (function-axioms) are
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #165.
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | (5542) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5542) gives:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | (5543) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5543) implies:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | (5544) op(e2, e2) = e0
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (36), (39), (158), (164),
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | (168), (206), (371), (372), (5483), (5508),
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | (5509), (5525), (5532), (5544), (function-axioms)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #542.
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | (5545) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5545) gives:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (5546) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5546) implies:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (5547) op(e1, e1) = e2
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (5547), (function-axioms) are
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (5548) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5548) implies:
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (5549) op(e0, e0) = all_56_31
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (5550) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (158), (371), (5483), (5509), (5525),
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (5549), (5550), (function-axioms) are inconsistent
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #543.
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.18 | | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.18 | | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | | End of split
% 133.56/19.18 | | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | End of split
% 133.56/19.18 | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | End of split
% 133.56/19.18 | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | Case 2:
% 133.56/19.18 | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | (5551) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 133.56/19.18 | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | REF_CLOSE: (278), (5154), (5156), (5503), (5551) are
% 133.56/19.18 | | | | | | | | | | | | | | | inconsistent by sub-proof #777.
% 133.56/19.18 | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | End of split
% 133.56/19.18 | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | Case 2:
% 133.56/19.18 | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | (5552) all_32_2 = e1
% 133.56/19.18 | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | COMBINE_EQS: (312), (5552) imply:
% 133.56/19.18 | | | | | | | | | | | | | | (5553) all_10_2 = e1
% 133.56/19.18 | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | SIMP: (5553) implies:
% 133.56/19.18 | | | | | | | | | | | | | | (5554) all_10_2 = e1
% 133.56/19.18 | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | REDUCE: (338), (5554) imply:
% 133.56/19.18 | | | | | | | | | | | | | | (5555) ~ (all_52_2 = e1)
% 133.56/19.18 | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | REDUCE: (340), (5554) imply:
% 133.56/19.18 | | | | | | | | | | | | | | (5556) ~ (all_52_3 = e1)
% 133.56/19.18 | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | REDUCE: (5156), (5554) imply:
% 133.56/19.18 | | | | | | | | | | | | | | (5557) ~ (e2 = e1)
% 133.56/19.18 | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | REDUCE: (45), (5554) imply:
% 133.56/19.18 | | | | | | | | | | | | | | (5558) op(e3, e3) = e1
% 133.56/19.18 | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 133.56/19.18 | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | Case 1:
% 133.56/19.18 | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | (5559) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 133.56/19.18 | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 133.56/19.18 | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | BETA: splitting (5559) gives:
% 133.56/19.18 | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | Case 1:
% 133.56/19.18 | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | (5560) all_57_4 = e1 & op(e3, e1) = e1
% 133.56/19.18 | | | | | | | | | | | | | | | |
% 133.56/19.18 | | | | | | | | | | | | | | | | ALPHA: (5560) implies:
% 133.56/19.18 | | | | | | | | | | | | | | | | (5561) all_57_4 = e1
% 133.56/19.18 | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (170), (232),
% 133.56/19.19 | | | | | | | | | | | | | | | | (236), (238), (5481), (5499), (5558), (5561),
% 133.56/19.19 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.56/19.19 | | | | | | | | | | | | | | | | #162.
% 133.56/19.19 | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | Case 2:
% 133.56/19.19 | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | (5562) all_57_5 = e1 & op(e2, e1) = e1
% 133.56/19.19 | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | REF_CLOSE: (165), (5147), (5562), (function-axioms) are
% 133.56/19.19 | | | | | | | | | | | | | | | | inconsistent by sub-proof #161.
% 133.56/19.19 | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | End of split
% 133.56/19.19 | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | Case 2:
% 133.56/19.19 | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | (5563) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 133.56/19.19 | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 133.56/19.19 | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | BETA: splitting (5563) gives:
% 133.56/19.19 | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | Case 1:
% 133.56/19.19 | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | (5564) all_57_8 = e1 & op(e1, e1) = e1
% 133.56/19.19 | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | ALPHA: (5564) implies:
% 133.56/19.19 | | | | | | | | | | | | | | | | (5565) op(e1, e1) = e1
% 133.56/19.19 | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (5483), (5565), (function-axioms) are
% 133.56/19.19 | | | | | | | | | | | | | | | | inconsistent by sub-proof #662.
% 133.56/19.19 | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | Case 2:
% 133.56/19.19 | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | (5566) all_57_14 = e1 & op(e0, e1) = e1
% 133.56/19.19 | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | ALPHA: (5566) implies:
% 133.56/19.19 | | | | | | | | | | | | | | | | (5567) all_57_14 = e1
% 133.56/19.19 | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 133.56/19.19 | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.19 | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | (5568) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 133.56/19.19 | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 133.56/19.19 | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | BETA: splitting (5568) gives:
% 133.56/19.19 | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.19 | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | (5569) all_57_12 = e2 & op(e0, e3) = e2
% 133.56/19.19 | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | ALPHA: (5569) implies:
% 133.56/19.19 | | | | | | | | | | | | | | | | | | (5570) all_57_12 = e2
% 133.56/19.19 | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.56/19.19 | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.19 | | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | (5571) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.56/19.19 | | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | BETA: splitting (5571) gives:
% 133.56/19.19 | | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | (5572) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | BETA: splitting (5572) gives:
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | (5573) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5573) implies:
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | (5574) op(e3, e3) = e2
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | (5570), (5574), (function-axioms) are inconsistent
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | by sub-proof #290.
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | (5575) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5575) implies:
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | (5576) ~ (all_56_13 = e2)
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | (5577) op(e1, e2) = all_56_13
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5501), (5576), (5577), (function-axioms) are
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #165.
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | (5578) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (5153), (5558), (5578),
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | #175.
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.19 | | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.19 | | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | (5579) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.56/19.19 | | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (36), (39), (82), (159),
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | (163), (168), (169), (170), (232), (236), (238),
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | (307), (349), (368), (371), (372), (5153), (5158),
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | (5481), (5483), (5499), (5501), (5555), (5556),
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | (5558), (5579), (function-axioms) are inconsistent
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | by sub-proof #159.
% 133.56/19.19 | | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.19 | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.19 | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | (5580) all_57_13 = e2 & op(e0, e2) = e2
% 133.56/19.19 | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | ALPHA: (5580) implies:
% 133.56/19.19 | | | | | | | | | | | | | | | | | | (5581) op(e0, e2) = e2
% 133.56/19.19 | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.56/19.19 | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.19 | | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | (5582) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.56/19.19 | | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | BETA: splitting (5582) gives:
% 133.56/19.19 | | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | (5583) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5501), (5558), (5583), (function-axioms) are
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #158.
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | (5584) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5153), (5581), (5584), (function-axioms) are
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #157.
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.19 | | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.19 | | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | (5585) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.56/19.19 | | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (36), (39), (82), (159),
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | (163), (168), (169), (170), (232), (236), (238),
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | (307), (349), (368), (371), (372), (5153), (5158),
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | (5481), (5483), (5499), (5501), (5555), (5556),
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | (5558), (5585), (function-axioms) are inconsistent
% 133.56/19.19 | | | | | | | | | | | | | | | | | | | by sub-proof #159.
% 133.56/19.19 | | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | End of split
% 133.56/19.19 | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | End of split
% 133.56/19.19 | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.19 | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | (5586) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 133.56/19.19 | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 133.56/19.19 | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | BETA: splitting (5586) gives:
% 133.56/19.19 | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | Case 1:
% 133.56/19.19 | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | (5587) all_57_14 = e2 & op(e0, e1) = e2
% 133.56/19.19 | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | ALPHA: (5587) implies:
% 133.56/19.19 | | | | | | | | | | | | | | | | | | (5588) all_57_14 = e2
% 133.56/19.19 | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5567), (5588) are inconsistent by sub-proof
% 133.56/19.19 | | | | | | | | | | | | | | | | | | #560.
% 133.56/19.19 | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | Case 2:
% 133.56/19.19 | | | | | | | | | | | | | | | | | |
% 133.56/19.19 | | | | | | | | | | | | | | | | | | (5589) all_57_15 = e2 & op(e0, e0) = e2
% 133.67/19.19 | | | | | | | | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | | | | | | | | ALPHA: (5589) implies:
% 133.67/19.19 | | | | | | | | | | | | | | | | | | (5590) op(e0, e0) = e2
% 133.67/19.19 | | | | | | | | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.67/19.19 | | | | | | | | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.19 | | | | | | | | | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | (5591) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.67/19.19 | | | | | | | | | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | BETA: splitting (5591) gives:
% 133.67/19.19 | | | | | | | | | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | (5592) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5501), (5558), (5592), (function-axioms) are
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #158.
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | (5593) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (5153), (5558), (5593),
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | #175.
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.19 | | | | | | | | | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.19 | | | | | | | | | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | (5594) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.67/19.19 | | | | | | | | | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | BETA: splitting (5594) gives:
% 133.67/19.19 | | | | | | | | | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | (5595) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (5501), (5555), (5595), (function-axioms)
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #160.
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | (5596) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (39), (372), (5153), (5158), (5590),
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | (5596), (function-axioms) are inconsistent by
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | | sub-proof #156.
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.19 | | | | | | | | | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.19 | | | | | | | | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | | | | | | | End of split
% 133.67/19.19 | | | | | | | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | | | | | | End of split
% 133.67/19.19 | | | | | | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | | | | | End of split
% 133.67/19.19 | | | | | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | | | | End of split
% 133.67/19.19 | | | | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | | | End of split
% 133.67/19.19 | | | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | | Case 2:
% 133.67/19.19 | | | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | | | (5597) all_54_9 = e1 | all_54_9 = e0
% 133.67/19.19 | | | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | | | REF_CLOSE: (5485), (5488), (5491), (5597) are inconsistent by
% 133.67/19.19 | | | | | | | | | | | | | sub-proof #155.
% 133.67/19.19 | | | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | | End of split
% 133.67/19.19 | | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | End of split
% 133.67/19.19 | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | Case 2:
% 133.67/19.19 | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | (5598) ~ (all_8_1 = e3) & op(e1, e1) = all_8_1 &
% 133.67/19.19 | | | | | | | | | | | $i(all_8_1)
% 133.67/19.19 | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | ALPHA: (5598) implies:
% 133.67/19.19 | | | | | | | | | | | (5599) ~ (all_8_1 = e3)
% 133.67/19.19 | | | | | | | | | | | (5600) op(e1, e1) = all_8_1
% 133.67/19.19 | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_8_1,
% 133.67/19.19 | | | | | | | | | | | e1, e1, simplifying with (5483), (5600) gives:
% 133.67/19.19 | | | | | | | | | | | (5601) all_8_1 = e3
% 133.67/19.19 | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | REDUCE: (5599), (5601) imply:
% 133.67/19.19 | | | | | | | | | | | (5602) $false
% 133.67/19.19 | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | | CLOSE: (5602) is inconsistent.
% 133.67/19.19 | | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | | End of split
% 133.67/19.19 | | | | | | | | | |
% 133.67/19.19 | | | | | | | | | End of split
% 133.67/19.19 | | | | | | | | |
% 133.67/19.19 | | | | | | | | Case 2:
% 133.67/19.19 | | | | | | | | |
% 133.67/19.19 | | | | | | | | | (5603) all_20_2 = e2
% 133.67/19.19 | | | | | | | | | (5604) ( ~ (all_20_0 = e3) & op(e2, e0) = all_20_0 &
% 133.67/19.19 | | | | | | | | | $i(all_20_0)) | ( ~ (all_20_1 = e1) & op(e2, e2) =
% 133.67/19.19 | | | | | | | | | all_20_1 & $i(all_20_1))
% 133.67/19.19 | | | | | | | | |
% 133.67/19.19 | | | | | | | | | COMBINE_EQS: (318), (5603) imply:
% 133.67/19.19 | | | | | | | | | (5605) all_4_2 = e2
% 133.67/19.19 | | | | | | | | |
% 133.67/19.19 | | | | | | | | | SIMP: (5605) implies:
% 133.67/19.19 | | | | | | | | | (5606) all_4_2 = e2
% 133.67/19.19 | | | | | | | | |
% 133.67/19.19 | | | | | | | | | REDUCE: (367), (5606) imply:
% 133.67/19.19 | | | | | | | | | (5607) ~ (all_52_11 = e2)
% 133.67/19.19 | | | | | | | | |
% 133.67/19.19 | | | | | | | | | REDUCE: (368), (5606) imply:
% 133.67/19.19 | | | | | | | | | (5608) ~ (all_52_12 = e2)
% 133.67/19.19 | | | | | | | | |
% 133.67/19.19 | | | | | | | | | REDUCE: (369), (5606) imply:
% 133.67/19.19 | | | | | | | | | (5609) ~ (all_52_13 = e2)
% 133.67/19.19 | | | | | | | | |
% 133.67/19.19 | | | | | | | | | REDUCE: (370), (5606) imply:
% 133.67/19.19 | | | | | | | | | (5610) ~ (all_52_14 = e2)
% 133.67/19.19 | | | | | | | | |
% 133.67/19.19 | | | | | | | | | REDUCE: (36), (5606) imply:
% 133.67/19.20 | | | | | | | | | (5611) op(e0, e0) = e2
% 133.67/19.20 | | | | | | | | |
% 133.67/19.20 | | | | | | | | | BETA: splitting (5604) gives:
% 133.67/19.20 | | | | | | | | |
% 133.67/19.20 | | | | | | | | | Case 1:
% 133.67/19.20 | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | (5612) ~ (all_20_0 = e3) & op(e2, e0) = all_20_0 &
% 133.67/19.20 | | | | | | | | | | $i(all_20_0)
% 133.67/19.20 | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | ALPHA: (5612) implies:
% 133.67/19.20 | | | | | | | | | | (5613) ~ (all_20_0 = e3)
% 133.67/19.20 | | | | | | | | | | (5614) op(e2, e0) = all_20_0
% 133.67/19.20 | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 133.67/19.20 | | | | | | | | | | all_20_0, e0, e2, simplifying with (164), (5614)
% 133.67/19.20 | | | | | | | | | | gives:
% 133.67/19.20 | | | | | | | | | | (5615) all_52_13 = all_20_0
% 133.67/19.20 | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | COMBINE_EQS: (259), (5615) imply:
% 133.67/19.20 | | | | | | | | | | (5616) all_54_7 = all_20_0
% 133.67/19.20 | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | REDUCE: (145), (5615) imply:
% 133.67/19.20 | | | | | | | | | | (5617) ~ (all_52_1 = all_20_0)
% 133.67/19.20 | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | REDUCE: (117), (5615) imply:
% 133.67/19.20 | | | | | | | | | | (5618) ~ (all_52_9 = all_20_0)
% 133.67/19.20 | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | REDUCE: (113), (5615) imply:
% 133.67/19.20 | | | | | | | | | | (5619) ~ (all_52_12 = all_20_0)
% 133.67/19.20 | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | REDUCE: (110), (5615) imply:
% 133.67/19.20 | | | | | | | | | | (5620) ~ (all_52_14 = all_20_0)
% 133.67/19.20 | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | SIMP: (5620) implies:
% 133.67/19.20 | | | | | | | | | | (5621) ~ (all_52_14 = all_20_0)
% 133.67/19.20 | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | REDUCE: (5609), (5615) imply:
% 133.67/19.20 | | | | | | | | | | (5622) ~ (all_20_0 = e2)
% 133.67/19.20 | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | REDUCE: (5148), (5615) imply:
% 133.67/19.20 | | | | | | | | | | (5623) ~ (all_20_0 = e1)
% 133.67/19.20 | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | BETA: splitting (197) gives:
% 133.67/19.20 | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | Case 1:
% 133.67/19.20 | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | (5624) all_54_7 = e3
% 133.67/19.20 | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | COMBINE_EQS: (5616), (5624) imply:
% 133.67/19.20 | | | | | | | | | | | (5625) all_20_0 = e3
% 133.67/19.20 | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | REDUCE: (5613), (5625) imply:
% 133.67/19.20 | | | | | | | | | | | (5626) $false
% 133.67/19.20 | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | CLOSE: (5626) is inconsistent.
% 133.67/19.20 | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | Case 2:
% 133.67/19.20 | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | (5627) ~ (all_54_7 = e3)
% 133.67/19.20 | | | | | | | | | | | (5628) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 133.67/19.20 | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | BETA: splitting (5628) gives:
% 133.67/19.20 | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | Case 1:
% 133.67/19.20 | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | (5629) all_54_7 = e2
% 133.67/19.20 | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | COMBINE_EQS: (5616), (5629) imply:
% 133.67/19.20 | | | | | | | | | | | | (5630) all_20_0 = e2
% 133.67/19.20 | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | REDUCE: (5622), (5630) imply:
% 133.67/19.20 | | | | | | | | | | | | (5631) $false
% 133.67/19.20 | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | CLOSE: (5631) is inconsistent.
% 133.67/19.20 | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | Case 2:
% 133.67/19.20 | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | (5632) ~ (all_54_7 = e2)
% 133.67/19.20 | | | | | | | | | | | | (5633) all_54_7 = e1 | all_54_7 = e0
% 133.67/19.20 | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | BETA: splitting (5633) gives:
% 133.67/19.20 | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | Case 1:
% 133.67/19.20 | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | (5634) all_54_7 = e1
% 133.67/19.20 | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | COMBINE_EQS: (5616), (5634) imply:
% 133.67/19.20 | | | | | | | | | | | | | (5635) all_20_0 = e1
% 133.67/19.20 | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | REDUCE: (5623), (5635) imply:
% 133.67/19.20 | | | | | | | | | | | | | (5636) $false
% 133.67/19.20 | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | CLOSE: (5636) is inconsistent.
% 133.67/19.20 | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | Case 2:
% 133.67/19.20 | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | (5637) all_54_7 = e0
% 133.67/19.20 | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | COMBINE_EQS: (5616), (5637) imply:
% 133.67/19.20 | | | | | | | | | | | | | (5638) all_20_0 = e0
% 133.67/19.20 | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | REDUCE: (5617), (5638) imply:
% 133.67/19.20 | | | | | | | | | | | | | (5639) ~ (all_52_1 = e0)
% 133.67/19.20 | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | REDUCE: (5618), (5638) imply:
% 133.67/19.20 | | | | | | | | | | | | | (5640) ~ (all_52_9 = e0)
% 133.67/19.20 | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | REDUCE: (5619), (5638) imply:
% 133.67/19.20 | | | | | | | | | | | | | (5641) ~ (all_52_12 = e0)
% 133.67/19.20 | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | REDUCE: (5621), (5638) imply:
% 133.67/19.20 | | | | | | | | | | | | | (5642) ~ (all_52_14 = e0)
% 133.67/19.20 | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | REDUCE: (5613), (5638) imply:
% 133.67/19.20 | | | | | | | | | | | | | (5643) ~ (e3 = e0)
% 133.67/19.20 | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | REDUCE: (5622), (5638) imply:
% 133.67/19.20 | | | | | | | | | | | | | (5644) ~ (e2 = e0)
% 133.67/19.20 | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | REDUCE: (5623), (5638) imply:
% 133.67/19.20 | | | | | | | | | | | | | (5645) ~ (e1 = e0)
% 133.67/19.20 | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | REDUCE: (5614), (5638) imply:
% 133.67/19.20 | | | | | | | | | | | | | (5646) op(e2, e0) = e0
% 133.67/19.20 | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | BETA: splitting (208) gives:
% 133.67/19.20 | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | Case 1:
% 133.67/19.20 | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | (5647) all_57_15 = e0 & op(e0, e0) = e0
% 133.67/19.20 | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | ALPHA: (5647) implies:
% 133.67/19.20 | | | | | | | | | | | | | | (5648) op(e0, e0) = e0
% 133.67/19.20 | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | REF_CLOSE: (5), (5611), (5648), (function-axioms) are
% 133.67/19.20 | | | | | | | | | | | | | | inconsistent by sub-proof #714.
% 133.67/19.20 | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | Case 2:
% 133.67/19.20 | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | (5649) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 133.67/19.20 | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 133.67/19.20 | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 133.67/19.20 | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 133.67/19.20 | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 133.67/19.20 | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | ALPHA: (5649) implies:
% 133.67/19.20 | | | | | | | | | | | | | | (5650) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 133.67/19.20 | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 133.67/19.20 | | | | | | | | | | | | | | e0) = e0)
% 133.67/19.20 | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | BETA: splitting (5650) gives:
% 133.67/19.20 | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | Case 1:
% 133.67/19.20 | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | (5651) all_57_9 = e0 & op(e3, e0) = e0
% 133.67/19.20 | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | REF_CLOSE: (168), (5641), (5651), (function-axioms) are
% 133.67/19.20 | | | | | | | | | | | | | | | inconsistent by sub-proof #618.
% 133.67/19.20 | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | Case 2:
% 133.67/19.20 | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | (5652) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 133.67/19.20 | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 133.67/19.20 | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | BETA: splitting (5652) gives:
% 133.67/19.20 | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | Case 1:
% 133.67/19.20 | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | (5653) all_57_10 = e0 & op(e2, e0) = e0
% 133.67/19.20 | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | ALPHA: (5653) implies:
% 133.67/19.20 | | | | | | | | | | | | | | | | (5654) all_57_10 = e0
% 133.67/19.20 | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 133.67/19.20 | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.20 | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | (5655) ~ (all_28_2 = e3)
% 133.67/19.20 | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | REDUCE: (316), (5655) imply:
% 133.67/19.20 | | | | | | | | | | | | | | | | | (5656) ~ (all_6_2 = e3)
% 133.67/19.20 | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 133.67/19.20 | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.20 | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | (5657) ~ (all_32_2 = e1)
% 133.67/19.20 | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | REDUCE: (312), (5657) imply:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | (5658) ~ (all_10_2 = e1)
% 133.67/19.20 | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 133.67/19.20 | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | (5659) all_54_0 = e3
% 133.67/19.20 | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (5659) imply:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | (5660) all_10_2 = e3
% 133.67/19.20 | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | REDUCE: (336), (5660) imply:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | (5661) ~ (all_52_1 = e3)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | REDUCE: (342), (5660) imply:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | (5662) ~ (all_52_4 = e3)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | REDUCE: (346), (5660) imply:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | (5663) ~ (all_52_12 = e3)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | (5664) all_54_4 = e3
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (5664) imply:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | (5665) all_52_1 = e3
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | REDUCE: (5661), (5665) imply:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | (5666) $false
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | CLOSE: (5666) is inconsistent.
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | (5667) ~ (all_54_4 = e3)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | (5668) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | BETA: splitting (5668) gives:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5669) all_54_4 = e2
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (5669) imply:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5670) all_52_1 = e2
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (5670) imply:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5671) ~ (all_52_9 = e2)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | SIMP: (5671) implies:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5672) ~ (all_52_9 = e2)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | REDUCE: (5661), (5670) imply:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5673) ~ (e3 = e2)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | (5674) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5674) gives:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | (5675) all_57_4 = e2 & op(e3, e1) = e2
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5675) implies:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | (5676) all_57_4 = e2
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | (5677) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5677) gives:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (5678) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5678) gives:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (5679) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5679) implies:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (5680) op(e3, e3) = e2
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (204), (278), (5154), (5156), (5658),
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (5680), (function-axioms) are inconsistent by
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #776.
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (5681) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5681) implies:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (5682) op(e3, e3) = e1
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (168), (170), (238), (5662), (5663),
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (5676), (5682), (function-axioms) are inconsistent
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #732.
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (5683) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (168), (5153), (5663), (5683),
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | #190.
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | (5684) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5684) gives:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (5685) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (165), (5656), (5672), (5685),
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | #769.
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (5686) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (39), (91), (157), (190), (246),
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (332), (364), (372), (5153), (5607), (5611),
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (5646), (5686), (function-axioms) are inconsistent
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #154.
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | (5687) all_57_5 = e2 & op(e2, e1) = e2
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5687) implies:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | (5688) op(e2, e1) = e2
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (5672), (5688), (function-axioms) are
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #770.
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | (5689) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (157), (372), (5607), (5689),
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | #511.
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5690) all_54_4 = e1 | all_54_4 = e0
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (5143), (5639), (5690) are inconsistent by
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | sub-proof #153.
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.20 | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | (5691) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 133.67/19.20 | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (5154), (5156), (5658), (5691) are
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #777.
% 133.67/19.20 | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.20 | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.20 | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | (5692) all_32_2 = e1
% 133.67/19.20 | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (312), (5692) imply:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | (5693) all_10_2 = e1
% 133.67/19.20 | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | SIMP: (5693) implies:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | (5694) all_10_2 = e1
% 133.67/19.20 | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | REDUCE: (344), (5694) imply:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | (5695) ~ (all_52_8 = e1)
% 133.67/19.20 | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | REDUCE: (346), (5694) imply:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | (5696) ~ (all_52_12 = e1)
% 133.67/19.20 | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | REDUCE: (5156), (5694) imply:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | (5697) ~ (e2 = e1)
% 133.67/19.20 | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | REDUCE: (45), (5694) imply:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | (5698) op(e3, e3) = e1
% 133.67/19.20 | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 133.67/19.20 | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | (5699) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | BETA: splitting (5699) gives:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | (5700) all_57_9 = e1 & op(e3, e0) = e1
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | ALPHA: (5700) implies:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | (5701) all_57_9 = e1
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5702) all_54_3 = e3
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (5702) imply:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5703) all_52_12 = e3
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (5703) imply:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5704) ~ (all_52_14 = e3)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | SIMP: (5704) implies:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5705) ~ (all_52_14 = e3)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (160), (165), (167), (214),
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (223), (5153), (5611), (5639), (5640), (5701),
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5705), (function-axioms) are inconsistent by
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | sub-proof #150.
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5706) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (5608), (5641), (5696), (5706) are
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #320.
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | (5707) all_57_10 = e1 & op(e2, e0) = e1
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | ALPHA: (5707) implies:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | (5708) op(e2, e0) = e1
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5646), (5708), (function-axioms) are
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #695.
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.20 | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | (5709) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | BETA: splitting (5709) gives:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | (5710) all_57_11 = e1 & op(e1, e0) = e1
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | ALPHA: (5710) implies:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | (5711) all_57_11 = e1
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5712) all_54_3 = e3
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (5712) imply:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5713) all_52_12 = e3
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (5713) imply:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5714) ~ (all_52_4 = e3)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (5713) imply:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5715) ~ (all_52_8 = e3)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (5713) imply:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5716) ~ (all_52_14 = e3)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | SIMP: (5716) implies:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5717) ~ (all_52_14 = e3)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | (5718) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5718) gives:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | (5719) all_57_9 = e3 & op(e3, e0) = e3
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5719) implies:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | (5720) all_57_9 = e3
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | (5721) all_54_11 = e3
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (5717), (5721) are inconsistent by
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #260.
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | (5722) ~ (all_54_11 = e3)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | (5723) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5723) gives:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (5724) all_54_11 = e2
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (5610), (5724) are inconsistent by
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #259.
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (5725) ~ (all_54_11 = e2)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (5726) all_54_11 = e1 | all_54_11 = e0
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (5727) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5727) gives:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5728) all_57_12 = e1 & op(e0, e3) = e1
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5728) implies:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5729) all_57_12 = e1
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (235), (237),
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5698), (5729), (function-axioms) are inconsistent
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #583.
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5730) all_57_13 = e1 & op(e0, e2) = e1
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5730) implies:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5731) all_57_13 = e1
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5732) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (170), (5153), (5714), (5732),
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #183.
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5733) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5733) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5734) all_57_7 = e3 & op(e1, e2) = e3
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5734) implies:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5735) all_57_7 = e3
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5736) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5736) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5737) all_57_6 = e2 & op(e1, e3) = e2
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5737) implies:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5738) op(e1, e3) = e2
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5739) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5739) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5740) all_57_1 = e0 & op(e3, e2) = e0
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5740) implies:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5741) all_57_1 = e0
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5742) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (5698), (5741), (5742),
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #148.
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5743) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5743) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5744) all_57_4 = e2 & op(e3, e1) = e2
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5744) implies:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5745) op(e3, e1) = e2
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5746) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5746) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5747) all_57_1 = e2 & op(e3, e2) = e2
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5741), (5747) are inconsistent by sub-proof
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #149.
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5748) all_57_3 = e2 & op(e2, e2) = e2
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5748) implies:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5749) op(e2, e2) = e2
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (39), (45), (91), (121), (123), (149),
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (163), (164), (165), (167), (169), (190),
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206), (246), (332), (344), (361), (364), (5154),
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5609), (5611), (5656), (5738), (5745), (5749),
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #522.
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5750) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5750) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5751) all_57_7 = e2 & op(e1, e2) = e2
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5751) implies:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5752) all_57_7 = e2
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5735), (5752) are inconsistent by sub-proof
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #486.
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5753) all_57_13 = e2 & op(e0, e2) = e2
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5753) implies:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5754) all_57_13 = e2
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5731), (5754) imply:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5755) e2 = e1
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (5755) imply:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5756) $false
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5756) is inconsistent.
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5757) all_57_9 = e2 & op(e3, e0) = e2
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (5608), (5757), (function-axioms) are
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #460.
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5758) all_57_3 = e0 & op(e2, e2) = e0
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5758) implies:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5759) all_57_3 = e0
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5760) op(e2, e2) = e0
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (224), (225), (226),
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5646), (5654), (5759), (5760), (function-axioms)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #446.
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5761) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5761) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5762) all_57_7 = e0 & op(e1, e2) = e0
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5735), (5762) are inconsistent by sub-proof
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #147.
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5763) all_57_13 = e0 & op(e0, e2) = e0
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5763) implies:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5764) all_57_13 = e0
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5731), (5764) imply:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5765) e1 = e0
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5711), (5765) imply:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5766) all_57_11 = e0
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (212), (5611), (5646), (5720),
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5766), (function-axioms) are inconsistent by
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #257.
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5767) all_57_7 = e2 & op(e1, e2) = e2
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5735), (5767) are inconsistent by sub-proof
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #385.
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5768) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (39), (208), (212),
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (5611), (5720), (5768), (function-axioms)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #146.
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5769) all_57_13 = e3 & op(e0, e2) = e3
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5769) implies:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5770) all_57_13 = e3
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5731), (5770) imply:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5771) e3 = e1
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (160), (165), (167), (214),
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223), (5153), (5611), (5639), (5640), (5717),
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5720), (5771), (function-axioms) are inconsistent
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #145.
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (5772) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5772) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5773) all_57_14 = e1 & op(e0, e1) = e1
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5773) implies:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5774) all_57_14 = e1
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5726) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5775) all_54_11 = e1
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (5775) imply:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5776) all_52_14 = e1
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5776) implies:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5777) all_52_14 = e1
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (5777) imply:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5778) ~ (all_6_2 = e1)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5778) implies:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5779) ~ (all_6_2 = e1)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5717), (5777) imply:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5780) ~ (e3 = e1)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5781) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5781) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5782) all_57_4 = e3 & op(e3, e1) = e3
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5782) implies:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5783) op(e3, e1) = e3
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (120), (169), (201), (269), (5608), (5641),
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5696), (5783), (function-axioms) are inconsistent
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #319.
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5784) all_57_5 = e3 & op(e2, e1) = e3
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5784) implies:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5785) all_57_5 = e3
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5786) all_54_10 = e3
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (5656), (5786) are inconsistent by
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #742.
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5787) ~ (all_54_10 = e3)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5788) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5788) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5789) all_54_10 = e2
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (372), (5789) are inconsistent by sub-proof
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #741.
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5790) ~ (all_54_10 = e2)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5791) all_54_10 = e1 | all_54_10 = e0
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5791) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5792) all_54_10 = e1
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (5779), (5792) are inconsistent by
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #736.
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5793) all_54_10 = e0
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (5793) imply:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5794) all_6_2 = e0
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5794) implies:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5795) all_6_2 = e0
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (5795) imply:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5796) op(e1, e1) = e0
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5797) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5797) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5798) all_57_2 = e2 & op(e2, e3) = e2
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5798) implies:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5799) all_57_2 = e2
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5800) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5800) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5801) all_57_4 = e2 & op(e3, e1) = e2
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5801) implies:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5802) all_57_4 = e2
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5803) all_54_2 = e3
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (5803) imply:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5804) all_52_8 = e3
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5804) implies:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5805) all_52_8 = e3
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5715), (5805) imply:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5806) $false
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5806) is inconsistent.
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5807) ~ (all_54_2 = e3)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5808) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5809) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5809) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5810) all_57_0 = e0 & op(e3, e3) = e0
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5810) implies:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5811) op(e3, e3) = e0
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5698), (5811), (function-axioms) are
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #717.
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5812) all_57_1 = e0 & op(e3, e2) = e0
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5812) implies:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5813) all_57_1 = e0
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5814) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5814) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5815) all_57_0 = e0 & op(e3, e3) = e0
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5815) implies:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5816) op(e3, e3) = e0
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5698), (5816), (function-axioms) are
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #717.
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5817) all_57_2 = e0 & op(e2, e3) = e0
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (5639), (5817), (function-axioms) are
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #225.
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5818) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5818) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5819) all_57_6 = e0 & op(e1, e3) = e0
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5819) implies:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5820) all_57_6 = e0
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5821) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5821) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5822) all_57_6 = e3 & op(e1, e3) = e3
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5822) implies:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5823) all_57_6 = e3
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5820), (5823) imply:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5824) e3 = e0
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5720), (5824) imply:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5825) all_57_9 = e0
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (170), (238), (5698), (5714),
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5802), (5825), (function-axioms) are inconsistent
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #613.
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5826) all_57_7 = e3 & op(e1, e2) = e3
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5826) implies:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5827) all_57_7 = e3
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5828) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5828) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5829) all_57_6 = e2 & op(e1, e3) = e2
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5829) implies:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5830) all_57_6 = e2
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5820), (5830) imply:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5831) e2 = e0
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5802), (5831) imply:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5832) all_57_4 = e0
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (39), (221), (222),
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (5656), (5774), (5832), (function-axioms)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #558.
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5833) all_57_7 = e2 & op(e1, e2) = e2
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5827), (5833) are inconsistent by sub-proof
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #385.
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5834) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (39), (208), (212),
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (5611), (5720), (5834), (function-axioms)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #146.
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5835) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5835) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5836) all_57_8 = e3 & op(e1, e1) = e3
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5836) implies:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5837) op(e1, e1) = e3
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5796), (5837), (function-axioms) are
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753.
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5838) all_57_11 = e3 & op(e1, e0) = e3
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (5717), (5838), (function-axioms) are
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #750.
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5839) all_57_12 = e0 & op(e0, e3) = e0
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5839) implies:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5840) all_57_12 = e0
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5808) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5841) all_54_2 = e2
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (5841) imply:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5842) all_52_8 = e2
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (5842) imply:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5843) ~ (all_52_9 = e2)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5843) implies:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5844) ~ (all_52_9 = e2)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (5842) imply:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5845) ~ (all_52_11 = e2)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5715), (5842) imply:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5846) ~ (e3 = e2)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5847) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5847) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5848) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5848) gives:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5849) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5849) implies:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5850) op(e3, e3) = e2
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (234), (5720), (5802), (5813),
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5850), (function-axioms) are inconsistent by
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #280.
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5851) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5851) implies:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5852) ~ (all_56_5 = e3)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5853) op(e1, e3) = all_56_5
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (237), (5698), (5799), (5840),
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5852), (5853), (function-axioms) are inconsistent
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #144.
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5854) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (5153), (5698), (5854),
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #175.
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5855) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5855) gives:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5856) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (165), (5796), (5844), (5856),
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #143.
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5857) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (39), (91), (157), (190), (246),
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332), (364), (372), (5153), (5607), (5611),
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5646), (5857), (function-axioms) are inconsistent
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #154.
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5858) all_54_2 = e1 | all_54_2 = e0
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (194), (270), (334), (361), (372), (5656),
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5695), (5796), (5858), (function-axioms) are
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #477.
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5859) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5859) gives:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5860) all_57_4 = e0 & op(e3, e1) = e0
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5860) implies:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5861) all_57_4 = e0
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (39), (221), (222),
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (5656), (5774), (5861), (function-axioms)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #558.
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5862) all_57_9 = e0 & op(e3, e0) = e0
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5862) implies:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5863) all_57_9 = e0
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (170), (238), (5698), (5714),
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5802), (5863), (function-axioms) are inconsistent
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #613.
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5864) all_57_5 = e2 & op(e2, e1) = e2
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5785), (5864) are inconsistent by sub-proof
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #677.
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5865) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (157), (372), (5607), (5865),
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #511.
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5866) all_57_3 = e2 & op(e2, e2) = e2
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5866) implies:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5867) all_57_3 = e2
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5152), (5867) are inconsistent by sub-proof
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #728.
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5868) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5868) gives:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5869) all_57_5 = e2 & op(e2, e1) = e2
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5869) implies:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5870) all_57_5 = e2
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5785), (5870) are inconsistent by sub-proof
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #501.
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5871) all_57_10 = e2 & op(e2, e0) = e2
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5871) implies:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5872) op(e2, e0) = e2
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (5609), (5872), (function-axioms) are
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5873) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5873) gives:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5874) all_57_8 = e3 & op(e1, e1) = e3
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5874) implies:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5875) op(e1, e1) = e3
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (5656), (5875), (function-axioms) are
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #771.
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5876) all_57_14 = e3 & op(e0, e1) = e3
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5876) implies:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5877) all_57_14 = e3
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5774), (5877) imply:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5878) e3 = e1
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (160), (165), (167), (214),
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223), (5153), (5611), (5639), (5640), (5717),
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5720), (5878), (function-axioms) are inconsistent
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #145.
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5879) all_54_11 = e0
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (5642), (5879) are inconsistent by
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #258.
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5880) all_57_15 = e1 & op(e0, e0) = e1
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5880) implies:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5881) op(e0, e0) = e1
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5611), (5881), (function-axioms) are
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #636.
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | (5882) all_57_10 = e3 & op(e2, e0) = e3
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5882) implies:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | (5883) all_57_10 = e3
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (165), (167), (223), (5153), (5639),
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | (5640), (5883), (function-axioms) are inconsistent
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #151.
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | (5884) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (160), (5611), (5717), (5884),
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | #330.
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | (5885) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (5608), (5641), (5696), (5885) are
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #320.
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | (5886) all_57_15 = e1 & op(e0, e0) = e1
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | ALPHA: (5886) implies:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | (5887) op(e0, e0) = e1
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5611), (5887), (function-axioms) are
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #636.
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.22 | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.22 | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | End of split
% 133.67/19.22 | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.22 | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | (5888) all_28_2 = e3
% 133.67/19.22 | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | COMBINE_EQS: (316), (5888) imply:
% 133.67/19.22 | | | | | | | | | | | | | | | | | (5889) all_6_2 = e3
% 133.67/19.22 | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | REDUCE: (362), (5889) imply:
% 133.67/19.22 | | | | | | | | | | | | | | | | | (5890) ~ (all_52_9 = e3)
% 133.67/19.22 | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | REDUCE: (364), (5889) imply:
% 133.67/19.22 | | | | | | | | | | | | | | | | | (5891) ~ (all_52_11 = e3)
% 133.67/19.22 | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | REDUCE: (366), (5889) imply:
% 133.67/19.22 | | | | | | | | | | | | | | | | | (5892) ~ (all_52_14 = e3)
% 133.67/19.22 | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | REDUCE: (39), (5889) imply:
% 133.67/19.22 | | | | | | | | | | | | | | | | | (5893) op(e1, e1) = e3
% 133.67/19.22 | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 133.67/19.22 | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.22 | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | (5894) all_54_6 = e3
% 133.67/19.22 | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (5894) imply:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | (5895) all_52_9 = e3
% 133.67/19.22 | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | REDUCE: (5890), (5895) imply:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | (5896) $false
% 133.67/19.22 | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | CLOSE: (5896) is inconsistent.
% 133.67/19.22 | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.22 | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | (5897) ~ (all_54_6 = e3)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | (5898) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 133.67/19.22 | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 133.67/19.22 | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | (5899) all_54_11 = e3
% 133.67/19.22 | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (5892), (5899) are inconsistent by
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | sub-proof #260.
% 133.67/19.22 | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | (5900) ~ (all_54_11 = e3)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | (5901) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 133.67/19.22 | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | BETA: splitting (5901) gives:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | (5902) all_54_11 = e2
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (5610), (5902) are inconsistent by
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | sub-proof #259.
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | (5903) ~ (all_54_11 = e2)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | (5904) all_54_11 = e1 | all_54_11 = e0
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | (5905) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5905) gives:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | (5906) all_57_2 = e3 & op(e2, e3) = e3
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5906) implies:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | (5907) all_57_2 = e3
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | (5908) op(e2, e3) = e3
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5898) gives:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | (5909) all_54_6 = e2
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (5909) imply:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | (5910) all_52_9 = e2
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (5910) imply:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | (5911) ~ (all_52_1 = e2)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (5910) imply:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | (5912) ~ (all_52_8 = e2)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (5910) imply:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | (5913) ~ (all_52_11 = e2)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | (5914) all_54_4 = e3
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (5914) imply:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | (5915) all_52_1 = e3
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (5915) imply:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | (5916) ~ (all_52_3 = e3)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5916) implies:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | (5917) ~ (all_52_3 = e3)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | (5918) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (167), (5156), (5911), (5918),
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | #535.
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | (5919) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5919) gives:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | (5920) all_57_6 = e2 & op(e1, e3) = e2
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5920) implies:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | (5921) all_57_6 = e2
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5922) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (167), (5154), (5639), (5922),
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | #142.
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5923) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5923) gives:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5924) all_57_6 = e0 & op(e1, e3) = e0
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5921), (5924) are inconsistent by sub-proof
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #520.
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5925) all_57_12 = e0 & op(e0, e3) = e0
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5925) implies:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5926) all_57_12 = e0
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5927) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5927) gives:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5928) all_57_12 = e1 & op(e0, e3) = e1
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5928) implies:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5929) all_57_12 = e1
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5926), (5929) are inconsistent by sub-proof
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #581.
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5930) all_57_13 = e1 & op(e0, e2) = e1
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5930) implies:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5931) all_57_13 = e1
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5904) gives:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5932) all_54_11 = e1
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (5932) imply:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5933) all_52_14 = e1
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5933) implies:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5934) all_52_14 = e1
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (5934) imply:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5935) ~ (all_52_2 = e1)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (5934) imply:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5936) ~ (all_52_12 = e1)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5892), (5934) imply:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5937) ~ (e3 = e1)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5610), (5934) imply:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5938) ~ (e2 = e1)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5939) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5939) gives:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5940) all_57_0 = e1 & op(e3, e3) = e1
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5940) implies:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5941) op(e3, e3) = e1
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5942) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (167), (5152), (5911), (5942),
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #141.
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5943) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5943) gives:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5944) all_57_5 = e2 & op(e2, e1) = e2
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5944) implies:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5945) all_57_5 = e2
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5946) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5946) gives:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5947) all_57_9 = e3 & op(e3, e0) = e3
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5947) implies:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5948) all_57_9 = e3
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5949) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5949) gives:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5950) all_57_0 = e2 & op(e3, e3) = e2
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5950) implies:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5951) op(e3, e3) = e2
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5941), (5951), (function-axioms) are
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743.
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5952) all_57_1 = e2 & op(e3, e2) = e2
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5952) implies:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5953) all_57_1 = e2
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5954) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5954) gives:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5955) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (120), (169), (201), (269), (5608), (5641),
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5936), (5941), (5955), (function-axioms) are
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #318.
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5956) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (5153), (5941), (5956),
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #175.
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5957) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5957) gives:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5958) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5958) gives:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5959) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5959) implies:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5960) op(e1, e3) = e1
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (5935), (5960), (function-axioms) are
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #725.
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5961) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2,
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5961) implies:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5962) ~ (all_56_5 = e3)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5963) op(e1, e3) = all_56_5
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5964) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5964) gives:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5965) all_57_0 = e0 & op(e3, e3) = e0
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5965) implies:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5966) op(e3, e3) = e0
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5941), (5966), (function-axioms) are
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #717.
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5967) all_57_1 = e0 & op(e3, e2) = e0
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5967) implies:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5968) all_57_1 = e0
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5953), (5968) imply:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5969) e2 = e0
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5921), (5969) imply:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5970) all_57_6 = e0
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (235), (237), (5926),
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5941), (5962), (5963), (5970), (function-axioms)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #139.
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5971) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5971) gives:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5972) all_57_4 = e0 & op(e3, e1) = e0
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5972) implies:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5973) all_57_4 = e0
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5974) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5974) gives:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5975) all_57_12 = e3 & op(e0, e3) = e3
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (5917), (5975), (function-axioms) are
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #628.
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5976) all_57_13 = e3 & op(e0, e2) = e3
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5976) implies:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5977) all_57_13 = e3
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5931), (5977) imply:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5978) e3 = e1
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5948), (5978) imply:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5979) all_57_9 = e1
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (236), (238), (5941),
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5973), (5979), (function-axioms) are inconsistent
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #688.
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5980) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5980) gives:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5981) all_57_14 = e3 & op(e0, e1) = e3
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5981) implies:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5982) all_57_14 = e3
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5983) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5983) gives:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5984) all_57_4 = e1 & op(e3, e1) = e1
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5973), (5984) are inconsistent by sub-proof
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #419.
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5985) all_57_5 = e1 & op(e2, e1) = e1
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5945), (5985) are inconsistent by sub-proof
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #500.
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5986) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5986) gives:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5987) all_57_8 = e1 & op(e1, e1) = e1
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5987) implies:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5988) op(e1, e1) = e1
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (5893), (5988), (function-axioms) are
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #662.
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5989) all_57_14 = e1 & op(e0, e1) = e1
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5982), (5989) are inconsistent by sub-proof
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #247.
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5990) all_57_15 = e3 & op(e0, e0) = e3
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5990) implies:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5991) op(e0, e0) = e3
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5611), (5991), (function-axioms) are
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #634.
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5992) all_57_9 = e0 & op(e3, e0) = e0
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (5641), (5992), (function-axioms) are
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #618.
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5993) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (39), (91), (157), (190),
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224), (246), (332), (364), (372), (5607), (5611),
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5646), (5907), (5945), (5993), (function-axioms)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #138.
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5994) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5994) gives:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5995) all_57_4 = e2 & op(e3, e1) = e2
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (5912), (5995), (function-axioms) are
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #442.
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5996) all_57_9 = e2 & op(e3, e0) = e2
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (5608), (5996), (function-axioms) are
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #460.
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5997) all_57_10 = e3 & op(e2, e0) = e3
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5997) implies:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5998) all_57_10 = e3
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (165), (167), (223), (5153), (5639),
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5640), (5998), (function-axioms) are inconsistent
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #151.
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5999) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (160), (5611), (5892), (5999),
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #330.
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6000) all_57_10 = e2 & op(e2, e0) = e2
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6000) implies:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6001) op(e2, e0) = e2
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (5609), (6001), (function-axioms) are
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6002) all_57_2 = e1 & op(e2, e3) = e1
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (5143), (6002), (function-axioms) are
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #676.
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6003) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (163), (5926), (5935), (6003),
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #137.
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6004) all_54_11 = e0
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (5642), (6004) are inconsistent by
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #258.
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6005) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6005) gives:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6006) all_57_14 = e1 & op(e0, e1) = e1
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6006) implies:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6007) all_57_14 = e1
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5904) gives:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6008) all_54_11 = e1
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (6008) imply:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6009) all_52_14 = e1
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6009) implies:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6010) all_52_14 = e1
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (6010) imply:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6011) ~ (all_52_2 = e1)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5892), (6010) imply:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6012) ~ (e3 = e1)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5610), (6010) imply:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6013) ~ (e2 = e1)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6014) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6014) gives:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6015) all_57_0 = e1 & op(e3, e3) = e1
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6015) implies:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6016) op(e3, e3) = e1
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6017) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (167), (5152), (5911), (6017),
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #141.
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6018) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6018) gives:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6019) all_57_5 = e2 & op(e2, e1) = e2
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6019) implies:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6020) all_57_5 = e2
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6021) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6021) gives:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6022) all_57_9 = e3 & op(e3, e0) = e3
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6022) implies:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6023) all_57_9 = e3
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6024) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6024) gives:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6025) all_57_0 = e2 & op(e3, e3) = e2
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6025) implies:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6026) op(e3, e3) = e2
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6016), (6026), (function-axioms) are
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743.
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6027) all_57_1 = e2 & op(e3, e2) = e2
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6027) implies:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6028) all_57_1 = e2
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6029) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6029) gives:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6030) all_57_9 = e1 & op(e3, e0) = e1
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6030) implies:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6031) all_57_9 = e1
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (160), (165), (167), (214),
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223), (5153), (5611), (5639), (5640), (5892),
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6031), (function-axioms) are inconsistent by
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #150.
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6032) all_57_10 = e1 & op(e2, e0) = e1
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6032) implies:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6033) op(e2, e0) = e1
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5646), (6033), (function-axioms) are
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #695.
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6034) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6034) gives:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6035) all_57_11 = e1 & op(e1, e0) = e1
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6035) implies:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6036) all_57_11 = e1
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6037) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6037) gives:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6038) all_57_4 = e0 & op(e3, e1) = e0
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6038) implies:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6039) all_57_4 = e0
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6040) op(e3, e1) = e0
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6041) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6041) gives:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6042) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6042) gives:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6043) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6043) implies:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6044) op(e3, e3) = e2
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6045) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6028), (6044), (6045), (function-axioms) are
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #239.
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6046) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6046) gives:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6047) all_57_4 = e1 & op(e3, e1) = e1
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6047) implies:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6048) all_57_4 = e1
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6039), (6048) imply:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6049) e1 = e0
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6049) implies:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6050) e1 = e0
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6007), (6050) imply:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6051) all_57_14 = e0
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (39), (220), (5893), (6020),
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6039), (6051), (function-axioms) are inconsistent
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #230.
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6052) all_57_9 = e1 & op(e3, e0) = e1
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6023), (6052) are inconsistent by sub-proof
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #640.
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6053) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6053) implies:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6054) op(e3, e1) = e3
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (169), (6040), (6054), (function-axioms) are
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #600.
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6055) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (5153), (6016), (6055),
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #175.
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6056) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6056) gives:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6057) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6057) gives:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6058) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6058) implies:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6059) op(e1, e3) = e1
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (6011), (6059), (function-axioms) are
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #725.
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6060) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 =
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2,
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6060) implies:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6061) ~ (all_56_5 = e3)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6062) op(e1, e1) = all_56_21
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6063) op(e1, e2) = all_56_13
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6064) op(e1, e3) = all_56_5
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5141) gives:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6065) ~ (all_8_0 = e0) & op(e1, e2) = all_8_0 &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_0)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6065) implies:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6066) ~ (all_8_0 = e0)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6067) op(e1, e2) = all_8_0
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6068) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6068) gives:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6069) all_57_6 = e0 & op(e1, e3) = e0
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6069) implies:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6070) all_57_6 = e0
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (235), (237), (5926),
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6016), (6061), (6064), (6070), (function-axioms)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #139.
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6071) all_57_7 = e0 & op(e1, e2) = e0
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6071) implies:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6072) op(e1, e2) = e0
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_0,
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13, e2, e1, simplifying with (6063), (6067)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6073) all_56_13 = all_8_0
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13, e2, e1, simplifying with (6063), (6072)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6074) all_56_13 = e0
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6073), (6074) imply:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6075) all_8_0 = e0
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6075) implies:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6076) all_8_0 = e0
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6066), (6076) imply:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6077) $false
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6077) is inconsistent.
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6078) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6078) gives:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6079) all_57_8 = e0 & op(e1, e1) = e0
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6079) implies:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6080) op(e1, e1) = e0
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (169), (361), (6040), (6080),
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #619.
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6081) all_57_11 = e0 & op(e1, e0) = e0
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6081) implies:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6082) all_57_11 = e0
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (212), (5611), (5646), (6023),
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6082), (function-axioms) are inconsistent by
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #257.
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6083) ~ (all_8_1 = e3) & op(e1, e1) = all_8_1 &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_1)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6083) implies:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6084) ~ (all_8_1 = e3)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6085) op(e1, e1) = all_8_1
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_1,
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21, e1, e1, simplifying with (6062), (6085)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6086) all_56_21 = all_8_1
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21, e1, e1, simplifying with (5893), (6062)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6087) all_56_21 = e3
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6086), (6087) imply:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6088) all_8_1 = e3
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6088) implies:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6089) all_8_1 = e3
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6084), (6089) imply:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6090) $false
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6090) is inconsistent.
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6091) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (39), (91), (157), (190),
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224), (246), (332), (364), (372), (5607), (5611),
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5646), (5907), (6020), (6091), (function-axioms)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #138.
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6092) all_57_5 = e0 & op(e2, e1) = e0
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (5640), (6092), (function-axioms) are
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #455.
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6093) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6093) gives:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6094) all_57_8 = e0 & op(e1, e1) = e0
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6094) implies:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6095) op(e1, e1) = e0
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5893), (6095), (function-axioms) are
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753.
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6096) all_57_14 = e0 & op(e0, e1) = e0
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6096) implies:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6097) all_57_14 = e0
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6007), (6097) imply:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6098) e1 = e0
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6098) implies:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6099) e1 = e0
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6036), (6099) imply:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6100) all_57_11 = e0
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (212), (5611), (5646), (6023),
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6100), (function-axioms) are inconsistent by
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #257.
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6101) all_57_15 = e1 & op(e0, e0) = e1
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6101) implies:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6102) op(e0, e0) = e1
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5611), (6102), (function-axioms) are
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #636.
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6103) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6103) gives:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6104) all_57_4 = e2 & op(e3, e1) = e2
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (5912), (6104), (function-axioms) are
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #442.
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6105) all_57_9 = e2 & op(e3, e0) = e2
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (5608), (6105), (function-axioms) are
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #460.
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6106) all_57_10 = e3 & op(e2, e0) = e3
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6106) implies:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6107) all_57_10 = e3
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (165), (167), (223), (5153), (5639),
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5640), (6107), (function-axioms) are inconsistent
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #151.
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6108) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (160), (5611), (5892), (6108),
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #330.
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6109) all_57_10 = e2 & op(e2, e0) = e2
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6109) implies:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6110) op(e2, e0) = e2
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (5609), (6110), (function-axioms) are
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6111) all_57_2 = e1 & op(e2, e3) = e1
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (5143), (6111), (function-axioms) are
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #676.
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6112) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (163), (5926), (6011), (6112),
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #137.
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6113) all_54_11 = e0
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (5642), (6113) are inconsistent by
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #258.
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6114) all_57_15 = e1 & op(e0, e0) = e1
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6114) implies:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6115) op(e0, e0) = e1
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5611), (6115), (function-axioms) are
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #636.
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | (6116) all_57_12 = e2 & op(e0, e3) = e2
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6116) implies:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | (6117) all_57_12 = e2
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (208), (209),
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (5611), (5891), (6117), (function-axioms)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #458.
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | (6118) ~ (all_54_4 = e3)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (268), (6118) imply:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | (6119) ~ (all_52_1 = e3)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (5908), (6119), (function-axioms) are
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #763.
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | (6120) all_54_6 = e1 | all_54_6 = e0
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (5147), (5640), (6120) are inconsistent by
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #479.
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | (6121) all_57_3 = e3 & op(e2, e2) = e3
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6121) implies:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | (6122) op(e2, e2) = e3
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5153), (6122), (function-axioms) are
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #325.
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | (6123) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6123) gives:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | (6124) all_57_5 = e3 & op(e2, e1) = e3
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (5890), (6124), (function-axioms) are
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547.
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | (6125) all_57_10 = e3 & op(e2, e0) = e3
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6125) implies:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | (6126) all_57_10 = e3
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (165), (167), (223), (5153), (5639),
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | (5640), (6126), (function-axioms) are inconsistent
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #151.
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | Case 2:
% 133.67/19.24 | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | (6127) all_57_11 = e0 & op(e1, e0) = e0
% 133.67/19.24 | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | ALPHA: (6127) implies:
% 133.67/19.24 | | | | | | | | | | | | | | | | (6128) all_57_11 = e0
% 133.67/19.24 | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 133.67/19.24 | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.24 | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | (6129) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 133.67/19.24 | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 133.67/19.24 | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | BETA: splitting (6129) gives:
% 133.67/19.24 | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.24 | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | (6130) all_57_9 = e3 & op(e3, e0) = e3
% 133.67/19.24 | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | ALPHA: (6130) implies:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | (6131) all_57_9 = e3
% 133.67/19.24 | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (212), (5611), (5646), (6128),
% 133.67/19.24 | | | | | | | | | | | | | | | | | | (6131), (function-axioms) are inconsistent by
% 133.67/19.24 | | | | | | | | | | | | | | | | | | sub-proof #257.
% 133.67/19.24 | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.24 | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | (6132) all_57_10 = e3 & op(e2, e0) = e3
% 133.67/19.24 | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | ALPHA: (6132) implies:
% 133.67/19.24 | | | | | | | | | | | | | | | | | | (6133) all_57_10 = e3
% 133.67/19.24 | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (165), (167), (223), (5153), (5639),
% 133.67/19.24 | | | | | | | | | | | | | | | | | | (5640), (6133), (function-axioms) are inconsistent
% 133.67/19.24 | | | | | | | | | | | | | | | | | | by sub-proof #151.
% 133.67/19.24 | | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.24 | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | (6134) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 133.67/19.24 | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 133.67/19.24 | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (5611), (6128), (6134),
% 133.67/19.24 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.67/19.24 | | | | | | | | | | | | | | | | | #255.
% 133.67/19.24 | | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | Case 2:
% 133.67/19.24 | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | (6135) ~ (all_20_1 = e1) & op(e2, e2) = all_20_1 &
% 133.67/19.24 | | | | | | | | | | $i(all_20_1)
% 133.67/19.24 | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | ALPHA: (6135) implies:
% 133.67/19.24 | | | | | | | | | | (6136) ~ (all_20_1 = e1)
% 133.67/19.24 | | | | | | | | | | (6137) op(e2, e2) = all_20_1
% 133.67/19.24 | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_20_1,
% 133.67/19.24 | | | | | | | | | | e2, e2, simplifying with (5153), (6137) gives:
% 133.67/19.24 | | | | | | | | | | (6138) all_20_1 = e1
% 133.67/19.24 | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | REDUCE: (6136), (6138) imply:
% 133.67/19.24 | | | | | | | | | | (6139) $false
% 133.67/19.24 | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | CLOSE: (6139) is inconsistent.
% 133.67/19.24 | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | End of split
% 133.67/19.24 | | | | | | | | |
% 133.67/19.24 | | | | | | | | End of split
% 133.67/19.24 | | | | | | | |
% 133.67/19.24 | | | | | | | Case 2:
% 133.67/19.24 | | | | | | | |
% 133.67/19.24 | | | | | | | | (6140) all_16_2 = e2
% 133.67/19.24 | | | | | | | |
% 133.67/19.24 | | | | | | | | COMBINE_EQS: (327), (6140) imply:
% 133.67/19.24 | | | | | | | | (6141) all_10_2 = e2
% 133.67/19.24 | | | | | | | |
% 133.67/19.24 | | | | | | | | COMBINE_EQS: (299), (6141) imply:
% 133.67/19.24 | | | | | | | | (6142) all_38_2 = e2
% 133.67/19.24 | | | | | | | |
% 133.67/19.24 | | | | | | | | REDUCE: (336), (6141) imply:
% 133.67/19.24 | | | | | | | | (6143) ~ (all_52_1 = e2)
% 133.67/19.24 | | | | | | | |
% 133.67/19.24 | | | | | | | | REDUCE: (338), (6141) imply:
% 133.67/19.24 | | | | | | | | (6144) ~ (all_52_2 = e2)
% 133.67/19.24 | | | | | | | |
% 133.67/19.24 | | | | | | | | REDUCE: (344), (6141) imply:
% 133.67/19.24 | | | | | | | | (6145) ~ (all_52_8 = e2)
% 133.67/19.24 | | | | | | | |
% 133.67/19.24 | | | | | | | | REDUCE: (45), (6141) imply:
% 133.67/19.24 | | | | | | | | (6146) op(e3, e3) = e2
% 133.67/19.24 | | | | | | | |
% 133.67/19.24 | | | | | | | | BETA: splitting (88) gives:
% 133.67/19.24 | | | | | | | |
% 133.67/19.24 | | | | | | | | Case 1:
% 133.67/19.24 | | | | | | | | |
% 133.67/19.24 | | | | | | | | | (6147) ~ (all_38_2 = e2)
% 133.67/19.24 | | | | | | | | |
% 133.67/19.24 | | | | | | | | | REDUCE: (6142), (6147) imply:
% 133.67/19.24 | | | | | | | | | (6148) $false
% 133.67/19.24 | | | | | | | | |
% 133.67/19.24 | | | | | | | | | CLOSE: (6148) is inconsistent.
% 133.67/19.24 | | | | | | | | |
% 133.67/19.24 | | | | | | | | Case 2:
% 133.67/19.24 | | | | | | | | |
% 133.67/19.24 | | | | | | | | | (6149) ( ~ (all_38_0 = e0) & op(e2, e3) = all_38_0 &
% 133.67/19.24 | | | | | | | | | $i(all_38_0)) | ( ~ (all_38_1 = e1) & op(e2, e2) =
% 133.67/19.24 | | | | | | | | | all_38_1 & $i(all_38_1))
% 133.67/19.24 | | | | | | | | |
% 133.67/19.24 | | | | | | | | | BETA: splitting (6149) gives:
% 133.67/19.24 | | | | | | | | |
% 133.67/19.24 | | | | | | | | | Case 1:
% 133.67/19.24 | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | (6150) ~ (all_38_0 = e0) & op(e2, e3) = all_38_0 &
% 133.67/19.24 | | | | | | | | | | $i(all_38_0)
% 133.67/19.24 | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | ALPHA: (6150) implies:
% 133.67/19.24 | | | | | | | | | | (6151) ~ (all_38_0 = e0)
% 133.67/19.24 | | | | | | | | | | (6152) op(e2, e3) = all_38_0
% 133.67/19.24 | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | BETA: splitting (235) gives:
% 133.67/19.24 | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | Case 1:
% 133.67/19.24 | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | (6153) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 133.67/19.24 | | | | | | | | | | | & op(e2, e3) = e2)
% 133.67/19.24 | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | BETA: splitting (6153) gives:
% 133.67/19.24 | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | Case 1:
% 133.67/19.24 | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | (6154) all_57_0 = e2 & op(e3, e3) = e2
% 133.67/19.24 | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | ALPHA: (6154) implies:
% 133.67/19.24 | | | | | | | | | | | | (6155) all_57_0 = e2
% 133.67/19.24 | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 133.67/19.24 | | | | | | | | | | | | all_38_0, e3, e2, simplifying with (167), (6152)
% 133.67/19.24 | | | | | | | | | | | | gives:
% 133.67/19.24 | | | | | | | | | | | | (6156) all_52_1 = all_38_0
% 133.67/19.24 | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | COMBINE_EQS: (268), (6156) imply:
% 133.67/19.24 | | | | | | | | | | | | (6157) all_54_4 = all_38_0
% 133.67/19.24 | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | REDUCE: (146), (6156) imply:
% 133.67/19.24 | | | | | | | | | | | | (6158) ~ (all_52_9 = all_38_0)
% 133.67/19.24 | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | SIMP: (6158) implies:
% 133.67/19.24 | | | | | | | | | | | | (6159) ~ (all_52_9 = all_38_0)
% 133.67/19.24 | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | REDUCE: (145), (6156) imply:
% 133.67/19.24 | | | | | | | | | | | | (6160) ~ (all_52_13 = all_38_0)
% 133.67/19.24 | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | SIMP: (6160) implies:
% 133.67/19.24 | | | | | | | | | | | | (6161) ~ (all_52_13 = all_38_0)
% 133.67/19.24 | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | REDUCE: (6143), (6156) imply:
% 133.67/19.24 | | | | | | | | | | | | (6162) ~ (all_38_0 = e2)
% 133.67/19.24 | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | REDUCE: (5143), (6156) imply:
% 133.67/19.24 | | | | | | | | | | | | (6163) ~ (all_38_0 = e1)
% 133.67/19.24 | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | BETA: splitting (200) gives:
% 133.67/19.24 | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | Case 1:
% 133.67/19.24 | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | (6164) all_54_4 = e3
% 133.67/19.24 | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | COMBINE_EQS: (6157), (6164) imply:
% 133.67/19.24 | | | | | | | | | | | | | (6165) all_38_0 = e3
% 133.67/19.24 | | | | | | | | | | | | |
% 133.67/19.24 | | | | | | | | | | | | | SIMP: (6165) implies:
% 133.67/19.25 | | | | | | | | | | | | | (6166) all_38_0 = e3
% 133.67/19.25 | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | REDUCE: (6159), (6166) imply:
% 133.67/19.25 | | | | | | | | | | | | | (6167) ~ (all_52_9 = e3)
% 133.67/19.25 | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | REDUCE: (6161), (6166) imply:
% 133.67/19.25 | | | | | | | | | | | | | (6168) ~ (all_52_13 = e3)
% 133.67/19.25 | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | BETA: splitting (226) gives:
% 133.67/19.25 | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | Case 1:
% 133.67/19.25 | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | (6169) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 133.67/19.25 | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 133.67/19.25 | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | BETA: splitting (6169) gives:
% 133.67/19.25 | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | Case 1:
% 133.67/19.25 | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | (6170) all_57_2 = e3 & op(e2, e3) = e3
% 133.67/19.25 | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | ALPHA: (6170) implies:
% 133.67/19.25 | | | | | | | | | | | | | | | (6171) all_57_2 = e3
% 133.67/19.25 | | | | | | | | | | | | | | | (6172) op(e2, e3) = e3
% 133.67/19.25 | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 133.67/19.25 | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | Case 1:
% 133.67/19.25 | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | (6173) ~ (all_20_2 = e2)
% 133.67/19.25 | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | REDUCE: (318), (6173) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | (6174) ~ (all_4_2 = e2)
% 133.67/19.25 | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 133.67/19.25 | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.25 | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | (6175) ~ (all_28_2 = e3)
% 133.67/19.25 | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | REDUCE: (316), (6175) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | (6176) ~ (all_6_2 = e3)
% 133.67/19.25 | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 133.67/19.25 | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.25 | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | (6177) ~ (all_34_2 = e3)
% 133.67/19.25 | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | REDUCE: (307), (6177) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | (6178) ~ (all_4_2 = e3)
% 133.67/19.25 | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 133.67/19.25 | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | (6179) all_54_15 = e3
% 133.67/19.25 | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (6179) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | (6180) all_4_2 = e3
% 133.67/19.25 | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | REDUCE: (6178), (6180) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | (6181) $false
% 133.67/19.25 | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | CLOSE: (6181) is inconsistent.
% 133.67/19.25 | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | (6182) ~ (all_54_15 = e3)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | (6183) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 133.67/19.25 | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | BETA: splitting (6183) gives:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | (6184) all_54_15 = e2
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (6184) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | (6185) all_4_2 = e2
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | REDUCE: (6174), (6185) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | (6186) $false
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | CLOSE: (6186) is inconsistent.
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | (6187) ~ (all_54_15 = e2)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | (6188) all_54_15 = e1 | all_54_15 = e0
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | BETA: splitting (6188) gives:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | (6189) all_54_15 = e1
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (6189) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | (6190) all_4_2 = e1
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (6190) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | (6191) $false
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | CLOSE: (6191) is inconsistent.
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | (6192) all_54_15 = e0
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (6192) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | (6193) all_4_2 = e0
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (6193) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | (6194) ~ (all_52_13 = e0)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | REDUCE: (6178), (6193) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | (6195) ~ (e3 = e0)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | REDUCE: (6174), (6193) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | (6196) ~ (e2 = e0)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (6193) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | (6197) ~ (e1 = e0)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (6193) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | (6198) op(e0, e0) = e0
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6199) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6199) gives:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | (6200) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6146), (6172), (6200), (function-axioms) are
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #335.
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | (6201) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (5153), (6146), (6201),
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | #136.
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6202) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (39), (103), (110), (117), (160),
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (165), (194), (197), (218), (259), (334), (362),
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (372), (5142), (5148), (5153), (6176), (6194),
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6198), (6202), (function-axioms) are inconsistent
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #135.
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.25 | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.25 | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.25 | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | (6203) all_34_2 = e3
% 133.67/19.25 | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (6203) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | (6204) all_4_2 = e3
% 133.67/19.25 | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | SIMP: (6204) implies:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | (6205) all_4_2 = e3
% 133.67/19.25 | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (6205) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | (6206) all_44_2 = e3
% 133.67/19.25 | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | REDUCE: (367), (6205) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | (6207) ~ (all_52_11 = e3)
% 133.67/19.25 | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 133.67/19.25 | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | (6208) ~ (all_44_2 = e3)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | REDUCE: (6206), (6208) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | (6209) $false
% 133.67/19.25 | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | CLOSE: (6209) is inconsistent.
% 133.67/19.25 | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | (6210) ( ~ (all_44_0 = e1) & op(e3, e0) = all_44_0 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | $i(all_44_0)) | ( ~ (all_44_1 = e2) & op(e3, e3)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | = all_44_1 & $i(all_44_1))
% 133.67/19.25 | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | (6211) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | BETA: splitting (6211) gives:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | (6212) all_57_4 = e3 & op(e3, e1) = e3
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | ALPHA: (6212) implies:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | (6213) all_57_4 = e3
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (170), (234), (5144), (6146), (6210),
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | (6213), (function-axioms) are inconsistent by
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | sub-proof #134.
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | (6214) all_57_5 = e3 & op(e2, e1) = e3
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (6167), (6214), (function-axioms) are
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547.
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | (6215) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (157), (6176), (6207), (6215),
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | #651.
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.25 | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.25 | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | End of split
% 133.67/19.25 | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.25 | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | (6216) all_28_2 = e3
% 133.67/19.25 | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | COMBINE_EQS: (316), (6216) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | (6217) all_6_2 = e3
% 133.67/19.25 | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | COMBINE_EQS: (302), (6217) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | (6218) all_36_2 = e3
% 133.67/19.25 | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | REDUCE: (359), (6217) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | (6219) ~ (all_52_6 = e3)
% 133.67/19.25 | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | REDUCE: (361), (6217) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | (6220) ~ (all_52_8 = e3)
% 133.67/19.25 | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | REDUCE: (364), (6217) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | (6221) ~ (all_52_11 = e3)
% 133.67/19.25 | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 133.67/19.25 | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.25 | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | (6222) ~ (all_36_2 = e3)
% 133.67/19.25 | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | REDUCE: (6218), (6222) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | (6223) $false
% 133.67/19.25 | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | CLOSE: (6223) is inconsistent.
% 133.67/19.25 | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.25 | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | (6224) ( ~ (all_36_0 = e0) & op(e3, e1) = all_36_0 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | $i(all_36_0)) | ( ~ (all_36_1 = e2) & op(e3, e3)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | = all_36_1 & $i(all_36_1))
% 133.67/19.25 | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 133.67/19.25 | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | (6225) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (6167), (6220), (6225),
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | #310.
% 133.67/19.25 | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | (6226) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | BETA: splitting (6226) gives:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | (6227) all_57_8 = e3 & op(e1, e1) = e3
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | ALPHA: (6227) implies:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | (6228) all_57_8 = e3
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | (6229) op(e1, e1) = e3
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | BETA: splitting (6224) gives:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | (6230) ~ (all_36_0 = e0) & op(e3, e1) = all_36_0 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | $i(all_36_0)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | ALPHA: (6230) implies:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | (6231) ~ (all_36_0 = e0)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | (6232) op(e3, e1) = all_36_0
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5141) gives:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6233) ~ (all_8_0 = e0) & op(e1, e2) = all_8_0 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | $i(all_8_0)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6233) implies:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6234) ~ (all_8_0 = e0)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6235) op(e1, e2) = all_8_0
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6,
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | all_8_0, e2, e1, simplifying with (162), (6235)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | gives:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6236) all_52_6 = all_8_0
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8,
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | all_36_0, e1, e3, simplifying with (169), (6232)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | gives:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6237) all_52_8 = all_36_0
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (6236) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6238) all_54_9 = all_8_0
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (6237) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6239) all_54_2 = all_36_0
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (6236) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6240) ~ (all_52_2 = all_8_0)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (6236) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6241) ~ (all_52_4 = all_8_0)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (6236) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6242) ~ (all_52_14 = all_8_0)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | SIMP: (6242) implies:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6243) ~ (all_52_14 = all_8_0)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6219), (6236) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6244) ~ (all_8_0 = e3)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5145), (6236) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6245) ~ (all_8_0 = e1)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6220), (6237) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6246) ~ (all_36_0 = e3)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6145), (6237) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6247) ~ (all_36_0 = e2)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | (6248) all_54_2 = e3
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6239), (6248) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | (6249) all_36_0 = e3
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6246), (6249) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | (6250) $false
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6250) is inconsistent.
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | (6251) ~ (all_54_2 = e3)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | (6252) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6252) gives:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | (6253) all_54_2 = e2
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6239), (6253) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | (6254) all_36_0 = e2
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6247), (6254) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | (6255) $false
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6255) is inconsistent.
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | (6256) ~ (all_54_2 = e2)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | (6257) all_54_2 = e1 | all_54_2 = e0
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | (6258) all_54_9 = e3
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6238), (6258) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | (6259) all_8_0 = e3
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6244), (6259) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | (6260) $false
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6260) is inconsistent.
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | (6261) ~ (all_54_9 = e3)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | (6262) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6262) gives:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (6263) all_54_9 = e2
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6238), (6263) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (6264) all_8_0 = e2
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6241), (6264) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (6265) ~ (all_52_4 = e2)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6243), (6264) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (6266) ~ (all_52_14 = e2)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6244), (6264) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (6267) ~ (e3 = e2)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6268) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6268) gives:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6269) all_57_6 = e2 & op(e1, e3) = e2
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (6144), (6269), (function-axioms) are
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #341.
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6270) all_57_7 = e2 & op(e1, e2) = e2
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6270) implies:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6271) all_57_7 = e2
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6272) op(e1, e2) = e2
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6273) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6273) gives:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6274) all_57_12 = e2 & op(e0, e3) = e2
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6274) implies:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6275) all_57_12 = e2
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (231), (233), (6155),
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6171), (6275) are inconsistent by sub-proof #133.
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6276) all_57_13 = e2 & op(e0, e2) = e2
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6276) implies:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6277) op(e0, e2) = e2
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6257) gives:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6278) all_54_2 = e1
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6239), (6278) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6279) all_36_0 = e1
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6279) implies:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6280) all_36_0 = e1
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6246), (6280) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6281) ~ (e3 = e1)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6247), (6280) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6282) ~ (e2 = e1)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6232), (6280) imply:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6283) op(e3, e1) = e1
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6284) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6284) gives:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6285) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6146), (6172), (6285), (function-axioms) are
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #335.
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6286) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5153), (6277), (6286), (function-axioms) are
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #157.
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6287) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (39), (372), (5153), (6172), (6229),
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6272), (6283), (6287), (function-axioms) are
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #131.
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6288) all_54_2 = e0
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6231), (6239), (6288) are inconsistent by
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #242.
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6289) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6289) gives:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6290) all_57_14 = e2 & op(e0, e1) = e2
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6290) implies:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6291) all_57_14 = e2
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6292) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6292) gives:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6293) all_57_4 = e1 & op(e3, e1) = e1
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6293) implies:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6294) op(e3, e1) = e1
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6295) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6295) gives:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6296) all_57_12 = e1 & op(e0, e3) = e1
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6296) implies:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6297) all_57_12 = e1
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6298) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6298) gives:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6299) all_57_0 = e0 & op(e3, e3) = e0
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6299) implies:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6300) op(e3, e3) = e0
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6146), (6300), (function-axioms) are
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495.
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6301) all_57_2 = e0 & op(e2, e3) = e0
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6301) implies:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6302) op(e2, e3) = e0
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_38_0,
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e2, simplifying with (6152), (6302) gives:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6303) all_38_0 = e0
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6151), (6303) imply:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6304) $false
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6304) is inconsistent.
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6305) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6305) gives:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6306) all_57_6 = e0 & op(e1, e3) = e0
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6306) implies:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6307) all_57_6 = e0
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6308) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6308) gives:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6309) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6309) gives:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6310) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6310) implies:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6311) ~ (all_56_3 = e3)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6312) op(e2, e3) = all_56_3
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6172), (6311), (6312), (function-axioms) are
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #347.
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6313) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6313) implies:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6314) op(e3, e3) = e1
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (235), (237), (6297),
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6307), (6314), (function-axioms) are inconsistent
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #585.
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6315) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (5153), (6146), (6315),
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #136.
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6316) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (39), (372), (5153), (6172), (6229),
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6272), (6294), (6316), (function-axioms) are
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #131.
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6317) all_57_12 = e0 & op(e0, e3) = e0
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6297), (6317) are inconsistent by sub-proof
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #584.
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6318) all_57_13 = e1 & op(e0, e2) = e1
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (5146), (6318), (function-axioms) are
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #178.
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6319) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (371), (6291), (6319),
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #350.
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6320) all_57_5 = e1 & op(e2, e1) = e1
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (5147), (6320), (function-axioms) are
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #161.
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6321) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6321) gives:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6322) all_57_8 = e1 & op(e1, e1) = e1
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6322) implies:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6323) op(e1, e1) = e1
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (6229), (6323), (function-axioms) are
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #662.
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6324) all_57_14 = e1 & op(e0, e1) = e1
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6324) implies:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6325) all_57_14 = e1
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6291), (6325) are inconsistent by sub-proof
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #560.
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6326) all_57_15 = e2 & op(e0, e0) = e2
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6326) implies:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6327) op(e0, e0) = e2
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6328) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6328) gives:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6329) all_57_9 = e3 & op(e3, e0) = e3
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6329) implies:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6330) all_57_9 = e3
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6331) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6331) gives:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6332) all_57_0 = e0 & op(e3, e3) = e0
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6332) implies:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6333) op(e3, e3) = e0
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6146), (6333), (function-axioms) are
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495.
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6334) all_57_1 = e0 & op(e3, e2) = e0
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6334) implies:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6335) all_57_1 = e0
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6336) op(e3, e2) = e0
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6337) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6337) gives:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6338) all_57_9 = e1 & op(e3, e0) = e1
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6338) implies:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6339) all_57_9 = e1
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (169), (238), (6146), (6220),
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6232), (6335), (6339), (function-axioms) are
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #344.
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6340) all_57_10 = e1 & op(e2, e0) = e1
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6340) implies:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6341) op(e2, e0) = e1
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (5148), (6341), (function-axioms) are
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #180.
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6342) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6342) gives:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6343) all_57_11 = e1 & op(e1, e0) = e1
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6343) implies:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6344) all_57_11 = e1
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6345) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (6146), (6336), (6345),
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #241.
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6346) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6346) gives:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6347) all_57_4 = e1 & op(e3, e1) = e1
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6347) implies:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6348) all_57_4 = e1
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6349) op(e3, e1) = e1
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6350) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6350) gives:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6351) all_57_6 = e0 & op(e1, e3) = e0
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6351) implies:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6352) all_57_6 = e0
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6353) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6353) gives:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6354) all_57_0 = e1 & op(e3, e3) = e1
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6354) implies:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6355) op(e3, e3) = e1
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (170), (232),
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236), (238), (6220), (6265), (6348), (6355),
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #162.
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6356) all_57_2 = e1 & op(e2, e3) = e1
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (5143), (6356), (function-axioms) are
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #676.
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6357) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6357) gives:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6358) all_57_6 = e1 & op(e1, e3) = e1
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6352), (6358) are inconsistent by sub-proof
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #130.
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6359) all_57_12 = e1 & op(e0, e3) = e1
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6359) implies:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6360) all_57_12 = e1
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6361) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6361) gives:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6362) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6362) gives:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6363) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6363) implies:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6364) ~ (all_56_3 = e3)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6365) op(e2, e3) = all_56_3
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6172), (6364), (6365), (function-axioms) are
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #347.
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6366) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6366) implies:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6367) op(e3, e3) = e1
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (235), (237),
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6360), (6367), (function-axioms) are inconsistent
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #583.
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6368) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (5153), (6146), (6368),
% 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #136.
% 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6369) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6369) gives:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6370) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6272), (6349), (6370), (function-axioms) are
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #132.
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6371) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (39), (372), (5153), (6174), (6327),
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6371), (function-axioms) are inconsistent by
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #156.
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6372) all_57_7 = e0 & op(e1, e2) = e0
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6372) implies:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6373) all_57_7 = e0
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6271), (6373) imply:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6374) e2 = e0
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6374) implies:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6375) e2 = e0
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (6375) imply:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6376) $false
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6376) is inconsistent.
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6377) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6377) gives:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6378) all_57_8 = e0 & op(e1, e1) = e0
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6378) implies:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6379) op(e1, e1) = e0
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6229), (6379), (function-axioms) are
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753.
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6380) all_57_11 = e0 & op(e1, e0) = e0
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6380) implies:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6381) all_57_11 = e0
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6344), (6381) imply:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6382) e1 = e0
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (6382) imply:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6383) $false
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6383) is inconsistent.
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6384) all_57_9 = e1 & op(e3, e0) = e1
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6384) implies:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6385) all_57_9 = e1
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (169), (238), (6146), (6220),
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6232), (6335), (6385), (function-axioms) are
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #344.
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6386) all_57_15 = e1 & op(e0, e0) = e1
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6386) implies:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6387) op(e0, e0) = e1
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6327), (6387), (function-axioms) are
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #636.
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6388) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6388) gives:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6389) all_57_4 = e0 & op(e3, e1) = e0
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6231), (6232), (6389), (function-axioms) are
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #332.
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6390) all_57_9 = e0 & op(e3, e0) = e0
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6390) implies:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6391) all_57_9 = e0
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6330), (6391) are inconsistent by sub-proof
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #670.
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6392) all_57_10 = e3 & op(e2, e0) = e3
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (6168), (6392), (function-axioms) are
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749.
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6393) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6393) gives:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6394) all_57_11 = e3 & op(e1, e0) = e3
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6394) implies:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6395) all_57_11 = e3
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6396) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6396) gives:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6397) all_57_6 = e0 & op(e1, e3) = e0
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6397) implies:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6398) all_57_6 = e0
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6399) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6399) gives:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6400) all_57_6 = e1 & op(e1, e3) = e1
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6398), (6400) are inconsistent by sub-proof
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #130.
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6401) all_57_7 = e1 & op(e1, e2) = e1
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6271), (6401) are inconsistent by sub-proof
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #727.
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6402) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6402) gives:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6403) all_57_8 = e1 & op(e1, e1) = e1
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6403) implies:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6404) op(e1, e1) = e1
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (6229), (6404), (function-axioms) are
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #662.
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6405) all_57_11 = e1 & op(e1, e0) = e1
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6405) implies:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6406) all_57_11 = e1
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6395), (6406) are inconsistent by sub-proof
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #167.
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6407) all_57_7 = e0 & op(e1, e2) = e0
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6271), (6407) are inconsistent by sub-proof
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #664.
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6408) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6408) gives:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6409) all_57_8 = e0 & op(e1, e1) = e0
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6409) implies:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6410) all_57_8 = e0
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6228), (6410) imply:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6411) e3 = e0
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (6411) imply:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6412) $false
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6412) is inconsistent.
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6413) all_57_11 = e0 & op(e1, e0) = e0
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6395), (6413) are inconsistent by sub-proof
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #129.
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6414) all_57_15 = e3 & op(e0, e0) = e3
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6414) implies:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6415) op(e0, e0) = e3
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6327), (6415), (function-axioms) are
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #634.
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6416) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (160), (372), (6266), (6416),
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | #513.
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | (6417) all_54_9 = e1 | all_54_9 = e0
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6234), (6238), (6245), (6417) are inconsistent by
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #155.
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | (6418) ~ (all_8_1 = e3) & op(e1, e1) = all_8_1 &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | $i(all_8_1)
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6229), (6418), (function-axioms) are inconsistent
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #128.
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | (6419) ~ (all_36_1 = e2) & op(e3, e3) = all_36_1 &
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | $i(all_36_1)
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6146), (6419), (function-axioms) are inconsistent
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | by sub-proof #342.
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | (6420) all_57_14 = e3 & op(e0, e1) = e3
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (6221), (6420), (function-axioms) are
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #652.
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | End of split
% 133.82/19.27 | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | Case 2:
% 133.82/19.27 | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | (6421) all_20_2 = e2
% 133.82/19.27 | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | COMBINE_EQS: (318), (6421) imply:
% 133.82/19.27 | | | | | | | | | | | | | | | | (6422) all_4_2 = e2
% 133.82/19.27 | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | REDUCE: (367), (6422) imply:
% 133.82/19.27 | | | | | | | | | | | | | | | | (6423) ~ (all_52_11 = e2)
% 133.82/19.27 | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | REDUCE: (369), (6422) imply:
% 133.82/19.27 | | | | | | | | | | | | | | | | (6424) ~ (all_52_13 = e2)
% 133.82/19.27 | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | REDUCE: (36), (6422) imply:
% 133.82/19.27 | | | | | | | | | | | | | | | | (6425) op(e0, e0) = e2
% 133.82/19.27 | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 133.82/19.27 | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | Case 1:
% 133.82/19.27 | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | (6426) all_54_7 = e3
% 133.82/19.27 | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (6426) imply:
% 133.82/19.27 | | | | | | | | | | | | | | | | | (6427) all_52_13 = e3
% 133.82/19.27 | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | REDUCE: (6168), (6427) imply:
% 133.82/19.27 | | | | | | | | | | | | | | | | | (6428) $false
% 133.82/19.27 | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | CLOSE: (6428) is inconsistent.
% 133.82/19.27 | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | Case 2:
% 133.82/19.27 | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | (6429) ~ (all_54_7 = e3)
% 133.82/19.27 | | | | | | | | | | | | | | | | | (6430) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 133.82/19.27 | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 133.82/19.27 | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | Case 1:
% 133.82/19.27 | | | | | | | | | | | | | | | | | |
% 133.82/19.27 | | | | | | | | | | | | | | | | | | (6431) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 133.82/19.27 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 133.82/19.27 | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (167), (5152), (6143), (6431),
% 133.84/19.27 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.84/19.27 | | | | | | | | | | | | | | | | | | #127.
% 133.84/19.27 | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.27 | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | (6432) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 133.84/19.27 | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 133.84/19.27 | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | BETA: splitting (6432) gives:
% 133.84/19.27 | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.27 | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | (6433) all_57_5 = e2 & op(e2, e1) = e2
% 133.84/19.27 | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | ALPHA: (6433) implies:
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | (6434) all_57_5 = e2
% 133.84/19.27 | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | BETA: splitting (6430) gives:
% 133.84/19.27 | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | (6435) all_54_7 = e2
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (6435) imply:
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | (6436) all_52_13 = e2
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | REDUCE: (6424), (6436) imply:
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | (6437) $false
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | CLOSE: (6437) is inconsistent.
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | (6438) ~ (all_54_7 = e2)
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | (6439) all_54_7 = e1 | all_54_7 = e0
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | BETA: splitting (6439) gives:
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | (6440) all_54_7 = e1
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (6440) imply:
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | (6441) all_52_13 = e1
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | REDUCE: (5148), (6441) imply:
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | (6442) $false
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | CLOSE: (6442) is inconsistent.
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | (6443) all_54_7 = e0
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (6443) imply:
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | (6444) all_52_13 = e0
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (6444) imply:
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | (6445) ~ (all_52_12 = e0)
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | REDUCE: (6168), (6444) imply:
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | (6446) ~ (e3 = e0)
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | REDUCE: (6424), (6444) imply:
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | (6447) ~ (e2 = e0)
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | REDUCE: (5148), (6444) imply:
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | (6448) ~ (e1 = e0)
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (6444) imply:
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | (6449) op(e2, e0) = e0
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | (6450) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6450) gives:
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | (6451) all_57_6 = e2 & op(e1, e3) = e2
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (6144), (6451), (function-axioms) are
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #341.
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | (6452) all_57_7 = e2 & op(e1, e2) = e2
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6452) implies:
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | (6453) op(e1, e2) = e2
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | (6454) ~ (all_28_2 = e3)
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (316), (6454) imply:
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | (6455) ~ (all_6_2 = e3)
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | (6456) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6456) gives:
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | (6457) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6146), (6449), (6457), (function-axioms) are
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #274.
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | (6458) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (5153), (6146), (6458),
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | #136.
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (6459) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6459) gives:
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (6460) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6460) gives:
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6461) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6461) implies:
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6462) op(e1, e1) = e3
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (6455), (6462), (function-axioms) are
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #771.
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6463) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2,
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6463) implies:
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6464) ~ (all_56_13 = e2)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6465) op(e1, e2) = all_56_13
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6453), (6464), (6465), (function-axioms) are
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #165.
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (6466) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (39), (91), (157), (190),
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (224), (246), (332), (364), (372), (6171), (6423),
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (6425), (6434), (6449), (6466), (function-axioms)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #138.
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | (6467) all_28_2 = e3
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (316), (6467) imply:
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | (6468) all_6_2 = e3
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6468) implies:
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | (6469) all_6_2 = e3
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (302), (6469) imply:
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | (6470) all_36_2 = e3
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (6469) imply:
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | (6471) ~ (all_52_14 = e3)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (6472) ~ (all_36_2 = e3)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6470), (6472) imply:
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (6473) $false
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6473) is inconsistent.
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (6474) ( ~ (all_36_0 = e0) & op(e3, e1) = all_36_0 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_36_0)) | ( ~ (all_36_1 = e2) & op(e3, e3)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | = all_36_1 & $i(all_36_1))
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (6475) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6475) gives:
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6476) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6146), (6449), (6476), (function-axioms) are
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #274.
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6477) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (5153), (6146), (6477),
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | #136.
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (6478) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6478) gives:
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6479) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6479) gives:
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6480) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6480) implies:
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6481) ~ (all_56_17 = e1)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6482) op(e3, e1) = all_56_17
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (160), (164), (168),
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (214), (232), (234), (6146), (6168), (6425),
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6445), (6471), (6474), (6481), (6482),
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #328.
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6483) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2,
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6483) implies:
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6484) ~ (all_56_13 = e2)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6485) op(e1, e2) = all_56_13
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6453), (6484), (6485), (function-axioms) are
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #165.
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6486) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (39), (91), (157), (190),
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (224), (246), (332), (364), (372), (6171), (6423),
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6425), (6434), (6449), (6486), (function-axioms)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #138.
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | (6487) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (164), (208),
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | (212), (214), (372), (6168), (6425), (6487),
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | #268.
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | | End of split
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | End of split
% 133.84/19.28 | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.28 | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | (6488) all_57_10 = e2 & op(e2, e0) = e2
% 133.84/19.28 | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | ALPHA: (6488) implies:
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | (6489) op(e2, e0) = e2
% 133.84/19.28 | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (6424), (6489), (function-axioms) are
% 133.84/19.28 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 133.84/19.28 | | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | | End of split
% 133.84/19.28 | | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | | End of split
% 133.84/19.28 | | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | | End of split
% 133.84/19.28 | | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | End of split
% 133.84/19.28 | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | Case 2:
% 133.84/19.28 | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | (6490) all_57_3 = e3 & op(e2, e2) = e3
% 133.84/19.28 | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | ALPHA: (6490) implies:
% 133.84/19.28 | | | | | | | | | | | | | | | (6491) op(e2, e2) = e3
% 133.84/19.28 | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | REF_CLOSE: (8), (5153), (6491), (function-axioms) are
% 133.84/19.28 | | | | | | | | | | | | | | | inconsistent by sub-proof #325.
% 133.84/19.28 | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | End of split
% 133.84/19.28 | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | Case 2:
% 133.84/19.28 | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | (6492) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 133.84/19.28 | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 133.84/19.28 | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | BETA: splitting (6492) gives:
% 133.84/19.28 | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | Case 1:
% 133.84/19.28 | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | (6493) all_57_5 = e3 & op(e2, e1) = e3
% 133.84/19.28 | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | REF_CLOSE: (165), (6167), (6493), (function-axioms) are
% 133.84/19.28 | | | | | | | | | | | | | | | inconsistent by sub-proof #547.
% 133.84/19.28 | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | Case 2:
% 133.84/19.28 | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | (6494) all_57_10 = e3 & op(e2, e0) = e3
% 133.84/19.28 | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | | REF_CLOSE: (164), (6168), (6494), (function-axioms) are
% 133.84/19.28 | | | | | | | | | | | | | | | inconsistent by sub-proof #749.
% 133.84/19.28 | | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | | End of split
% 133.84/19.28 | | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | End of split
% 133.84/19.28 | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | Case 2:
% 133.84/19.28 | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | (6495) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 133.84/19.28 | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | | REF_CLOSE: (6151), (6157), (6162), (6163), (6495) are
% 133.84/19.28 | | | | | | | | | | | | | inconsistent by sub-proof #126.
% 133.84/19.28 | | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | End of split
% 133.84/19.28 | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | Case 2:
% 133.84/19.28 | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | (6496) all_57_2 = e2 & op(e2, e3) = e2
% 133.84/19.28 | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | ALPHA: (6496) implies:
% 133.84/19.28 | | | | | | | | | | | | (6497) op(e2, e3) = e2
% 133.84/19.28 | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | REF_CLOSE: (167), (6143), (6497), (function-axioms) are
% 133.84/19.28 | | | | | | | | | | | | inconsistent by sub-proof #779.
% 133.84/19.28 | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | End of split
% 133.84/19.28 | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | Case 2:
% 133.84/19.28 | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | (6498) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 133.84/19.28 | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 133.84/19.28 | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | BETA: splitting (6498) gives:
% 133.84/19.28 | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | Case 1:
% 133.84/19.28 | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | (6499) all_57_6 = e2 & op(e1, e3) = e2
% 133.84/19.28 | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | REF_CLOSE: (163), (6144), (6499), (function-axioms) are
% 133.84/19.28 | | | | | | | | | | | | inconsistent by sub-proof #341.
% 133.84/19.28 | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | Case 2:
% 133.84/19.28 | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | (6500) all_57_12 = e2 & op(e0, e3) = e2
% 133.84/19.28 | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | ALPHA: (6500) implies:
% 133.84/19.28 | | | | | | | | | | | | (6501) all_57_12 = e2
% 133.84/19.28 | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 133.84/19.28 | | | | | | | | | | | | (6146), (6501), (function-axioms) are inconsistent
% 133.84/19.28 | | | | | | | | | | | | by sub-proof #290.
% 133.84/19.28 | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | End of split
% 133.84/19.28 | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | End of split
% 133.84/19.28 | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | Case 2:
% 133.84/19.28 | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | (6502) ~ (all_38_1 = e1) & op(e2, e2) = all_38_1 &
% 133.84/19.28 | | | | | | | | | | $i(all_38_1)
% 133.84/19.28 | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | REF_CLOSE: (5153), (6502), (function-axioms) are inconsistent
% 133.84/19.28 | | | | | | | | | | by sub-proof #125.
% 133.84/19.28 | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | End of split
% 133.84/19.28 | | | | | | | | |
% 133.84/19.28 | | | | | | | | End of split
% 133.84/19.28 | | | | | | | |
% 133.84/19.28 | | | | | | | End of split
% 133.84/19.28 | | | | | | |
% 133.84/19.28 | | | | | | Case 2:
% 133.84/19.28 | | | | | | |
% 133.84/19.28 | | | | | | | (6503) all_10_2 = e0
% 133.84/19.28 | | | | | | |
% 133.84/19.28 | | | | | | | COMBINE_EQS: (319), (6503) imply:
% 133.84/19.28 | | | | | | | (6504) all_24_2 = e0
% 133.84/19.28 | | | | | | |
% 133.84/19.28 | | | | | | | REDUCE: (336), (6503) imply:
% 133.84/19.28 | | | | | | | (6505) ~ (all_52_1 = e0)
% 133.84/19.28 | | | | | | |
% 133.84/19.28 | | | | | | | REDUCE: (338), (6503) imply:
% 133.84/19.28 | | | | | | | (6506) ~ (all_52_2 = e0)
% 133.84/19.28 | | | | | | |
% 133.84/19.28 | | | | | | | REDUCE: (340), (6503) imply:
% 133.84/19.28 | | | | | | | (6507) ~ (all_52_3 = e0)
% 133.84/19.28 | | | | | | |
% 133.84/19.28 | | | | | | | REDUCE: (342), (6503) imply:
% 133.84/19.28 | | | | | | | (6508) ~ (all_52_4 = e0)
% 133.84/19.28 | | | | | | |
% 133.84/19.28 | | | | | | | REDUCE: (45), (6503) imply:
% 133.84/19.28 | | | | | | | (6509) op(e3, e3) = e0
% 133.84/19.28 | | | | | | |
% 133.84/19.28 | | | | | | | BETA: splitting (61) gives:
% 133.84/19.28 | | | | | | |
% 133.84/19.28 | | | | | | | Case 1:
% 133.84/19.28 | | | | | | | |
% 133.84/19.28 | | | | | | | | (6510) ~ (all_20_2 = e2)
% 133.84/19.28 | | | | | | | |
% 133.84/19.28 | | | | | | | | REDUCE: (318), (6510) imply:
% 133.84/19.28 | | | | | | | | (6511) ~ (all_4_2 = e2)
% 133.84/19.28 | | | | | | | |
% 133.84/19.28 | | | | | | | | BETA: splitting (73) gives:
% 133.84/19.28 | | | | | | | |
% 133.84/19.28 | | | | | | | | Case 1:
% 133.84/19.28 | | | | | | | | |
% 133.84/19.28 | | | | | | | | | (6512) ~ (all_28_2 = e3)
% 133.84/19.28 | | | | | | | | |
% 133.84/19.28 | | | | | | | | | REDUCE: (316), (6512) imply:
% 133.84/19.28 | | | | | | | | | (6513) ~ (all_6_2 = e3)
% 133.84/19.28 | | | | | | | | |
% 133.84/19.28 | | | | | | | | | BETA: splitting (82) gives:
% 133.84/19.28 | | | | | | | | |
% 133.84/19.28 | | | | | | | | | Case 1:
% 133.84/19.28 | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | (6514) ~ (all_34_2 = e3)
% 133.84/19.28 | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | REDUCE: (307), (6514) imply:
% 133.84/19.28 | | | | | | | | | | (6515) ~ (all_4_2 = e3)
% 133.84/19.28 | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | BETA: splitting (189) gives:
% 133.84/19.28 | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | Case 1:
% 133.84/19.28 | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | (6516) all_54_15 = e3
% 133.84/19.28 | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | COMBINE_EQS: (245), (6516) imply:
% 133.84/19.28 | | | | | | | | | | | (6517) all_4_2 = e3
% 133.84/19.28 | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | REDUCE: (6515), (6517) imply:
% 133.84/19.28 | | | | | | | | | | | (6518) $false
% 133.84/19.28 | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | CLOSE: (6518) is inconsistent.
% 133.84/19.28 | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | Case 2:
% 133.84/19.28 | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | (6519) ~ (all_54_15 = e3)
% 133.84/19.28 | | | | | | | | | | | (6520) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 133.84/19.28 | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | BETA: splitting (6520) gives:
% 133.84/19.28 | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | Case 1:
% 133.84/19.28 | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | (6521) all_54_15 = e2
% 133.84/19.28 | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | COMBINE_EQS: (245), (6521) imply:
% 133.84/19.28 | | | | | | | | | | | | (6522) all_4_2 = e2
% 133.84/19.28 | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | REDUCE: (6511), (6522) imply:
% 133.84/19.28 | | | | | | | | | | | | (6523) $false
% 133.84/19.28 | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | CLOSE: (6523) is inconsistent.
% 133.84/19.28 | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | Case 2:
% 133.84/19.28 | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | (6524) ~ (all_54_15 = e2)
% 133.84/19.28 | | | | | | | | | | | | (6525) all_54_15 = e1 | all_54_15 = e0
% 133.84/19.28 | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | BETA: splitting (6525) gives:
% 133.84/19.28 | | | | | | | | | | | |
% 133.84/19.28 | | | | | | | | | | | | Case 1:
% 133.84/19.28 | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | (6526) all_54_15 = e1
% 133.84/19.29 | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | COMBINE_EQS: (245), (6526) imply:
% 133.84/19.29 | | | | | | | | | | | | | (6527) all_4_2 = e1
% 133.84/19.29 | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | REDUCE: (371), (6527) imply:
% 133.84/19.29 | | | | | | | | | | | | | (6528) $false
% 133.84/19.29 | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | CLOSE: (6528) is inconsistent.
% 133.84/19.29 | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | Case 2:
% 133.84/19.29 | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | (6529) all_54_15 = e0
% 133.84/19.29 | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | COMBINE_EQS: (245), (6529) imply:
% 133.84/19.29 | | | | | | | | | | | | | (6530) all_4_2 = e0
% 133.84/19.29 | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | REDUCE: (369), (6530) imply:
% 133.84/19.29 | | | | | | | | | | | | | (6531) ~ (all_52_13 = e0)
% 133.84/19.29 | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | REDUCE: (6515), (6530) imply:
% 133.84/19.29 | | | | | | | | | | | | | (6532) ~ (e3 = e0)
% 133.84/19.29 | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | REDUCE: (6511), (6530) imply:
% 133.84/19.29 | | | | | | | | | | | | | (6533) ~ (e2 = e0)
% 133.84/19.29 | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | REDUCE: (371), (6530) imply:
% 133.84/19.29 | | | | | | | | | | | | | (6534) ~ (e1 = e0)
% 133.84/19.29 | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | REDUCE: (36), (6530) imply:
% 133.84/19.29 | | | | | | | | | | | | | (6535) op(e0, e0) = e0
% 133.84/19.29 | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.84/19.29 | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | Case 1:
% 133.84/19.29 | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | (6536) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.84/19.29 | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.84/19.29 | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.84/19.29 | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.84/19.29 | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.84/19.29 | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.84/19.29 | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.84/19.29 | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.84/19.29 | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.84/19.29 | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.84/19.29 | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.84/19.29 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.84/19.29 | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.84/19.29 | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.84/19.29 | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.84/19.29 | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.84/19.29 | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.84/19.29 | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.84/19.29 | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.84/19.29 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.84/19.29 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.84/19.29 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.84/19.29 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.84/19.29 | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.84/19.29 | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | BETA: splitting (6536) gives:
% 133.84/19.29 | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | Case 1:
% 133.84/19.29 | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | (6537) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.84/19.29 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.84/19.29 | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.84/19.29 | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.84/19.29 | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.84/19.29 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.84/19.29 | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.84/19.29 | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.84/19.29 | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.84/19.29 | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.84/19.29 | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.84/19.29 | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.84/19.29 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.84/19.29 | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 133.84/19.29 | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6509), (6537), (function-axioms) are
% 133.84/19.29 | | | | | | | | | | | | | | | inconsistent by sub-proof #229.
% 133.84/19.29 | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | Case 2:
% 133.84/19.29 | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | (6538) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.84/19.29 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.84/19.29 | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.84/19.29 | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.84/19.29 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.84/19.29 | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.84/19.29 | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.84/19.29 | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.84/19.29 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.84/19.29 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.84/19.29 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.84/19.29 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.84/19.29 | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.84/19.29 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.84/19.29 | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | BETA: splitting (6538) gives:
% 133.84/19.29 | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | Case 1:
% 133.84/19.29 | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | (6539) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.84/19.29 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.84/19.29 | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3,
% 133.84/19.29 | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.84/19.29 | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 133.84/19.29 | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.84/19.29 | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 133.84/19.29 | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | ALPHA: (6539) implies:
% 133.84/19.29 | | | | | | | | | | | | | | | | (6540) ~ (all_56_31 = e0)
% 133.84/19.29 | | | | | | | | | | | | | | | | (6541) op(e0, e0) = all_56_31
% 133.84/19.29 | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | REF_CLOSE: (6535), (6540), (6541), (function-axioms) are
% 133.84/19.29 | | | | | | | | | | | | | | | | inconsistent by sub-proof #712.
% 133.84/19.29 | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | Case 2:
% 133.84/19.29 | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | (6542) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.84/19.29 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.84/19.29 | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.84/19.29 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.84/19.29 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2,
% 133.84/19.29 | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.84/19.29 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 133.84/19.29 | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | ALPHA: (6542) implies:
% 133.84/19.29 | | | | | | | | | | | | | | | | (6543) op(e2, e2) = e3
% 133.84/19.29 | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5153), (6543), (function-axioms) are
% 133.84/19.29 | | | | | | | | | | | | | | | | inconsistent by sub-proof #325.
% 133.84/19.29 | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | End of split
% 133.84/19.29 | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | End of split
% 133.84/19.29 | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | Case 2:
% 133.84/19.29 | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | (6544) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.84/19.29 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.84/19.29 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.84/19.29 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.84/19.29 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.84/19.29 | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.84/19.29 | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.84/19.29 | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.84/19.29 | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.84/19.29 | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.84/19.29 | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.84/19.29 | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.84/19.29 | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.84/19.29 | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.84/19.29 | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.84/19.29 | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.84/19.29 | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.84/19.29 | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.84/19.29 | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.84/19.29 | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.84/19.29 | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.84/19.29 | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.84/19.29 | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.84/19.29 | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.84/19.29 | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.84/19.29 | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.84/19.29 | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.84/19.29 | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.84/19.29 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.84/19.29 | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.84/19.29 | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.84/19.29 | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.84/19.29 | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.84/19.29 | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.84/19.29 | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.84/19.29 | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.84/19.29 | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.84/19.29 | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.84/19.29 | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.84/19.29 | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.84/19.29 | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.84/19.29 | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.84/19.29 | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.84/19.29 | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.84/19.29 | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.84/19.29 | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.84/19.29 | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.84/19.29 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.84/19.29 | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.84/19.29 | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (39), (103), (110), (117), (160),
% 133.84/19.29 | | | | | | | | | | | | | | (165), (194), (197), (218), (259), (334), (362),
% 133.84/19.29 | | | | | | | | | | | | | | (372), (5142), (5148), (5153), (6513), (6531),
% 133.84/19.29 | | | | | | | | | | | | | | (6535), (6544), (function-axioms) are inconsistent
% 133.84/19.29 | | | | | | | | | | | | | | by sub-proof #135.
% 133.84/19.29 | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | End of split
% 133.84/19.29 | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | End of split
% 133.84/19.29 | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | End of split
% 133.84/19.29 | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | End of split
% 133.84/19.29 | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | Case 2:
% 133.84/19.29 | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | (6545) all_34_2 = e3
% 133.84/19.29 | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | COMBINE_EQS: (307), (6545) imply:
% 133.84/19.29 | | | | | | | | | | (6546) all_4_2 = e3
% 133.84/19.29 | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | SIMP: (6546) implies:
% 133.84/19.29 | | | | | | | | | | (6547) all_4_2 = e3
% 133.84/19.29 | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | REDUCE: (360), (6547) imply:
% 133.84/19.29 | | | | | | | | | | (6548) ~ (all_52_7 = e3)
% 133.84/19.29 | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | REDUCE: (367), (6547) imply:
% 133.84/19.29 | | | | | | | | | | (6549) ~ (all_52_11 = e3)
% 133.84/19.29 | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | REDUCE: (368), (6547) imply:
% 133.84/19.29 | | | | | | | | | | (6550) ~ (all_52_12 = e3)
% 133.84/19.29 | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | REDUCE: (370), (6547) imply:
% 133.84/19.29 | | | | | | | | | | (6551) ~ (all_52_14 = e3)
% 133.84/19.29 | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | REDUCE: (36), (6547) imply:
% 133.84/19.29 | | | | | | | | | | (6552) op(e0, e0) = e3
% 133.84/19.29 | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | BETA: splitting (91) gives:
% 133.84/19.29 | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | Case 1:
% 133.84/19.29 | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | (6553) ~ (all_40_2 = e0)
% 133.84/19.29 | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | REDUCE: (332), (6553) imply:
% 133.84/19.29 | | | | | | | | | | | (6554) ~ (all_6_2 = e0)
% 133.84/19.29 | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | BETA: splitting (206) gives:
% 133.84/19.29 | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | Case 1:
% 133.84/19.29 | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | (6555) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.84/19.29 | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.84/19.29 | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.84/19.29 | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.84/19.29 | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.84/19.29 | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.84/19.29 | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.84/19.29 | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.84/19.29 | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.84/19.29 | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.84/19.29 | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.84/19.29 | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.84/19.29 | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.84/19.29 | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.84/19.29 | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.84/19.29 | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.84/19.29 | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.84/19.29 | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.84/19.29 | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.84/19.29 | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.84/19.29 | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.84/19.29 | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.84/19.29 | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.84/19.29 | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.84/19.29 | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.84/19.29 | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.84/19.29 | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.84/19.29 | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.84/19.29 | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | BETA: splitting (6555) gives:
% 133.84/19.29 | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | Case 1:
% 133.84/19.29 | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | (6556) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.84/19.29 | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.84/19.29 | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.84/19.29 | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.84/19.29 | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.84/19.29 | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.84/19.29 | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.84/19.29 | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.84/19.29 | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.84/19.29 | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.84/19.29 | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.84/19.29 | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.84/19.29 | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.84/19.29 | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 133.84/19.29 | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6509), (6556), (function-axioms) are
% 133.84/19.29 | | | | | | | | | | | | | inconsistent by sub-proof #229.
% 133.84/19.29 | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | Case 2:
% 133.84/19.29 | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | (6557) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.84/19.29 | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.84/19.29 | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.84/19.29 | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.84/19.29 | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.84/19.29 | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.84/19.29 | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.84/19.29 | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.84/19.29 | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.84/19.29 | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.84/19.29 | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.84/19.29 | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.84/19.29 | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.84/19.29 | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.84/19.29 | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | REF_CLOSE: (8), (168), (5153), (6550), (6557),
% 133.84/19.29 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.84/19.29 | | | | | | | | | | | | | #190.
% 133.84/19.29 | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | End of split
% 133.84/19.29 | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | Case 2:
% 133.84/19.29 | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | (6558) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.84/19.29 | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.84/19.29 | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.84/19.29 | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.84/19.29 | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.84/19.29 | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.84/19.29 | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.84/19.29 | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.84/19.29 | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.84/19.29 | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.84/19.29 | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.84/19.29 | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.84/19.29 | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.84/19.29 | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.84/19.29 | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.84/19.29 | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.84/19.29 | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.84/19.29 | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.84/19.29 | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.84/19.29 | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.84/19.29 | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.84/19.29 | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.84/19.29 | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.84/19.29 | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.84/19.29 | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.84/19.29 | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.84/19.29 | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.84/19.29 | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.84/19.29 | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.84/19.29 | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.84/19.29 | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.84/19.29 | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.84/19.29 | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.84/19.29 | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.84/19.29 | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.84/19.29 | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.84/19.29 | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.84/19.29 | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.84/19.29 | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.84/19.29 | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.84/19.29 | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.84/19.29 | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.84/19.29 | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.84/19.29 | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.84/19.29 | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.84/19.29 | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.84/19.29 | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.84/19.29 | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.84/19.29 | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.84/19.29 | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.84/19.29 | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.84/19.29 | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.84/19.29 | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.84/19.29 | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.84/19.29 | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.84/19.29 | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.84/19.29 | | | | | | | | | | | | & $i(all_56_29))))
% 133.84/19.29 | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | BETA: splitting (6558) gives:
% 133.84/19.29 | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | Case 1:
% 133.84/19.29 | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | (6559) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.84/19.29 | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.84/19.29 | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.84/19.29 | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.84/19.29 | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.84/19.29 | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.84/19.29 | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.84/19.29 | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.84/19.29 | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.84/19.29 | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.84/19.29 | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.84/19.29 | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.84/19.29 | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.84/19.29 | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.84/19.29 | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | BETA: splitting (6559) gives:
% 133.84/19.29 | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | Case 1:
% 133.84/19.29 | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | (6560) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.84/19.29 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.84/19.29 | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.84/19.29 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.84/19.29 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 133.84/19.29 | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 133.84/19.29 | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | ALPHA: (6560) implies:
% 133.84/19.29 | | | | | | | | | | | | | | (6561) op(e1, e1) = e3
% 133.84/19.29 | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | REF_CLOSE: (39), (6513), (6561), (function-axioms) are
% 133.84/19.29 | | | | | | | | | | | | | | inconsistent by sub-proof #771.
% 133.84/19.29 | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | Case 2:
% 133.84/19.29 | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | (6562) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 =
% 133.84/19.29 | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.84/19.29 | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2,
% 133.84/19.29 | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.84/19.29 | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.84/19.29 | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 133.84/19.29 | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | ALPHA: (6562) implies:
% 133.84/19.29 | | | | | | | | | | | | | | (6563) ~ (all_56_21 = e1)
% 133.84/19.29 | | | | | | | | | | | | | | (6564) op(e1, e1) = all_56_21
% 133.84/19.29 | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | REF_CLOSE: (39), (194), (334), (372), (6513), (6554), (6563),
% 133.84/19.29 | | | | | | | | | | | | | | (6564), (function-axioms) are inconsistent by
% 133.84/19.29 | | | | | | | | | | | | | | sub-proof #124.
% 133.84/19.29 | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | End of split
% 133.84/19.29 | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | Case 2:
% 133.84/19.29 | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | (6565) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.84/19.29 | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.84/19.29 | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 133.84/19.29 | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 133.84/19.29 | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.84/19.29 | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.84/19.29 | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.84/19.29 | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.84/19.29 | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.84/19.29 | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.84/19.29 | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.84/19.29 | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.84/19.29 | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.84/19.29 | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.84/19.29 | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.84/19.29 | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.84/19.29 | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.84/19.29 | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.84/19.29 | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.84/19.29 | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.84/19.29 | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.84/19.29 | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.84/19.29 | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.84/19.29 | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.84/19.29 | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.84/19.29 | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.84/19.29 | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.84/19.29 | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.84/19.29 | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.84/19.29 | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.84/19.29 | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.84/19.29 | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.84/19.29 | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.84/19.29 | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.84/19.29 | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.84/19.29 | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.84/19.29 | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.84/19.29 | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.84/19.29 | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.84/19.29 | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.84/19.29 | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.84/19.29 | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.84/19.29 | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.84/19.29 | | | | | | | | | | | | | & $i(all_56_29))))
% 133.84/19.29 | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | BETA: splitting (6565) gives:
% 133.84/19.29 | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | Case 1:
% 133.84/19.29 | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | (6566) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.84/19.29 | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.84/19.29 | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 133.84/19.29 | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.84/19.29 | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 133.84/19.29 | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 133.84/19.29 | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | ALPHA: (6566) implies:
% 133.84/19.29 | | | | | | | | | | | | | | (6567) op(e2, e2) = e0
% 133.84/19.29 | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | REF_CLOSE: (4), (5153), (6567), (function-axioms) are
% 133.84/19.29 | | | | | | | | | | | | | | inconsistent by sub-proof #675.
% 133.84/19.29 | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | Case 2:
% 133.84/19.29 | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | (6568) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.84/19.29 | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.84/19.29 | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.84/19.29 | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.84/19.29 | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.84/19.29 | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.84/19.29 | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.84/19.29 | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.84/19.29 | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.84/19.29 | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.84/19.29 | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.84/19.29 | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.84/19.29 | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.84/19.29 | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.84/19.29 | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.84/19.29 | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.84/19.29 | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.84/19.29 | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.84/19.29 | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.84/19.29 | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.84/19.29 | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.84/19.29 | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.84/19.29 | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.84/19.29 | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.84/19.29 | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.84/19.29 | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.84/19.29 | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.84/19.29 | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.84/19.29 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.84/19.29 | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.84/19.29 | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | BETA: splitting (6568) gives:
% 133.84/19.29 | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | Case 1:
% 133.84/19.29 | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | (6569) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.84/19.29 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 133.84/19.29 | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.84/19.29 | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.84/19.29 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 133.84/19.29 | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.84/19.29 | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 133.84/19.29 | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | ALPHA: (6569) implies:
% 133.84/19.29 | | | | | | | | | | | | | | | (6570) op(e1, e1) = e2
% 133.84/19.29 | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (6570), (function-axioms) are
% 133.84/19.29 | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 133.84/19.29 | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | Case 2:
% 133.84/19.29 | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | (6571) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.84/19.29 | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.84/19.29 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 133.84/19.29 | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.84/19.29 | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 133.84/19.29 | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.84/19.29 | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.84/19.29 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 133.84/19.29 | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 133.84/19.29 | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.84/19.29 | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.84/19.29 | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.84/19.29 | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.84/19.29 | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.84/19.29 | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 133.84/19.29 | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.84/19.29 | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.84/19.29 | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.84/19.29 | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.84/19.29 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.84/19.29 | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 133.84/19.29 | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 133.84/19.29 | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 133.84/19.29 | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 133.84/19.29 | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 133.84/19.29 | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.84/19.29 | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 133.84/19.29 | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 133.84/19.29 | | | | | | | | | | | | | | | $i(all_56_29)))
% 133.84/19.29 | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | ALPHA: (6571) implies:
% 133.84/19.29 | | | | | | | | | | | | | | | (6572) op(e0, e0) = all_56_31
% 133.84/19.29 | | | | | | | | | | | | | | | (6573) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.84/19.29 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.84/19.29 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.84/19.29 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.84/19.29 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 133.84/19.29 | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 133.84/19.29 | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 133.84/19.29 | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 133.84/19.29 | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 133.84/19.29 | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 133.84/19.29 | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 133.84/19.29 | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 133.84/19.29 | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 133.84/19.29 | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.84/19.29 | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.84/19.29 | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 133.84/19.29 | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.84/19.29 | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 133.84/19.29 | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 133.84/19.29 | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 133.84/19.29 | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.84/19.29 | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 133.84/19.29 | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 133.84/19.29 | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 133.84/19.29 | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 133.84/19.29 | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.84/19.29 | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 133.84/19.29 | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | Case 1:
% 133.84/19.29 | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | (6574) all_54_10 = e3
% 133.84/19.29 | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | REF_CLOSE: (334), (6513), (6574) are inconsistent by
% 133.84/19.29 | | | | | | | | | | | | | | | | sub-proof #742.
% 133.84/19.29 | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | Case 2:
% 133.84/19.29 | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | (6575) ~ (all_54_10 = e3)
% 133.84/19.29 | | | | | | | | | | | | | | | | (6576) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 133.84/19.29 | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | BETA: splitting (6576) gives:
% 133.84/19.29 | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.29 | | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | | (6577) all_54_10 = e2
% 133.84/19.29 | | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (372), (6577) are inconsistent by sub-proof
% 133.84/19.29 | | | | | | | | | | | | | | | | | #741.
% 133.84/19.29 | | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.29 | | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | | (6578) ~ (all_54_10 = e2)
% 133.84/19.29 | | | | | | | | | | | | | | | | | (6579) all_54_10 = e1 | all_54_10 = e0
% 133.84/19.29 | | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | | BETA: splitting (6579) gives:
% 133.84/19.29 | | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.29 | | | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | | | (6580) all_54_10 = e1
% 133.84/19.29 | | | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (6580) imply:
% 133.84/19.29 | | | | | | | | | | | | | | | | | | (6581) all_6_2 = e1
% 133.84/19.29 | | | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | | | SIMP: (6581) implies:
% 133.84/19.29 | | | | | | | | | | | | | | | | | | (6582) all_6_2 = e1
% 133.84/19.29 | | | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | | | REDUCE: (348), (6582) imply:
% 133.84/19.29 | | | | | | | | | | | | | | | | | | (6583) ~ (all_52_2 = e1)
% 133.84/19.29 | | | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | | | REDUCE: (366), (6582) imply:
% 133.84/19.29 | | | | | | | | | | | | | | | | | | (6584) ~ (all_52_14 = e1)
% 133.84/19.29 | | | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | | | REDUCE: (6513), (6582) imply:
% 133.84/19.29 | | | | | | | | | | | | | | | | | | (6585) ~ (e3 = e1)
% 133.84/19.29 | | | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | | | REDUCE: (372), (6582) imply:
% 133.84/19.29 | | | | | | | | | | | | | | | | | | (6586) ~ (e2 = e1)
% 133.84/19.29 | | | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 133.84/19.29 | | | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.29 | | | | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | (6587) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 133.84/19.29 | | | | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | BETA: splitting (6587) gives:
% 133.84/19.29 | | | | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | | (6588) all_57_9 = e1 & op(e3, e0) = e1
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | | ALPHA: (6588) implies:
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | | (6589) all_57_9 = e1
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | (6590) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6590) gives:
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | | (6591) all_57_0 = e1 & op(e3, e3) = e1
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6591) implies:
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | | (6592) op(e3, e3) = e1
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (236),
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | | (238), (6508), (6589), (6592), (function-axioms)
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #686.
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | | (6593) all_57_2 = e1 & op(e2, e3) = e1
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (5143), (6593), (function-axioms) are
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #676.
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.29 | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | (6594) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6594) gives:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | (6595) all_57_6 = e1 & op(e1, e3) = e1
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6595) implies:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | (6596) op(e1, e3) = e1
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (6583), (6596), (function-axioms) are
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #725.
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | (6597) all_57_12 = e1 & op(e0, e3) = e1
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6597) implies:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | (6598) all_57_12 = e1
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6573) gives:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | (6599) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27))
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6599) gives:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | (6600) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6600) implies:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | (6601) op(e0, e3) = e0
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (6507), (6601), (function-axioms) are
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #219.
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | (6602) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6602) implies:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | (6603) all_56_31 = e2
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6572), (6603) imply:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | (6604) op(e0, e0) = e2
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (157), (158), (211), (6548), (6549),
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | (6598), (6604), (function-axioms) are inconsistent
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #123.
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | (6605) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6605) gives:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | (6606) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6606) implies:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | (6607) op(e1, e0) = e1
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (6584), (6607), (function-axioms) are
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #327.
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | (6608) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6608) implies:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | (6609) ~ (all_56_21 = e1)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | (6610) op(e1, e1) = all_56_21
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (194), (334), (372), (6513), (6554), (6609),
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | (6610), (function-axioms) are inconsistent by
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #124.
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | End of split
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | (6611) all_57_10 = e1 & op(e2, e0) = e1
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | ALPHA: (6611) implies:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | (6612) op(e2, e0) = e1
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (5148), (6612), (function-axioms) are
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #180.
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | End of split
% 133.84/19.30 | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | (6613) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | BETA: splitting (6613) gives:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | (6614) all_57_11 = e1 & op(e1, e0) = e1
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | ALPHA: (6614) implies:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | (6615) op(e1, e0) = e1
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (6584), (6615), (function-axioms) are
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #327.
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | (6616) all_57_15 = e1 & op(e0, e0) = e1
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | ALPHA: (6616) implies:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | (6617) op(e0, e0) = e1
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6552), (6617), (function-axioms) are
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #606.
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | End of split
% 133.84/19.30 | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | End of split
% 133.84/19.30 | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.30 | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | (6618) all_54_10 = e0
% 133.84/19.30 | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (6554), (6618) are inconsistent by
% 133.84/19.30 | | | | | | | | | | | | | | | | | | sub-proof #506.
% 133.84/19.30 | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | End of split
% 133.84/19.30 | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | End of split
% 133.84/19.30 | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | End of split
% 133.84/19.30 | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | End of split
% 133.84/19.30 | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | End of split
% 133.84/19.30 | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | End of split
% 133.84/19.30 | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | End of split
% 133.84/19.30 | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | Case 2:
% 133.84/19.30 | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | (6619) all_40_2 = e0
% 133.84/19.30 | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | COMBINE_EQS: (332), (6619) imply:
% 133.84/19.30 | | | | | | | | | | | (6620) all_6_2 = e0
% 133.84/19.30 | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | SIMP: (6620) implies:
% 133.84/19.30 | | | | | | | | | | | (6621) all_6_2 = e0
% 133.84/19.30 | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | COMBINE_EQS: (295), (6621) imply:
% 133.84/19.30 | | | | | | | | | | | (6622) all_46_2 = e0
% 133.84/19.30 | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | REDUCE: (359), (6621) imply:
% 133.84/19.30 | | | | | | | | | | | (6623) ~ (all_52_6 = e0)
% 133.84/19.30 | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | REDUCE: (362), (6621) imply:
% 133.84/19.30 | | | | | | | | | | | (6624) ~ (all_52_9 = e0)
% 133.84/19.30 | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | REDUCE: (6513), (6621) imply:
% 133.84/19.30 | | | | | | | | | | | (6625) ~ (e3 = e0)
% 133.84/19.30 | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | REDUCE: (372), (6621) imply:
% 133.84/19.30 | | | | | | | | | | | (6626) ~ (e2 = e0)
% 133.84/19.30 | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | REDUCE: (39), (6621) imply:
% 133.84/19.30 | | | | | | | | | | | (6627) op(e1, e1) = e0
% 133.84/19.30 | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | BETA: splitting (100) gives:
% 133.84/19.30 | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | Case 1:
% 133.84/19.30 | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | (6628) ~ (all_46_2 = e0)
% 133.84/19.30 | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | REDUCE: (6622), (6628) imply:
% 133.84/19.30 | | | | | | | | | | | | (6629) $false
% 133.84/19.30 | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | CLOSE: (6629) is inconsistent.
% 133.84/19.30 | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | Case 2:
% 133.84/19.30 | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | (6630) ( ~ (all_46_0 = e2) & op(e0, e1) = all_46_0 &
% 133.84/19.30 | | | | | | | | | | | | $i(all_46_0)) | ( ~ (all_46_1 = e3) & op(e0, e0)
% 133.84/19.30 | | | | | | | | | | | | = all_46_1 & $i(all_46_1))
% 133.84/19.30 | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | BETA: splitting (103) gives:
% 133.84/19.30 | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | Case 1:
% 133.84/19.30 | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | (6631) ~ (all_48_2 = e1)
% 133.84/19.30 | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | REDUCE: (5142), (6631) imply:
% 133.84/19.30 | | | | | | | | | | | | | (6632) $false
% 133.84/19.30 | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | CLOSE: (6632) is inconsistent.
% 133.84/19.30 | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | Case 2:
% 133.84/19.30 | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | (6633) ( ~ (all_48_0 = e3) & op(e1, e2) = all_48_0 &
% 133.84/19.30 | | | | | | | | | | | | | $i(all_48_0)) | ( ~ (all_48_1 = e0) & op(e1, e1)
% 133.84/19.30 | | | | | | | | | | | | | = all_48_1 & $i(all_48_1))
% 133.84/19.30 | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | BETA: splitting (6630) gives:
% 133.84/19.30 | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | Case 1:
% 133.84/19.30 | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | (6634) ~ (all_46_0 = e2) & op(e0, e1) = all_46_0 &
% 133.84/19.30 | | | | | | | | | | | | | | $i(all_46_0)
% 133.84/19.30 | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | ALPHA: (6634) implies:
% 133.84/19.30 | | | | | | | | | | | | | | (6635) ~ (all_46_0 = e2)
% 133.84/19.30 | | | | | | | | | | | | | | (6636) op(e0, e1) = all_46_0
% 133.84/19.30 | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 133.84/19.30 | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | Case 1:
% 133.84/19.30 | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | (6637) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 133.84/19.30 | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 133.84/19.30 | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | REF_CLOSE: (4), (167), (5153), (6505), (6637),
% 133.84/19.30 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.84/19.30 | | | | | | | | | | | | | | | #152.
% 133.84/19.30 | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | Case 2:
% 133.84/19.30 | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | (6638) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 133.84/19.30 | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 133.84/19.30 | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | BETA: splitting (6638) gives:
% 133.84/19.30 | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | Case 1:
% 133.84/19.30 | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | (6639) all_57_5 = e0 & op(e2, e1) = e0
% 133.84/19.30 | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | REF_CLOSE: (165), (6624), (6639), (function-axioms) are
% 133.84/19.30 | | | | | | | | | | | | | | | | inconsistent by sub-proof #455.
% 133.84/19.30 | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | Case 2:
% 133.84/19.30 | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | (6640) all_57_10 = e0 & op(e2, e0) = e0
% 133.84/19.30 | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | ALPHA: (6640) implies:
% 133.84/19.30 | | | | | | | | | | | | | | | | (6641) all_57_10 = e0
% 133.84/19.30 | | | | | | | | | | | | | | | | (6642) op(e2, e0) = e0
% 133.84/19.30 | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 133.84/19.30 | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.30 | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | (6643) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 133.84/19.30 | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 133.84/19.30 | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (224), (225),
% 133.84/19.30 | | | | | | | | | | | | | | | | | (226), (6508), (6641), (6642), (6643),
% 133.84/19.30 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.84/19.30 | | | | | | | | | | | | | | | | | #445.
% 133.84/19.30 | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.30 | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | (6644) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 133.84/19.30 | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 133.84/19.30 | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | BETA: splitting (6644) gives:
% 133.84/19.30 | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.30 | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | (6645) all_57_7 = e0 & op(e1, e2) = e0
% 133.84/19.30 | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (6623), (6645), (function-axioms) are
% 133.84/19.30 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #505.
% 133.84/19.30 | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.30 | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | (6646) all_57_13 = e0 & op(e0, e2) = e0
% 133.84/19.30 | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | ALPHA: (6646) implies:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | (6647) all_57_13 = e0
% 133.84/19.30 | | | | | | | | | | | | | | | | | | (6648) op(e0, e2) = e0
% 133.84/19.30 | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | BETA: splitting (6633) gives:
% 133.84/19.30 | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | (6649) ~ (all_48_0 = e3) & op(e1, e2) = all_48_0 &
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | $i(all_48_0)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | ALPHA: (6649) implies:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | (6650) ~ (all_48_0 = e3)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | (6651) op(e1, e2) = all_48_0
% 133.84/19.30 | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | all_46_0, e1, e0, simplifying with (157), (6636)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | gives:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | (6652) all_52_11 = all_46_0
% 133.84/19.30 | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0,
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (158), (6648) gives:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | (6653) all_52_7 = e0
% 133.84/19.30 | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6,
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | all_48_0, e2, e1, simplifying with (162), (6651)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | gives:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | (6654) all_52_6 = all_48_0
% 133.84/19.30 | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | e0, e0, e2, simplifying with (164), (6642) gives:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | (6655) all_52_13 = e0
% 133.84/19.30 | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (6654) imply:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | (6656) all_54_9 = all_48_0
% 133.84/19.30 | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | REDUCE: (143), (6654) imply:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | (6657) ~ (all_52_2 = all_48_0)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | REDUCE: (126), (6654) imply:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | (6658) ~ (all_52_14 = all_48_0)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | SIMP: (6658) implies:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | (6659) ~ (all_52_14 = all_48_0)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | REDUCE: (6623), (6654) imply:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | (6660) ~ (all_48_0 = e0)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | REDUCE: (110), (6655) imply:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | (6661) ~ (all_52_14 = e0)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | SIMP: (6661) implies:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | (6662) ~ (all_52_14 = e0)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | (6663) all_54_9 = e3
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6650), (6656), (6663) are inconsistent by
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | sub-proof #176.
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | (6664) ~ (all_54_9 = e3)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | (6665) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | BETA: splitting (6665) gives:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | (6666) all_54_9 = e2
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6656), (6666) imply:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | (6667) all_48_0 = e2
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | SIMP: (6667) implies:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | (6668) all_48_0 = e2
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | REDUCE: (6657), (6668) imply:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | (6669) ~ (all_52_2 = e2)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | REDUCE: (6659), (6668) imply:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | (6670) ~ (all_52_14 = e2)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | REDUCE: (6650), (6668) imply:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | (6671) ~ (e3 = e2)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | (6672) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6672) gives:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | (6673) all_57_9 = e2 & op(e3, e0) = e2
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6673) implies:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | (6674) all_57_9 = e2
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | (6675) all_54_11 = e3
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (6551), (6675) are inconsistent by
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #260.
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | (6676) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6676) gives:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | (6677) all_54_11 = e2
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (6670), (6677) are inconsistent by
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #259.
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | (6678) all_54_11 = e1 | all_54_11 = e0
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6678) gives:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | (6679) all_54_11 = e1
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (6679) imply:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | (6680) all_52_14 = e1
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6680) implies:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | (6681) all_52_14 = e1
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (6681) imply:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | (6682) ~ (all_52_2 = e1)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6683) all_54_8 = e3
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (6683) imply:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6684) all_52_2 = e3
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (6684) imply:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6685) ~ (all_52_1 = e3)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (6684) imply:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6686) ~ (all_52_3 = e3)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6686) implies:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6687) ~ (all_52_3 = e3)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6688) all_54_4 = e3
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (6685), (6688) are inconsistent by
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #481.
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6689) ~ (all_54_4 = e3)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6690) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6690) gives:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6691) all_54_4 = e2
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (6691) imply:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6692) all_52_1 = e2
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6692) implies:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6693) all_52_1 = e2
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (6693) imply:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6694) ~ (all_52_3 = e2)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6694) implies:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6695) ~ (all_52_3 = e2)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (6693) imply:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6696) op(e2, e3) = e2
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6697) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6697) gives:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6698) all_57_0 = e1 & op(e3, e3) = e1
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6698) implies:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6699) op(e3, e3) = e1
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (39), (169), (170), (232), (361),
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6508), (6627), (6674), (6699), (function-axioms)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #487.
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6700) all_57_2 = e1 & op(e2, e3) = e1
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6700) implies:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6701) op(e2, e3) = e1
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6696), (6701), (function-axioms) are
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #450.
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6702) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6702) gives:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6703) all_57_6 = e1 & op(e1, e3) = e1
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (144), (163), (192), (248), (6507), (6687),
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6695), (6703), (function-axioms) are inconsistent
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #422.
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6704) all_57_12 = e1 & op(e0, e3) = e1
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6704) implies:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6705) all_57_12 = e1
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6706) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6706) gives:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6707) all_57_12 = e2 & op(e0, e3) = e2
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6707) implies:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6708) all_57_12 = e2
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6705), (6708) imply:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6709) e2 = e1
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (6709) imply:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6710) $false
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6710) is inconsistent.
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6711) all_57_13 = e2 & op(e0, e2) = e2
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6647), (6711) are inconsistent by sub-proof
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #122.
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6712) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6712) gives:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6713) all_57_14 = e2 & op(e0, e1) = e2
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6713) implies:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6714) op(e0, e1) = e2
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6635), (6636), (6714), (function-axioms) are
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #759.
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6715) all_57_15 = e2 & op(e0, e0) = e2
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6715) implies:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6716) op(e0, e0) = e2
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (157), (158), (211), (6548), (6549),
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6705), (6716), (function-axioms) are inconsistent
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #123.
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6717) all_54_4 = e1 | all_54_4 = e0
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (5143), (6505), (6717) are inconsistent by
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #153.
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6718) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (6506), (6669), (6682), (6718) are
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #429.
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | (6719) all_54_11 = e0
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (6662), (6719) are inconsistent by
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #258.
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | (6720) all_57_10 = e2 & op(e2, e0) = e2
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6720) implies:
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | (6721) op(e2, e0) = e2
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6642), (6721), (function-axioms) are
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #451.
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | (6722) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6722) gives:
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | (6723) all_57_11 = e2 & op(e1, e0) = e2
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (6670), (6723), (function-axioms) are
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #514.
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | (6724) all_57_15 = e2 & op(e0, e0) = e2
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6724) implies:
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | (6725) op(e0, e0) = e2
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6552), (6725), (function-axioms) are
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #634.
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | (6726) all_54_9 = e1 | all_54_9 = e0
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (5145), (6623), (6726) are inconsistent by
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | sub-proof #168.
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.30 | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.30 | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | (6727) ~ (all_48_1 = e0) & op(e1, e1) = all_48_1 &
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | $i(all_48_1)
% 133.90/19.30 | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6627), (6727), (function-axioms) are inconsistent
% 133.90/19.30 | | | | | | | | | | | | | | | | | | | by sub-proof #187.
% 133.90/19.30 | | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.30 | | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | | End of split
% 133.90/19.30 | | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | | End of split
% 133.90/19.30 | | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | | End of split
% 133.90/19.30 | | | | | | | | | | | | | | |
% 133.90/19.30 | | | | | | | | | | | | | | End of split
% 133.90/19.31 | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | Case 2:
% 133.90/19.31 | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | (6728) ~ (all_46_1 = e3) & op(e0, e0) = all_46_1 &
% 133.90/19.31 | | | | | | | | | | | | | | $i(all_46_1)
% 133.90/19.31 | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | REF_CLOSE: (6552), (6728), (function-axioms) are inconsistent
% 133.90/19.31 | | | | | | | | | | | | | | by sub-proof #758.
% 133.90/19.31 | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | End of split
% 133.90/19.31 | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | End of split
% 133.90/19.31 | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | End of split
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | End of split
% 133.90/19.31 | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | End of split
% 133.90/19.31 | | | | | | | | |
% 133.90/19.31 | | | | | | | | Case 2:
% 133.90/19.31 | | | | | | | | |
% 133.90/19.31 | | | | | | | | | (6729) all_28_2 = e3
% 133.90/19.31 | | | | | | | | | (6730) ( ~ (all_28_0 = e2) & op(e3, e1) = all_28_0 &
% 133.90/19.31 | | | | | | | | | $i(all_28_0)) | ( ~ (all_28_1 = e0) & op(e3, e3) =
% 133.90/19.31 | | | | | | | | | all_28_1 & $i(all_28_1))
% 133.90/19.31 | | | | | | | | |
% 133.90/19.31 | | | | | | | | | COMBINE_EQS: (316), (6729) imply:
% 133.90/19.31 | | | | | | | | | (6731) all_6_2 = e3
% 133.90/19.31 | | | | | | | | |
% 133.90/19.31 | | | | | | | | | REDUCE: (348), (6731) imply:
% 133.90/19.31 | | | | | | | | | (6732) ~ (all_52_2 = e3)
% 133.90/19.31 | | | | | | | | |
% 133.90/19.31 | | | | | | | | | REDUCE: (359), (6731) imply:
% 133.90/19.31 | | | | | | | | | (6733) ~ (all_52_6 = e3)
% 133.90/19.31 | | | | | | | | |
% 133.90/19.31 | | | | | | | | | REDUCE: (39), (6731) imply:
% 133.90/19.31 | | | | | | | | | (6734) op(e1, e1) = e3
% 133.90/19.31 | | | | | | | | |
% 133.90/19.31 | | | | | | | | | BETA: splitting (6730) gives:
% 133.90/19.31 | | | | | | | | |
% 133.90/19.31 | | | | | | | | | Case 1:
% 133.90/19.31 | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | (6735) ~ (all_28_0 = e2) & op(e3, e1) = all_28_0 &
% 133.90/19.31 | | | | | | | | | | $i(all_28_0)
% 133.90/19.31 | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | ALPHA: (6735) implies:
% 133.90/19.31 | | | | | | | | | | (6736) ~ (all_28_0 = e2)
% 133.90/19.31 | | | | | | | | | | (6737) op(e3, e1) = all_28_0
% 133.90/19.31 | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | BETA: splitting (5141) gives:
% 133.90/19.31 | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | Case 1:
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | (6738) ~ (all_8_0 = e0) & op(e1, e2) = all_8_0 &
% 133.90/19.31 | | | | | | | | | | | $i(all_8_0)
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | ALPHA: (6738) implies:
% 133.90/19.31 | | | | | | | | | | | (6739) ~ (all_8_0 = e0)
% 133.90/19.31 | | | | | | | | | | | (6740) op(e1, e2) = all_8_0
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6,
% 133.90/19.31 | | | | | | | | | | | all_8_0, e2, e1, simplifying with (162), (6740)
% 133.90/19.31 | | | | | | | | | | | gives:
% 133.90/19.31 | | | | | | | | | | | (6741) all_52_6 = all_8_0
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8,
% 133.90/19.31 | | | | | | | | | | | all_28_0, e1, e3, simplifying with (169), (6737)
% 133.90/19.31 | | | | | | | | | | | gives:
% 133.90/19.31 | | | | | | | | | | | (6742) all_52_8 = all_28_0
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | COMBINE_EQS: (257), (6741) imply:
% 133.90/19.31 | | | | | | | | | | | (6743) all_54_9 = all_8_0
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | REDUCE: (143), (6741) imply:
% 133.90/19.31 | | | | | | | | | | | (6744) ~ (all_52_2 = all_8_0)
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | REDUCE: (136), (6741) imply:
% 133.90/19.31 | | | | | | | | | | | (6745) ~ (all_52_4 = all_8_0)
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | REDUCE: (6733), (6741) imply:
% 133.90/19.31 | | | | | | | | | | | (6746) ~ (all_8_0 = e3)
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | REDUCE: (5145), (6741) imply:
% 133.90/19.31 | | | | | | | | | | | (6747) ~ (all_8_0 = e1)
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | BETA: splitting (195) gives:
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | Case 1:
% 133.90/19.31 | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | (6748) all_54_9 = e3
% 133.90/19.31 | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | COMBINE_EQS: (6743), (6748) imply:
% 133.90/19.31 | | | | | | | | | | | | (6749) all_8_0 = e3
% 133.90/19.31 | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | REDUCE: (6746), (6749) imply:
% 133.90/19.31 | | | | | | | | | | | | (6750) $false
% 133.90/19.31 | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | CLOSE: (6750) is inconsistent.
% 133.90/19.31 | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | Case 2:
% 133.90/19.31 | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | (6751) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 133.90/19.31 | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | BETA: splitting (6751) gives:
% 133.90/19.31 | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | Case 1:
% 133.90/19.31 | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | (6752) all_54_9 = e2
% 133.90/19.31 | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | COMBINE_EQS: (6743), (6752) imply:
% 133.90/19.31 | | | | | | | | | | | | | (6753) all_8_0 = e2
% 133.90/19.31 | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | REDUCE: (6744), (6753) imply:
% 133.90/19.31 | | | | | | | | | | | | | (6754) ~ (all_52_2 = e2)
% 133.90/19.31 | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | REDUCE: (6745), (6753) imply:
% 133.90/19.31 | | | | | | | | | | | | | (6755) ~ (all_52_4 = e2)
% 133.90/19.31 | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | BETA: splitting (196) gives:
% 133.90/19.31 | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | Case 1:
% 133.90/19.31 | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | (6756) all_54_8 = e3
% 133.90/19.31 | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | REF_CLOSE: (258), (6732), (6756) are inconsistent by
% 133.90/19.31 | | | | | | | | | | | | | | sub-proof #121.
% 133.90/19.31 | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | Case 2:
% 133.90/19.31 | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | (6757) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 133.90/19.31 | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | BETA: splitting (6757) gives:
% 133.90/19.31 | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | Case 1:
% 133.90/19.31 | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | (6758) all_54_8 = e2
% 133.90/19.31 | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | REF_CLOSE: (258), (6754), (6758) are inconsistent by
% 133.90/19.31 | | | | | | | | | | | | | | | sub-proof #430.
% 133.90/19.31 | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | Case 2:
% 133.90/19.31 | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | (6759) ~ (all_54_8 = e2)
% 133.90/19.31 | | | | | | | | | | | | | | | (6760) all_54_8 = e1 | all_54_8 = e0
% 133.90/19.31 | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | BETA: splitting (6760) gives:
% 133.90/19.31 | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | Case 1:
% 133.90/19.31 | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | (6761) all_54_8 = e1
% 133.90/19.31 | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (6761) imply:
% 133.90/19.31 | | | | | | | | | | | | | | | | (6762) all_52_2 = e1
% 133.90/19.31 | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | SIMP: (6762) implies:
% 133.90/19.31 | | | | | | | | | | | | | | | | (6763) all_52_2 = e1
% 133.90/19.31 | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | REDUCE: (141), (6763) imply:
% 133.90/19.31 | | | | | | | | | | | | | | | | (6764) ~ (all_52_14 = e1)
% 133.90/19.31 | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | SIMP: (6764) implies:
% 133.90/19.31 | | | | | | | | | | | | | | | | (6765) ~ (all_52_14 = e1)
% 133.90/19.31 | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | REDUCE: (6754), (6763) imply:
% 133.90/19.31 | | | | | | | | | | | | | | | | (6766) ~ (e2 = e1)
% 133.90/19.31 | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 133.90/19.31 | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.31 | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | (6767) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 133.90/19.31 | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 133.90/19.31 | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | BETA: splitting (6767) gives:
% 133.90/19.31 | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.31 | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | (6768) all_57_9 = e1 & op(e3, e0) = e1
% 133.90/19.31 | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | ALPHA: (6768) implies:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | (6769) all_57_9 = e1
% 133.90/19.31 | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 133.90/19.31 | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | (6770) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 133.90/19.31 | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | BETA: splitting (6770) gives:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | (6771) all_57_0 = e2 & op(e3, e3) = e2
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | ALPHA: (6771) implies:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | (6772) op(e3, e3) = e2
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6509), (6772), (function-axioms) are
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495.
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | (6773) all_57_1 = e2 & op(e3, e2) = e2
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (6755), (6773), (function-axioms) are
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #396.
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.31 | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | (6774) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 133.90/19.31 | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | BETA: splitting (6774) gives:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | (6775) all_57_4 = e2 & op(e3, e1) = e2
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6736), (6737), (6775), (function-axioms) are
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #218.
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | (6776) all_57_9 = e2 & op(e3, e0) = e2
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | ALPHA: (6776) implies:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | (6777) all_57_9 = e2
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6769), (6777) imply:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | (6778) e2 = e1
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (6778) imply:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | (6779) $false
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | CLOSE: (6779) is inconsistent.
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.31 | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.31 | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.31 | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | (6780) all_57_10 = e1 & op(e2, e0) = e1
% 133.90/19.31 | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | ALPHA: (6780) implies:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | (6781) op(e2, e0) = e1
% 133.90/19.31 | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (5148), (6781), (function-axioms) are
% 133.90/19.31 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #180.
% 133.90/19.31 | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | End of split
% 133.90/19.31 | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.31 | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | (6782) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 133.90/19.31 | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 133.90/19.31 | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | BETA: splitting (6782) gives:
% 133.90/19.31 | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.31 | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | (6783) all_57_11 = e1 & op(e1, e0) = e1
% 133.90/19.31 | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | ALPHA: (6783) implies:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | (6784) op(e1, e0) = e1
% 133.90/19.31 | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (6765), (6784), (function-axioms) are
% 133.90/19.31 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #327.
% 133.90/19.31 | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.31 | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | (6785) all_57_15 = e1 & op(e0, e0) = e1
% 133.90/19.31 | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | ALPHA: (6785) implies:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | (6786) op(e0, e0) = e1
% 133.90/19.31 | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (371), (6786), (function-axioms) are
% 133.90/19.31 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #354.
% 133.90/19.31 | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | End of split
% 133.90/19.31 | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | End of split
% 133.90/19.31 | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | Case 2:
% 133.90/19.31 | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | (6787) all_54_8 = e0
% 133.90/19.31 | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | REF_CLOSE: (258), (6506), (6787) are inconsistent by
% 133.90/19.31 | | | | | | | | | | | | | | | | sub-proof #475.
% 133.90/19.31 | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | End of split
% 133.90/19.31 | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | End of split
% 133.90/19.31 | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | End of split
% 133.90/19.31 | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | Case 2:
% 133.90/19.31 | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | (6788) all_54_9 = e1 | all_54_9 = e0
% 133.90/19.31 | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | REF_CLOSE: (6739), (6743), (6747), (6788) are inconsistent by
% 133.90/19.31 | | | | | | | | | | | | | sub-proof #155.
% 133.90/19.31 | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | End of split
% 133.90/19.31 | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | End of split
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | Case 2:
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | (6789) ~ (all_8_1 = e3) & op(e1, e1) = all_8_1 &
% 133.90/19.31 | | | | | | | | | | | $i(all_8_1)
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | REF_CLOSE: (6734), (6789), (function-axioms) are inconsistent
% 133.90/19.31 | | | | | | | | | | | by sub-proof #128.
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | End of split
% 133.90/19.31 | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | Case 2:
% 133.90/19.31 | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | (6790) ~ (all_28_1 = e0) & op(e3, e3) = all_28_1 &
% 133.90/19.31 | | | | | | | | | | $i(all_28_1)
% 133.90/19.31 | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | REF_CLOSE: (6509), (6790), (function-axioms) are inconsistent
% 133.90/19.31 | | | | | | | | | | by sub-proof #211.
% 133.90/19.31 | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | End of split
% 133.90/19.31 | | | | | | | | |
% 133.90/19.31 | | | | | | | | End of split
% 133.90/19.31 | | | | | | | |
% 133.90/19.31 | | | | | | | Case 2:
% 133.90/19.31 | | | | | | | |
% 133.90/19.31 | | | | | | | | (6791) all_20_2 = e2
% 133.90/19.31 | | | | | | | | (6792) ( ~ (all_20_0 = e3) & op(e2, e0) = all_20_0 &
% 133.90/19.31 | | | | | | | | $i(all_20_0)) | ( ~ (all_20_1 = e1) & op(e2, e2) =
% 133.90/19.31 | | | | | | | | all_20_1 & $i(all_20_1))
% 133.90/19.31 | | | | | | | |
% 133.90/19.31 | | | | | | | | COMBINE_EQS: (318), (6791) imply:
% 133.90/19.31 | | | | | | | | (6793) all_4_2 = e2
% 133.90/19.31 | | | | | | | |
% 133.90/19.31 | | | | | | | | SIMP: (6793) implies:
% 133.90/19.31 | | | | | | | | (6794) all_4_2 = e2
% 133.90/19.31 | | | | | | | |
% 133.90/19.31 | | | | | | | | REDUCE: (349), (6794) imply:
% 133.90/19.31 | | | | | | | | (6795) ~ (all_52_3 = e2)
% 133.90/19.31 | | | | | | | |
% 133.90/19.31 | | | | | | | | REDUCE: (367), (6794) imply:
% 133.90/19.31 | | | | | | | | (6796) ~ (all_52_11 = e2)
% 133.90/19.31 | | | | | | | |
% 133.90/19.31 | | | | | | | | REDUCE: (368), (6794) imply:
% 133.90/19.31 | | | | | | | | (6797) ~ (all_52_12 = e2)
% 133.90/19.31 | | | | | | | |
% 133.90/19.31 | | | | | | | | REDUCE: (369), (6794) imply:
% 133.90/19.31 | | | | | | | | (6798) ~ (all_52_13 = e2)
% 133.90/19.31 | | | | | | | |
% 133.90/19.31 | | | | | | | | REDUCE: (370), (6794) imply:
% 133.90/19.31 | | | | | | | | (6799) ~ (all_52_14 = e2)
% 133.90/19.31 | | | | | | | |
% 133.90/19.31 | | | | | | | | REDUCE: (36), (6794) imply:
% 133.90/19.31 | | | | | | | | (6800) op(e0, e0) = e2
% 133.90/19.31 | | | | | | | |
% 133.90/19.31 | | | | | | | | BETA: splitting (67) gives:
% 133.90/19.31 | | | | | | | |
% 133.90/19.31 | | | | | | | | Case 1:
% 133.90/19.31 | | | | | | | | |
% 133.90/19.31 | | | | | | | | | (6801) ~ (all_24_2 = e0)
% 133.90/19.31 | | | | | | | | |
% 133.90/19.31 | | | | | | | | | REDUCE: (6504), (6801) imply:
% 133.90/19.31 | | | | | | | | | (6802) $false
% 133.90/19.31 | | | | | | | | |
% 133.90/19.31 | | | | | | | | | CLOSE: (6802) is inconsistent.
% 133.90/19.31 | | | | | | | | |
% 133.90/19.31 | | | | | | | | Case 2:
% 133.90/19.31 | | | | | | | | |
% 133.90/19.31 | | | | | | | | | (6803) ( ~ (all_24_0 = e1) & op(e0, e3) = all_24_0 &
% 133.90/19.31 | | | | | | | | | $i(all_24_0)) | ( ~ (all_24_1 = e2) & op(e0, e0) =
% 133.90/19.31 | | | | | | | | | all_24_1 & $i(all_24_1))
% 133.90/19.31 | | | | | | | | |
% 133.90/19.31 | | | | | | | | | BETA: splitting (6792) gives:
% 133.90/19.31 | | | | | | | | |
% 133.90/19.31 | | | | | | | | | Case 1:
% 133.90/19.31 | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | (6804) ~ (all_20_0 = e3) & op(e2, e0) = all_20_0 &
% 133.90/19.31 | | | | | | | | | | $i(all_20_0)
% 133.90/19.31 | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | ALPHA: (6804) implies:
% 133.90/19.31 | | | | | | | | | | (6805) ~ (all_20_0 = e3)
% 133.90/19.31 | | | | | | | | | | (6806) op(e2, e0) = all_20_0
% 133.90/19.31 | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | BETA: splitting (6803) gives:
% 133.90/19.31 | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | Case 1:
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | (6807) ~ (all_24_0 = e1) & op(e0, e3) = all_24_0 &
% 133.90/19.31 | | | | | | | | | | | $i(all_24_0)
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | ALPHA: (6807) implies:
% 133.90/19.31 | | | | | | | | | | | (6808) ~ (all_24_0 = e1)
% 133.90/19.31 | | | | | | | | | | | (6809) op(e0, e3) = all_24_0
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 133.90/19.31 | | | | | | | | | | | all_24_0, e3, e0, simplifying with (159), (6809)
% 133.90/19.31 | | | | | | | | | | | gives:
% 133.90/19.31 | | | | | | | | | | | (6810) all_52_3 = all_24_0
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 133.90/19.31 | | | | | | | | | | | all_20_0, e0, e2, simplifying with (164), (6806)
% 133.90/19.31 | | | | | | | | | | | gives:
% 133.90/19.31 | | | | | | | | | | | (6811) all_52_13 = all_20_0
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | COMBINE_EQS: (248), (6810) imply:
% 133.90/19.31 | | | | | | | | | | | (6812) all_54_12 = all_24_0
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | COMBINE_EQS: (259), (6811) imply:
% 133.90/19.31 | | | | | | | | | | | (6813) all_54_7 = all_20_0
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | REDUCE: (148), (6810) imply:
% 133.90/19.31 | | | | | | | | | | | (6814) ~ (all_52_1 = all_24_0)
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | REDUCE: (145), (6811) imply:
% 133.90/19.31 | | | | | | | | | | | (6815) ~ (all_52_1 = all_20_0)
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | REDUCE: (144), (6810) imply:
% 133.90/19.31 | | | | | | | | | | | (6816) ~ (all_52_2 = all_24_0)
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | REDUCE: (140), (6810) imply:
% 133.90/19.31 | | | | | | | | | | | (6817) ~ (all_52_7 = all_24_0)
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | SIMP: (6817) implies:
% 133.90/19.31 | | | | | | | | | | | (6818) ~ (all_52_7 = all_24_0)
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | REDUCE: (139), (6810) imply:
% 133.90/19.31 | | | | | | | | | | | (6819) ~ (all_52_11 = all_24_0)
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | SIMP: (6819) implies:
% 133.90/19.31 | | | | | | | | | | | (6820) ~ (all_52_11 = all_24_0)
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | REDUCE: (6795), (6810) imply:
% 133.90/19.31 | | | | | | | | | | | (6821) ~ (all_24_0 = e2)
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | REDUCE: (6507), (6810) imply:
% 133.90/19.31 | | | | | | | | | | | (6822) ~ (all_24_0 = e0)
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | REDUCE: (117), (6811) imply:
% 133.90/19.31 | | | | | | | | | | | (6823) ~ (all_52_9 = all_20_0)
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | REDUCE: (6798), (6811) imply:
% 133.90/19.31 | | | | | | | | | | | (6824) ~ (all_20_0 = e2)
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | REDUCE: (5148), (6811) imply:
% 133.90/19.31 | | | | | | | | | | | (6825) ~ (all_20_0 = e1)
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | BETA: splitting (209) gives:
% 133.90/19.31 | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | Case 1:
% 133.90/19.31 | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | (6826) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 133.90/19.31 | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 133.90/19.31 | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | BETA: splitting (6826) gives:
% 133.90/19.31 | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | Case 1:
% 133.90/19.31 | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | (6827) all_57_12 = e1 & op(e0, e3) = e1
% 133.90/19.31 | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | ALPHA: (6827) implies:
% 133.90/19.31 | | | | | | | | | | | | | (6828) all_57_12 = e1
% 133.90/19.31 | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | REF_CLOSE: (157), (158), (192), (211), (6800), (6808),
% 133.90/19.31 | | | | | | | | | | | | | (6812), (6818), (6820), (6821), (6822), (6828),
% 133.90/19.31 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.90/19.31 | | | | | | | | | | | | | #120.
% 133.90/19.31 | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | Case 2:
% 133.90/19.31 | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | (6829) all_57_13 = e1 & op(e0, e2) = e1
% 133.90/19.31 | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | REF_CLOSE: (158), (5146), (6829), (function-axioms) are
% 133.90/19.31 | | | | | | | | | | | | | inconsistent by sub-proof #178.
% 133.90/19.31 | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | End of split
% 133.90/19.31 | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | Case 2:
% 133.90/19.31 | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | (6830) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 133.90/19.31 | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 133.90/19.31 | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | BETA: splitting (6830) gives:
% 133.90/19.31 | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | Case 1:
% 133.90/19.31 | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | (6831) all_57_14 = e1 & op(e0, e1) = e1
% 133.90/19.31 | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | ALPHA: (6831) implies:
% 133.90/19.31 | | | | | | | | | | | | | (6832) all_57_14 = e1
% 133.90/19.31 | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | BETA: splitting (192) gives:
% 133.90/19.31 | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | Case 1:
% 133.90/19.31 | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | (6833) all_54_12 = e3
% 133.90/19.31 | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | COMBINE_EQS: (6812), (6833) imply:
% 133.90/19.31 | | | | | | | | | | | | | | (6834) all_24_0 = e3
% 133.90/19.31 | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | SIMP: (6834) implies:
% 133.90/19.31 | | | | | | | | | | | | | | (6835) all_24_0 = e3
% 133.90/19.31 | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | REDUCE: (6814), (6835) imply:
% 133.90/19.31 | | | | | | | | | | | | | | (6836) ~ (all_52_1 = e3)
% 133.90/19.31 | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | REDUCE: (6816), (6835) imply:
% 133.90/19.31 | | | | | | | | | | | | | | (6837) ~ (all_52_2 = e3)
% 133.90/19.31 | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | REDUCE: (6818), (6835) imply:
% 133.90/19.31 | | | | | | | | | | | | | | (6838) ~ (all_52_7 = e3)
% 133.90/19.31 | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | REDUCE: (6820), (6835) imply:
% 133.90/19.31 | | | | | | | | | | | | | | (6839) ~ (all_52_11 = e3)
% 133.90/19.31 | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 133.90/19.31 | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | Case 1:
% 133.90/19.31 | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | (6840) all_57_15 = e0 & op(e0, e0) = e0
% 133.90/19.31 | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | ALPHA: (6840) implies:
% 133.90/19.31 | | | | | | | | | | | | | | | (6841) op(e0, e0) = e0
% 133.90/19.31 | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | REF_CLOSE: (5), (6800), (6841), (function-axioms) are
% 133.90/19.31 | | | | | | | | | | | | | | | inconsistent by sub-proof #714.
% 133.90/19.31 | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | Case 2:
% 133.90/19.31 | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | (6842) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 133.90/19.31 | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 133.90/19.31 | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 133.90/19.31 | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 133.90/19.31 | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 133.90/19.31 | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | ALPHA: (6842) implies:
% 133.90/19.31 | | | | | | | | | | | | | | | (6843) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 133.90/19.31 | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 133.90/19.31 | | | | | | | | | | | | | | | e1) = e0)
% 133.90/19.31 | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 133.90/19.31 | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | Case 1:
% 133.90/19.31 | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | (6844) all_54_7 = e3
% 133.90/19.31 | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | REF_CLOSE: (6805), (6813), (6844) are inconsistent by
% 133.90/19.31 | | | | | | | | | | | | | | | | sub-proof #119.
% 133.90/19.31 | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | Case 2:
% 133.90/19.31 | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | (6845) ~ (all_54_7 = e3)
% 133.90/19.31 | | | | | | | | | | | | | | | | (6846) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 133.90/19.31 | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 133.90/19.31 | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.31 | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | (6847) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 133.90/19.31 | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 133.90/19.31 | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (167), (5143), (6509), (6847),
% 133.90/19.31 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.90/19.31 | | | | | | | | | | | | | | | | | #118.
% 133.90/19.31 | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.31 | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | (6848) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 133.90/19.31 | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 133.90/19.31 | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | BETA: splitting (6848) gives:
% 133.90/19.31 | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.31 | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | (6849) all_57_6 = e1 & op(e1, e3) = e1
% 133.90/19.31 | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | ALPHA: (6849) implies:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | (6850) op(e1, e3) = e1
% 133.90/19.31 | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 133.90/19.31 | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | (6851) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 133.90/19.31 | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (167), (6509), (6836), (6851),
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | #210.
% 133.90/19.31 | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | (6852) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 133.90/19.31 | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | BETA: splitting (6852) gives:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | (6853) all_57_6 = e3 & op(e1, e3) = e3
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (6837), (6853), (function-axioms) are
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #761.
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | (6854) all_57_12 = e3 & op(e0, e3) = e3
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | ALPHA: (6854) implies:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | (6855) all_57_12 = e3
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | (6856) op(e0, e3) = e3
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | (6857) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6857) gives:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | (6858) all_57_6 = e2 & op(e1, e3) = e2
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6858) implies:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | (6859) op(e1, e3) = e2
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (6850), (6859), (function-axioms) are
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #517.
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | (6860) all_57_7 = e2 & op(e1, e2) = e2
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6860) implies:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | (6861) all_57_7 = e2
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6843) gives:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | (6862) all_57_12 = e0 & op(e0, e3) = e0
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6862) implies:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | (6863) op(e0, e3) = e0
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (6507), (6863), (function-axioms) are
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #219.
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | (6864) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6864) gives:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | (6865) all_57_13 = e0 & op(e0, e2) = e0
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6865) implies:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | (6866) all_57_13 = e0
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | (6867) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6867) gives:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (6868) all_57_0 = e2 & op(e3, e3) = e2
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6868) implies:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (6869) op(e3, e3) = e2
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6509), (6869), (function-axioms) are
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495.
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (6870) all_57_2 = e2 & op(e2, e3) = e2
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6870) implies:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (6871) all_57_2 = e2
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6872) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6872) gives:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6873) all_57_1 = e3 & op(e3, e2) = e3
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6873) implies:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6874) all_57_1 = e3
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6846) gives:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6875) all_54_7 = e2
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6813), (6875) imply:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6876) all_20_0 = e2
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6824), (6876) imply:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6877) $false
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6877) is inconsistent.
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6878) ~ (all_54_7 = e2)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6879) all_54_7 = e1 | all_54_7 = e0
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6880) all_54_4 = e3
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (6836), (6880) are inconsistent by
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #481.
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6881) ~ (all_54_4 = e3)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6882) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6883) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6883) gives:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6884) all_57_0 = e2 & op(e3, e3) = e2
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6884) implies:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6885) op(e3, e3) = e2
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (231), (233), (6855),
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6871), (6885), (function-axioms) are inconsistent
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #489.
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6886) all_57_1 = e2 & op(e3, e2) = e2
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (208), (209),
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (6800), (6839), (6855), (6874), (6886),
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #207.
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6887) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6887) gives:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6888) all_57_4 = e2 & op(e3, e1) = e2
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6888) implies:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6889) all_57_4 = e2
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6879) gives:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6890) all_54_7 = e1
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6813), (6890) imply:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6891) all_20_0 = e1
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6825), (6891) imply:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6892) $false
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6892) is inconsistent.
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6893) all_54_7 = e0
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6813), (6893) imply:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6894) all_20_0 = e0
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6823), (6894) imply:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6895) ~ (all_52_9 = e0)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6805), (6894) imply:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6896) ~ (e3 = e0)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6824), (6894) imply:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6897) ~ (e2 = e0)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6825), (6894) imply:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6898) ~ (e1 = e0)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6899) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (170), (5144), (6509), (6899),
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #117.
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6900) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6900) gives:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6901) all_57_4 = e1 & op(e3, e1) = e1
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6889), (6901) are inconsistent by sub-proof
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #462.
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6902) all_57_9 = e1 & op(e3, e0) = e1
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6902) implies:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6903) all_57_9 = e1
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6904) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6904) gives:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6905) all_57_2 = e0 & op(e2, e3) = e0
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (6505), (6905), (function-axioms) are
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #225.
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6906) all_57_3 = e0 & op(e2, e2) = e0
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6906) implies:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6907) all_57_3 = e0
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6908) op(e2, e2) = e0
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6909) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (170), (5144), (6908), (6909),
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #564.
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6910) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6910) gives:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6911) all_57_7 = e1 & op(e1, e2) = e1
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6911) implies:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6912) all_57_7 = e1
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6872) gives:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6913) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6913) gives:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6914) all_57_1 = e2 & op(e3, e2) = e2
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6874), (6914) are inconsistent by sub-proof
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #563.
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6915) all_57_3 = e2 & op(e2, e2) = e2
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6915) implies:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6916) all_57_3 = e2
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6907), (6916) are inconsistent by sub-proof
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #679.
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6917) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6917) gives:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6861), (6912) imply:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6918) e2 = e1
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (6918) imply:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6919) $false
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6919) is inconsistent.
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6920) all_57_13 = e2 & op(e0, e2) = e2
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6866), (6920) are inconsistent by sub-proof
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #122.
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6921) all_57_3 = e3 & op(e2, e2) = e3
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6921) implies:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6922) op(e2, e2) = e3
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6908), (6922), (function-axioms) are
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641.
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6923) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6923) gives:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6924) all_57_7 = e3 & op(e1, e2) = e3
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6924) implies:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6925) all_57_7 = e3
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6912), (6925) are inconsistent by sub-proof
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #390.
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6926) all_57_13 = e3 & op(e0, e2) = e3
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6926) implies:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6927) all_57_13 = e3
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6866), (6927) are inconsistent by sub-proof
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #484.
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6928) all_57_13 = e1 & op(e0, e2) = e1
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6928) implies:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6929) all_57_13 = e1
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6866), (6929) are inconsistent by sub-proof
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #681.
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6930) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6930) gives:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6931) all_57_5 = e0 & op(e2, e1) = e0
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (6895), (6931), (function-axioms) are
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #455.
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6932) all_57_10 = e0 & op(e2, e0) = e0
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6932) implies:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6933) all_57_10 = e0
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6934) op(e2, e0) = e0
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6882) gives:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6935) all_54_4 = e2
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (6935) imply:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6936) all_52_1 = e2
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (6936) imply:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6937) ~ (all_52_9 = e2)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6937) implies:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6938) ~ (all_52_9 = e2)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6939) all_54_6 = e3
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (6939) imply:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6940) all_52_9 = e3
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (6940) imply:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6941) ~ (all_6_2 = e3)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6941) implies:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6942) ~ (all_6_2 = e3)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (6940) imply:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6943) op(e2, e1) = e3
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6944) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6944) gives:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6945) all_57_4 = e0 & op(e3, e1) = e0
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6945) implies:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6946) all_57_4 = e0
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (39), (221), (222),
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (6832), (6942), (6946), (function-axioms)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #558.
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6947) all_57_5 = e0 & op(e2, e1) = e0
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (6895), (6947), (function-axioms) are
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #455.
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6948) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6948) gives:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6949) all_57_8 = e0 & op(e1, e1) = e0
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6949) implies:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6950) op(e1, e1) = e0
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6951) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6951) gives:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6952) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (231), (232),
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (236), (238), (6508), (6855), (6871),
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6903), (6952), (function-axioms) are inconsistent
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #116.
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6953) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5153), (6856), (6953), (function-axioms) are
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #115.
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6954) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6954) gives:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6955) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6955) gives:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6956) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6956) implies:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6957) op(e1, e1) = e3
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6950), (6957), (function-axioms) are
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753.
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6958) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2,
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6943), (6958), (function-axioms) are
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #114.
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6959) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (39), (91), (157), (190), (246),
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332), (364), (372), (5153), (6796), (6800),
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6934), (6959), (function-axioms) are inconsistent
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #154.
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6960) all_57_14 = e0 & op(e0, e1) = e0
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6960) implies:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6961) all_57_14 = e0
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6832), (6961) imply:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6962) e1 = e0
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6962) implies:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6963) e1 = e0
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5152), (6963) imply:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6964) all_57_3 = e0
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6965) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (167), (5153), (6836), (6965),
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #166.
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6966) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (224), (225),
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6933), (6934), (6964), (6966), (function-axioms)
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #447.
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6967) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (5147), (6895), (6938), (6967) are
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #478.
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6968) all_54_4 = e1 | all_54_4 = e0
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (163), (268), (6505), (6850), (6968),
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #243.
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6969) all_57_9 = e2 & op(e3, e0) = e2
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (6797), (6969), (function-axioms) are
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #460.
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6970) all_57_3 = e3 & op(e2, e2) = e3
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6970) implies:
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6971) op(e2, e2) = e3
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5153), (6971), (function-axioms) are
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #325.
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6972) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6972) gives:
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6973) all_57_7 = e3 & op(e1, e2) = e3
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6973) implies:
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6974) all_57_7 = e3
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6861), (6974) imply:
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6975) e3 = e2
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6855), (6975) imply:
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6976) all_57_12 = e2
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (208), (209),
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (6800), (6839), (6976), (function-axioms)
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #458.
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6977) all_57_13 = e3 & op(e0, e2) = e3
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (6838), (6977), (function-axioms) are
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #556.
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | (6978) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6978) gives:
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (6979) all_57_6 = e2 & op(e1, e3) = e2
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6979) implies:
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (6980) op(e1, e3) = e2
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (6850), (6980), (function-axioms) are
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #517.
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (6981) all_57_12 = e2 & op(e0, e3) = e2
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6981) implies:
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (6982) all_57_12 = e2
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (208), (209),
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (6800), (6839), (6982), (function-axioms)
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #458.
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | (6983) all_57_14 = e0 & op(e0, e1) = e0
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6983) implies:
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | (6984) all_57_14 = e0
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6832), (6984) are inconsistent by sub-proof
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | #221.
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | (6985) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (160), (372), (6799), (6985),
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | #513.
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.33 | | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | End of split
% 133.90/19.33 | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | Case 2:
% 133.90/19.33 | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | (6986) all_57_12 = e1 & op(e0, e3) = e1
% 133.90/19.33 | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | ALPHA: (6986) implies:
% 133.90/19.33 | | | | | | | | | | | | | | | | | | (6987) all_57_12 = e1
% 133.90/19.33 | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (157), (158), (211), (6800), (6838),
% 133.90/19.33 | | | | | | | | | | | | | | | | | | (6839), (6987), (function-axioms) are inconsistent
% 133.90/19.33 | | | | | | | | | | | | | | | | | | by sub-proof #123.
% 133.90/19.33 | | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | | End of split
% 133.90/19.33 | | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | | End of split
% 133.90/19.33 | | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | | End of split
% 133.90/19.33 | | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | End of split
% 133.90/19.33 | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | Case 2:
% 133.90/19.33 | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | (6988) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 133.90/19.33 | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | | REF_CLOSE: (6808), (6812), (6821), (6822), (6988) are
% 133.90/19.33 | | | | | | | | | | | | | | inconsistent by sub-proof #205.
% 133.90/19.33 | | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | End of split
% 133.90/19.33 | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | Case 2:
% 133.90/19.33 | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | (6989) all_57_15 = e1 & op(e0, e0) = e1
% 133.90/19.33 | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | ALPHA: (6989) implies:
% 133.90/19.33 | | | | | | | | | | | | | (6990) op(e0, e0) = e1
% 133.90/19.33 | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | | REF_CLOSE: (6), (6800), (6990), (function-axioms) are
% 133.90/19.33 | | | | | | | | | | | | | inconsistent by sub-proof #636.
% 133.90/19.33 | | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | | End of split
% 133.90/19.33 | | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | End of split
% 133.90/19.33 | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | Case 2:
% 133.90/19.33 | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | (6991) ~ (all_24_1 = e2) & op(e0, e0) = all_24_1 &
% 133.90/19.33 | | | | | | | | | | | $i(all_24_1)
% 133.90/19.33 | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | | REF_CLOSE: (6800), (6991), (function-axioms) are inconsistent
% 133.90/19.33 | | | | | | | | | | | by sub-proof #204.
% 133.90/19.33 | | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | End of split
% 133.90/19.33 | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | Case 2:
% 133.90/19.33 | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | (6992) ~ (all_20_1 = e1) & op(e2, e2) = all_20_1 &
% 133.90/19.33 | | | | | | | | | | $i(all_20_1)
% 133.90/19.33 | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | | REF_CLOSE: (5153), (6992), (function-axioms) are inconsistent
% 133.90/19.33 | | | | | | | | | | by sub-proof #113.
% 133.90/19.33 | | | | | | | | | |
% 133.90/19.33 | | | | | | | | | End of split
% 133.90/19.33 | | | | | | | | |
% 133.90/19.33 | | | | | | | | End of split
% 133.90/19.33 | | | | | | | |
% 133.90/19.33 | | | | | | | End of split
% 133.90/19.33 | | | | | | |
% 133.90/19.33 | | | | | | End of split
% 133.90/19.33 | | | | | |
% 133.90/19.33 | | | | | End of split
% 133.90/19.33 | | | | |
% 133.90/19.33 | | | | Case 2:
% 133.90/19.33 | | | | |
% 133.90/19.33 | | | | | (6993) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2,
% 133.90/19.33 | | | | | e0) = e1)
% 133.90/19.33 | | | | |
% 133.90/19.33 | | | | | REF_CLOSE: (164), (165), (5147), (5148), (6993), (function-axioms) are
% 133.90/19.33 | | | | | inconsistent by sub-proof #112.
% 133.90/19.33 | | | | |
% 133.90/19.33 | | | | End of split
% 133.90/19.33 | | | |
% 133.90/19.33 | | | End of split
% 133.90/19.33 | | |
% 133.90/19.33 | | Case 2:
% 133.90/19.33 | | |
% 133.90/19.33 | | | (6994) all_6_2 = e2
% 133.90/19.33 | | | (6995) ( ~ (all_6_0 = e0) & op(e2, e1) = all_6_0 & $i(all_6_0)) | ( ~
% 133.90/19.33 | | | (all_6_1 = e3) & op(e2, e2) = all_6_1 & $i(all_6_1))
% 133.90/19.33 | | |
% 133.90/19.33 | | | COMBINE_EQS: (324), (6994) imply:
% 133.90/19.33 | | | (6996) all_18_2 = e2
% 133.90/19.33 | | |
% 133.90/19.33 | | | REDUCE: (348), (6994) imply:
% 133.90/19.33 | | | (6997) ~ (all_52_2 = e2)
% 133.90/19.33 | | |
% 133.90/19.33 | | | REDUCE: (359), (6994) imply:
% 133.90/19.33 | | | (6998) ~ (all_52_6 = e2)
% 133.90/19.33 | | |
% 133.90/19.33 | | | REDUCE: (361), (6994) imply:
% 133.90/19.33 | | | (6999) ~ (all_52_8 = e2)
% 133.90/19.33 | | |
% 133.90/19.33 | | | REDUCE: (362), (6994) imply:
% 133.90/19.33 | | | (7000) ~ (all_52_9 = e2)
% 133.90/19.33 | | |
% 133.90/19.33 | | | REDUCE: (364), (6994) imply:
% 133.90/19.33 | | | (7001) ~ (all_52_11 = e2)
% 133.90/19.33 | | |
% 133.90/19.33 | | | REDUCE: (366), (6994) imply:
% 133.97/19.33 | | | (7002) ~ (all_52_14 = e2)
% 133.97/19.33 | | |
% 133.97/19.33 | | | BETA: splitting (221) gives:
% 133.97/19.33 | | |
% 133.97/19.33 | | | Case 1:
% 133.97/19.33 | | | |
% 133.97/19.33 | | | | (7003) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2,
% 133.97/19.33 | | | | e1) = e2)
% 133.97/19.33 | | | |
% 133.97/19.33 | | | | REF_CLOSE: (165), (169), (6999), (7000), (7003), (function-axioms) are
% 133.97/19.33 | | | | inconsistent by sub-proof #441.
% 133.97/19.33 | | | |
% 133.97/19.33 | | | Case 2:
% 133.97/19.33 | | | |
% 133.97/19.33 | | | | (7004) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0,
% 133.97/19.33 | | | | e1) = e2)
% 133.97/19.33 | | | |
% 133.97/19.33 | | | | BETA: splitting (7004) gives:
% 133.97/19.33 | | | |
% 133.97/19.33 | | | | Case 1:
% 133.97/19.33 | | | | |
% 133.97/19.33 | | | | | (7005) all_57_8 = e2 & op(e1, e1) = e2
% 133.97/19.33 | | | | |
% 133.97/19.33 | | | | | ALPHA: (7005) implies:
% 133.97/19.33 | | | | | (7006) all_57_8 = e2
% 133.97/19.33 | | | | | (7007) op(e1, e1) = e2
% 133.97/19.33 | | | | |
% 133.97/19.33 | | | | | BETA: splitting (43) gives:
% 133.97/19.33 | | | | |
% 133.97/19.33 | | | | | Case 1:
% 133.97/19.33 | | | | | |
% 133.97/19.33 | | | | | | (7008) ~ (all_8_2 = e1)
% 133.97/19.33 | | | | | |
% 133.97/19.33 | | | | | | BETA: splitting (46) gives:
% 133.97/19.33 | | | | | |
% 133.97/19.33 | | | | | | Case 1:
% 133.97/19.33 | | | | | | |
% 133.97/19.33 | | | | | | | (7009) ~ (all_10_2 = e0)
% 133.97/19.33 | | | | | | |
% 133.97/19.33 | | | | | | | BETA: splitting (52) gives:
% 133.97/19.33 | | | | | | |
% 133.97/19.33 | | | | | | | Case 1:
% 133.97/19.33 | | | | | | | |
% 133.97/19.33 | | | | | | | | (7010) ~ (all_14_2 = e3)
% 133.97/19.33 | | | | | | | |
% 133.97/19.33 | | | | | | | | REDUCE: (329), (7010) imply:
% 133.97/19.33 | | | | | | | | (7011) ~ (all_8_2 = e3)
% 133.97/19.33 | | | | | | | |
% 133.97/19.33 | | | | | | | | BETA: splitting (58) gives:
% 133.97/19.33 | | | | | | | |
% 133.97/19.33 | | | | | | | | Case 1:
% 133.97/19.33 | | | | | | | | |
% 133.97/19.33 | | | | | | | | | (7012) ~ (all_18_2 = e2)
% 133.97/19.33 | | | | | | | | |
% 133.97/19.33 | | | | | | | | | REDUCE: (6996), (7012) imply:
% 133.97/19.33 | | | | | | | | | (7013) $false
% 133.97/19.33 | | | | | | | | |
% 133.97/19.33 | | | | | | | | | CLOSE: (7013) is inconsistent.
% 133.97/19.33 | | | | | | | | |
% 133.97/19.33 | | | | | | | | Case 2:
% 133.97/19.33 | | | | | | | | |
% 133.97/19.33 | | | | | | | | | (7014) ( ~ (all_18_0 = e3) & op(e2, e1) = all_18_0 &
% 133.97/19.33 | | | | | | | | | $i(all_18_0)) | ( ~ (all_18_1 = e0) & op(e2, e2) =
% 133.97/19.33 | | | | | | | | | all_18_1 & $i(all_18_1))
% 133.97/19.33 | | | | | | | | |
% 133.97/19.33 | | | | | | | | | BETA: splitting (55) gives:
% 133.97/19.33 | | | | | | | | |
% 133.97/19.33 | | | | | | | | | Case 1:
% 133.97/19.33 | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | (7015) ~ (all_16_2 = e2)
% 133.97/19.33 | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | REDUCE: (327), (7015) imply:
% 133.97/19.33 | | | | | | | | | | (7016) ~ (all_10_2 = e2)
% 133.97/19.33 | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | BETA: splitting (61) gives:
% 133.97/19.33 | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | Case 1:
% 133.97/19.33 | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | (7017) ~ (all_20_2 = e2)
% 133.97/19.33 | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | REDUCE: (318), (7017) imply:
% 133.97/19.33 | | | | | | | | | | | (7018) ~ (all_4_2 = e2)
% 133.97/19.33 | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | BETA: splitting (79) gives:
% 133.97/19.33 | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | Case 1:
% 133.97/19.33 | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | (7019) ~ (all_32_2 = e1)
% 133.97/19.33 | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | REDUCE: (312), (7019) imply:
% 133.97/19.33 | | | | | | | | | | | | (7020) ~ (all_10_2 = e1)
% 133.97/19.33 | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | BETA: splitting (204) gives:
% 133.97/19.33 | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | Case 1:
% 133.97/19.33 | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | (7021) all_54_0 = e3
% 133.97/19.33 | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | COMBINE_EQS: (278), (7021) imply:
% 133.97/19.33 | | | | | | | | | | | | | (7022) all_10_2 = e3
% 133.97/19.33 | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | REDUCE: (336), (7022) imply:
% 133.97/19.33 | | | | | | | | | | | | | (7023) ~ (all_52_1 = e3)
% 133.97/19.33 | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | REDUCE: (342), (7022) imply:
% 133.97/19.33 | | | | | | | | | | | | | (7024) ~ (all_52_4 = e3)
% 133.97/19.33 | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | REDUCE: (344), (7022) imply:
% 133.97/19.33 | | | | | | | | | | | | | (7025) ~ (all_52_8 = e3)
% 133.97/19.33 | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | REDUCE: (346), (7022) imply:
% 133.97/19.33 | | | | | | | | | | | | | (7026) ~ (all_52_12 = e3)
% 133.97/19.33 | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | REDUCE: (45), (7022) imply:
% 133.97/19.33 | | | | | | | | | | | | | (7027) op(e3, e3) = e3
% 133.97/19.33 | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | BETA: splitting (76) gives:
% 133.97/19.33 | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | Case 1:
% 133.97/19.33 | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | (7028) ~ (all_30_2 = e0)
% 133.97/19.33 | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | REDUCE: (309), (7028) imply:
% 133.97/19.33 | | | | | | | | | | | | | | (7029) ~ (all_8_2 = e0)
% 133.97/19.33 | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 133.97/19.33 | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | Case 1:
% 133.97/19.33 | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | (7030) all_54_5 = e3
% 133.97/19.33 | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | REF_CLOSE: (267), (7011), (7030) are inconsistent by
% 133.97/19.33 | | | | | | | | | | | | | | | sub-proof #554.
% 133.97/19.33 | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | Case 2:
% 133.97/19.33 | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | (7031) ~ (all_54_5 = e3)
% 133.97/19.33 | | | | | | | | | | | | | | | (7032) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 133.97/19.33 | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | BETA: splitting (7032) gives:
% 133.97/19.33 | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | Case 1:
% 133.97/19.33 | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | (7033) all_54_5 = e2
% 133.97/19.33 | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (7033) imply:
% 133.97/19.33 | | | | | | | | | | | | | | | | (7034) all_8_2 = e2
% 133.97/19.33 | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | SIMP: (7034) implies:
% 133.97/19.33 | | | | | | | | | | | | | | | | (7035) all_8_2 = e2
% 133.97/19.33 | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | REDUCE: (347), (7035) imply:
% 133.97/19.33 | | | | | | | | | | | | | | | | (7036) ~ (all_52_1 = e2)
% 133.97/19.33 | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | REDUCE: (358), (7035) imply:
% 133.97/19.33 | | | | | | | | | | | | | | | | (7037) ~ (all_52_13 = e2)
% 133.97/19.33 | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | REDUCE: (7011), (7035) imply:
% 133.97/19.33 | | | | | | | | | | | | | | | | (7038) ~ (e3 = e2)
% 133.97/19.33 | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 133.97/19.33 | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.33 | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | (7039) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 133.97/19.33 | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 133.97/19.33 | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | BETA: splitting (7039) gives:
% 133.97/19.33 | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.33 | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | (7040) all_57_9 = e2 & op(e3, e0) = e2
% 133.97/19.33 | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | ALPHA: (7040) implies:
% 133.97/19.33 | | | | | | | | | | | | | | | | | | (7041) all_57_9 = e2
% 133.97/19.33 | | | | | | | | | | | | | | | | | | (7042) op(e3, e0) = e2
% 133.97/19.33 | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 133.97/19.33 | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.33 | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | (7043) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 133.97/19.33 | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | BETA: splitting (7043) gives:
% 133.97/19.33 | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | (7044) all_57_2 = e2 & op(e2, e3) = e2
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | ALPHA: (7044) implies:
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | (7045) op(e2, e3) = e2
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (7036), (7045), (function-axioms) are
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #779.
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | (7046) all_57_3 = e2 & op(e2, e2) = e2
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | ALPHA: (7046) implies:
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | (7047) all_57_3 = e2
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | (7048) op(e2, e2) = e2
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | (7049) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7049) gives:
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | (7050) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7050) gives:
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | (7051) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7051) implies:
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | (7052) op(e3, e3) = e2
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (234),
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | (238), (7024), (7041), (7052), (function-axioms)
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #250.
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | (7053) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7053) implies:
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | (7054) op(e3, e3) = e1
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7027), (7054), (function-axioms) are
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #775.
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | (7055) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (42), (168), (7011), (7042), (7055),
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | #110.
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | (7056) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7056) gives:
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | (7057) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (7000), (7007), (7057),
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | #108.
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | (7058) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7058) gives:
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | (7059) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7059) implies:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (7060) op(e2, e0) = e2
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (7037), (7060), (function-axioms) are
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (7061) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7061) gives:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (7062) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7062) implies:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (7063) ~ (all_56_11 = e2)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (7064) op(e2, e2) = all_56_11
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7048), (7063), (7064), (function-axioms) are
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #531.
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (7065) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7065) implies:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (7066) op(e0, e0) = all_56_31
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (7067) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (39), (45), (100), (118), (157), (160),
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (163), (164), (165), (167), (189), (190), (204),
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (218), (226), (245), (246), (278), (295), (336),
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (338), (364), (369), (370), (371), (7009), (7016),
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (7018), (7020), (7047), (7066), (7067),
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | #744.
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.34 | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | (7068) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (165), (7000), (7037), (7068),
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | #625.
% 133.97/19.34 | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.34 | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.34 | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | (7069) all_57_10 = e2 & op(e2, e0) = e2
% 133.97/19.34 | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | ALPHA: (7069) implies:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | (7070) op(e2, e0) = e2
% 133.97/19.34 | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (7037), (7070), (function-axioms) are
% 133.97/19.34 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 133.97/19.34 | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | End of split
% 133.97/19.34 | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.34 | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | (7071) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 133.97/19.34 | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | BETA: splitting (7071) gives:
% 133.97/19.34 | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.34 | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | (7072) all_57_11 = e2 & op(e1, e0) = e2
% 133.97/19.34 | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (7002), (7072), (function-axioms) are
% 133.97/19.34 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #514.
% 133.97/19.34 | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.34 | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | (7073) all_57_15 = e2 & op(e0, e0) = e2
% 133.97/19.34 | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (7018), (7073), (function-axioms) are
% 133.97/19.34 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #107.
% 133.97/19.34 | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | End of split
% 133.97/19.34 | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | End of split
% 133.97/19.34 | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | Case 2:
% 133.97/19.34 | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | (7074) all_54_5 = e1 | all_54_5 = e0
% 133.97/19.34 | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | REF_CLOSE: (267), (7008), (7029), (7074) are inconsistent by
% 133.97/19.34 | | | | | | | | | | | | | | | | sub-proof #624.
% 133.97/19.34 | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | End of split
% 133.97/19.34 | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | End of split
% 133.97/19.34 | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | Case 2:
% 133.97/19.34 | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | (7075) all_30_2 = e0
% 133.97/19.34 | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | COMBINE_EQS: (309), (7075) imply:
% 133.97/19.34 | | | | | | | | | | | | | | (7076) all_8_2 = e0
% 133.97/19.34 | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | SIMP: (7076) implies:
% 133.97/19.34 | | | | | | | | | | | | | | (7077) all_8_2 = e0
% 133.97/19.34 | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | REDUCE: (347), (7077) imply:
% 133.97/19.34 | | | | | | | | | | | | | | (7078) ~ (all_52_1 = e0)
% 133.97/19.34 | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | REDUCE: (356), (7077) imply:
% 133.97/19.34 | | | | | | | | | | | | | | (7079) ~ (all_52_9 = e0)
% 133.97/19.34 | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | REDUCE: (42), (7077) imply:
% 133.97/19.34 | | | | | | | | | | | | | | (7080) op(e2, e2) = e0
% 133.97/19.34 | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | BETA: splitting (7014) gives:
% 133.97/19.34 | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | Case 1:
% 133.97/19.34 | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | (7081) ~ (all_18_0 = e3) & op(e2, e1) = all_18_0 &
% 133.97/19.34 | | | | | | | | | | | | | | | $i(all_18_0)
% 133.97/19.34 | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | ALPHA: (7081) implies:
% 133.97/19.34 | | | | | | | | | | | | | | | (7082) ~ (all_18_0 = e3)
% 133.97/19.34 | | | | | | | | | | | | | | | (7083) op(e2, e1) = all_18_0
% 133.97/19.34 | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 133.97/19.34 | | | | | | | | | | | | | | | all_18_0, e1, e2, simplifying with (165), (7083)
% 133.97/19.34 | | | | | | | | | | | | | | | gives:
% 133.97/19.34 | | | | | | | | | | | | | | | (7084) all_52_9 = all_18_0
% 133.97/19.34 | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | COMBINE_EQS: (260), (7084) imply:
% 133.97/19.34 | | | | | | | | | | | | | | | (7085) all_54_6 = all_18_0
% 133.97/19.34 | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | REDUCE: (146), (7084) imply:
% 133.97/19.34 | | | | | | | | | | | | | | | (7086) ~ (all_52_1 = all_18_0)
% 133.97/19.34 | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | REDUCE: (123), (7084) imply:
% 133.97/19.34 | | | | | | | | | | | | | | | (7087) ~ (all_52_8 = all_18_0)
% 133.97/19.34 | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | REDUCE: (7000), (7084) imply:
% 133.97/19.34 | | | | | | | | | | | | | | | (7088) ~ (all_18_0 = e2)
% 133.97/19.34 | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | REDUCE: (7079), (7084) imply:
% 133.97/19.34 | | | | | | | | | | | | | | | (7089) ~ (all_18_0 = e0)
% 133.97/19.34 | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 133.97/19.34 | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | Case 1:
% 133.97/19.34 | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | (7090) all_54_6 = e3
% 133.97/19.34 | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | COMBINE_EQS: (7085), (7090) imply:
% 133.97/19.34 | | | | | | | | | | | | | | | | (7091) all_18_0 = e3
% 133.97/19.34 | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | REDUCE: (7082), (7091) imply:
% 133.97/19.34 | | | | | | | | | | | | | | | | (7092) $false
% 133.97/19.34 | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | CLOSE: (7092) is inconsistent.
% 133.97/19.34 | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | Case 2:
% 133.97/19.34 | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | (7093) ~ (all_54_6 = e3)
% 133.97/19.34 | | | | | | | | | | | | | | | | (7094) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 133.97/19.34 | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | BETA: splitting (7094) gives:
% 133.97/19.34 | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.34 | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | (7095) all_54_6 = e2
% 133.97/19.34 | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | COMBINE_EQS: (7085), (7095) imply:
% 133.97/19.34 | | | | | | | | | | | | | | | | | (7096) all_18_0 = e2
% 133.97/19.34 | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | REDUCE: (7088), (7096) imply:
% 133.97/19.34 | | | | | | | | | | | | | | | | | (7097) $false
% 133.97/19.34 | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | CLOSE: (7097) is inconsistent.
% 133.97/19.34 | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.34 | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | (7098) all_54_6 = e1 | all_54_6 = e0
% 133.97/19.34 | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | BETA: splitting (7098) gives:
% 133.97/19.34 | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.34 | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | (7099) all_54_6 = e1
% 133.97/19.34 | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7085), (7099) imply:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | (7100) all_18_0 = e1
% 133.97/19.34 | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | REDUCE: (7086), (7100) imply:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | (7101) ~ (all_52_1 = e1)
% 133.97/19.34 | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | REDUCE: (7087), (7100) imply:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | (7102) ~ (all_52_8 = e1)
% 133.97/19.34 | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | REDUCE: (7082), (7100) imply:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | (7103) ~ (e3 = e1)
% 133.97/19.34 | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | REDUCE: (7083), (7100) imply:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | (7104) op(e2, e1) = e1
% 133.97/19.34 | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 133.97/19.34 | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | (7105) all_54_4 = e3
% 133.97/19.34 | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (7105) imply:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | (7106) all_52_1 = e3
% 133.97/19.34 | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | REDUCE: (7023), (7106) imply:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | (7107) $false
% 133.97/19.34 | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | CLOSE: (7107) is inconsistent.
% 133.97/19.34 | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | (7108) ~ (all_54_4 = e3)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | (7109) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 133.97/19.34 | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | BETA: splitting (7109) gives:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | (7110) all_54_4 = e2
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (7110) imply:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | (7111) all_52_1 = e2
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (7111) imply:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | (7112) ~ (all_52_13 = e2)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | SIMP: (7112) implies:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | (7113) ~ (all_52_13 = e2)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | REDUCE: (7023), (7111) imply:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | (7114) ~ (e3 = e2)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | (7115) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7115) gives:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | (7116) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (7027), (7116), (function-axioms) are
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #623.
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | (7117) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7117) gives:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (7118) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3,
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7118) implies:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (7119) op(e3, e0) = e3
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (7026), (7119), (function-axioms) are
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #733.
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (7120) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2,
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7120) implies:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (7121) op(e2, e2) = e3
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (39), (45), (165), (168), (169), (202),
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (204), (206), (270), (278), (344), (346), (361),
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (371), (6999), (7000), (7007), (7009), (7016),
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (7020), (7102), (7104), (7121), (function-axioms)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #104.
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | (7122) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7122) gives:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | (7123) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (7000), (7007), (7123),
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | #108.
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | (7124) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7124) gives:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (7125) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7125) implies:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (7126) op(e2, e0) = e2
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (7113), (7126), (function-axioms) are
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (7127) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7127) gives:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (7128) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7128) implies:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (7129) ~ (all_56_19 = e1)
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (7130) op(e2, e1) = all_56_19
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7104), (7129), (7130), (function-axioms) are
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #106.
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (7131) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7131) implies:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | (7132) op(e0, e0) = all_56_31
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | (7133) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (39), (169), (202), (270), (361), (371),
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | (6999), (7025), (7027), (7102), (7104), (7132),
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | (7133), (function-axioms) are inconsistent by
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #105.
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | (7134) all_54_4 = e1 | all_54_4 = e0
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (7078), (7101), (7134) are inconsistent by
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | sub-proof #153.
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.35 | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.35 | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.35 | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | (7135) all_54_6 = e0
% 133.97/19.35 | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7085), (7135) imply:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | (7136) all_18_0 = e0
% 133.97/19.35 | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | REDUCE: (7089), (7136) imply:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | (7137) $false
% 133.97/19.35 | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | CLOSE: (7137) is inconsistent.
% 133.97/19.35 | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | End of split
% 133.97/19.35 | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | End of split
% 133.97/19.35 | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | End of split
% 133.97/19.35 | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | Case 2:
% 133.97/19.35 | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | (7138) ~ (all_18_1 = e0) & op(e2, e2) = all_18_1 &
% 133.97/19.35 | | | | | | | | | | | | | | | $i(all_18_1)
% 133.97/19.35 | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | REF_CLOSE: (7080), (7138), (function-axioms) are inconsistent
% 133.97/19.35 | | | | | | | | | | | | | | | by sub-proof #103.
% 133.97/19.35 | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | End of split
% 133.97/19.35 | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | End of split
% 133.97/19.35 | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | Case 2:
% 133.97/19.35 | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | (7139) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 133.97/19.35 | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | REF_CLOSE: (278), (7009), (7016), (7020), (7139) are
% 133.97/19.35 | | | | | | | | | | | | | inconsistent by sub-proof #777.
% 133.97/19.35 | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | End of split
% 133.97/19.35 | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | Case 2:
% 133.97/19.35 | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | (7140) all_32_2 = e1
% 133.97/19.35 | | | | | | | | | | | | (7141) ( ~ (all_32_0 = e0) & op(e1, e3) = all_32_0 &
% 133.97/19.35 | | | | | | | | | | | | $i(all_32_0)) | ( ~ (all_32_1 = e2) & op(e1, e1)
% 133.97/19.35 | | | | | | | | | | | | = all_32_1 & $i(all_32_1))
% 133.97/19.35 | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | COMBINE_EQS: (312), (7140) imply:
% 133.97/19.35 | | | | | | | | | | | | (7142) all_10_2 = e1
% 133.97/19.35 | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | REDUCE: (336), (7142) imply:
% 133.97/19.35 | | | | | | | | | | | | (7143) ~ (all_52_1 = e1)
% 133.97/19.35 | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | REDUCE: (338), (7142) imply:
% 133.97/19.35 | | | | | | | | | | | | (7144) ~ (all_52_2 = e1)
% 133.97/19.35 | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | REDUCE: (340), (7142) imply:
% 133.97/19.35 | | | | | | | | | | | | (7145) ~ (all_52_3 = e1)
% 133.97/19.35 | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | REDUCE: (45), (7142) imply:
% 133.97/19.35 | | | | | | | | | | | | (7146) op(e3, e3) = e1
% 133.97/19.35 | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | BETA: splitting (7141) gives:
% 133.97/19.35 | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | Case 1:
% 133.97/19.35 | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | (7147) ~ (all_32_0 = e0) & op(e1, e3) = all_32_0 &
% 133.97/19.35 | | | | | | | | | | | | | $i(all_32_0)
% 133.97/19.35 | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | ALPHA: (7147) implies:
% 133.97/19.35 | | | | | | | | | | | | | (7148) ~ (all_32_0 = e0)
% 133.97/19.35 | | | | | | | | | | | | | (7149) op(e1, e3) = all_32_0
% 133.97/19.35 | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2,
% 133.97/19.35 | | | | | | | | | | | | | all_32_0, e3, e1, simplifying with (163), (7149)
% 133.97/19.35 | | | | | | | | | | | | | gives:
% 133.97/19.35 | | | | | | | | | | | | | (7150) all_52_2 = all_32_0
% 133.97/19.35 | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | COMBINE_EQS: (258), (7150) imply:
% 133.97/19.35 | | | | | | | | | | | | | (7151) all_54_8 = all_32_0
% 133.97/19.35 | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | REDUCE: (149), (7150) imply:
% 133.97/19.35 | | | | | | | | | | | | | (7152) ~ (all_52_1 = all_32_0)
% 133.97/19.35 | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | REDUCE: (144), (7150) imply:
% 133.97/19.35 | | | | | | | | | | | | | (7153) ~ (all_52_3 = all_32_0)
% 133.97/19.35 | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | SIMP: (7153) implies:
% 133.97/19.35 | | | | | | | | | | | | | (7154) ~ (all_52_3 = all_32_0)
% 133.97/19.35 | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | REDUCE: (143), (7150) imply:
% 133.97/19.35 | | | | | | | | | | | | | (7155) ~ (all_52_6 = all_32_0)
% 133.97/19.35 | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | SIMP: (7155) implies:
% 133.97/19.35 | | | | | | | | | | | | | (7156) ~ (all_52_6 = all_32_0)
% 133.97/19.35 | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | REDUCE: (141), (7150) imply:
% 133.97/19.35 | | | | | | | | | | | | | (7157) ~ (all_52_14 = all_32_0)
% 133.97/19.35 | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | SIMP: (7157) implies:
% 133.97/19.35 | | | | | | | | | | | | | (7158) ~ (all_52_14 = all_32_0)
% 133.97/19.35 | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | REDUCE: (6997), (7150) imply:
% 133.97/19.35 | | | | | | | | | | | | | (7159) ~ (all_32_0 = e2)
% 133.97/19.35 | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | REDUCE: (7144), (7150) imply:
% 133.97/19.35 | | | | | | | | | | | | | (7160) ~ (all_32_0 = e1)
% 133.97/19.35 | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | BETA: splitting (196) gives:
% 133.97/19.35 | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | Case 1:
% 133.97/19.35 | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | (7161) all_54_8 = e3
% 133.97/19.35 | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | COMBINE_EQS: (7151), (7161) imply:
% 133.97/19.35 | | | | | | | | | | | | | | (7162) all_32_0 = e3
% 133.97/19.35 | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | REDUCE: (7152), (7162) imply:
% 133.97/19.35 | | | | | | | | | | | | | | (7163) ~ (all_52_1 = e3)
% 133.97/19.35 | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | REDUCE: (7154), (7162) imply:
% 133.97/19.35 | | | | | | | | | | | | | | (7164) ~ (all_52_3 = e3)
% 133.97/19.35 | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | REDUCE: (7156), (7162) imply:
% 133.97/19.35 | | | | | | | | | | | | | | (7165) ~ (all_52_6 = e3)
% 133.97/19.35 | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | REDUCE: (7158), (7162) imply:
% 133.97/19.35 | | | | | | | | | | | | | | (7166) ~ (all_52_14 = e3)
% 133.97/19.35 | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 133.97/19.35 | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | Case 1:
% 133.97/19.35 | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | (7167) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 133.97/19.35 | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 133.97/19.35 | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | BETA: splitting (7167) gives:
% 133.97/19.35 | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | Case 1:
% 133.97/19.35 | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | (7168) all_57_6 = e3 & op(e1, e3) = e3
% 133.97/19.35 | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | ALPHA: (7168) implies:
% 133.97/19.35 | | | | | | | | | | | | | | | | (7169) all_57_6 = e3
% 133.97/19.35 | | | | | | | | | | | | | | | | (7170) op(e1, e3) = e3
% 133.97/19.35 | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 133.97/19.35 | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.35 | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | (7171) ~ (all_30_2 = e0)
% 133.97/19.35 | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | REDUCE: (309), (7171) imply:
% 133.97/19.35 | | | | | | | | | | | | | | | | | (7172) ~ (all_8_2 = e0)
% 133.97/19.35 | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 133.97/19.35 | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.35 | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | (7173) all_54_5 = e3
% 133.97/19.35 | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (7173) imply:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | (7174) all_8_2 = e3
% 133.97/19.35 | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | REDUCE: (7011), (7174) imply:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | (7175) $false
% 133.97/19.35 | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | CLOSE: (7175) is inconsistent.
% 133.97/19.35 | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.35 | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | (7176) ~ (all_54_5 = e3)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | (7177) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 133.97/19.35 | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | BETA: splitting (7177) gives:
% 133.97/19.35 | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | (7178) all_54_5 = e2
% 133.97/19.35 | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (7178) imply:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | (7179) all_8_2 = e2
% 133.97/19.35 | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | REDUCE: (347), (7179) imply:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | (7180) ~ (all_52_1 = e2)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | REDUCE: (350), (7179) imply:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | (7181) ~ (all_52_4 = e2)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | REDUCE: (354), (7179) imply:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | (7182) ~ (all_52_7 = e2)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | REDUCE: (358), (7179) imply:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | (7183) ~ (all_52_13 = e2)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | REDUCE: (7011), (7179) imply:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | (7184) ~ (e3 = e2)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | (7185) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | BETA: splitting (7185) gives:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | (7186) all_57_9 = e2 & op(e3, e0) = e2
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | ALPHA: (7186) implies:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | (7187) op(e3, e0) = e2
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | (7188) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7188) gives:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | (7189) all_57_1 = e2 & op(e3, e2) = e2
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (7181), (7189), (function-axioms) are
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #396.
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | (7190) all_57_3 = e2 & op(e2, e2) = e2
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7190) implies:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | (7191) all_57_3 = e2
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | (7192) op(e2, e2) = e2
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | (7193) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7193) gives:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | (7194) all_57_12 = e2 & op(e0, e3) = e2
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7194) implies:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | (7195) all_57_12 = e2
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (7196) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7196) gives:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7197) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7170), (7195), (7197), (function-axioms) are
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #102.
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7198) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (42), (168), (7011), (7187), (7198),
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | #110.
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (7199) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7199) gives:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7200) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (7000), (7007), (7200),
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | #108.
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7201) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7201) gives:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7202) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7202) implies:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7203) op(e2, e0) = e2
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (7183), (7203), (function-axioms) are
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7204) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7204) gives:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7205) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7205) implies:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7206) ~ (all_56_11 = e2)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7207) op(e2, e2) = all_56_11
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7192), (7206), (7207), (function-axioms) are
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #531.
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7208) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7208) implies:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7209) op(e0, e0) = all_56_31
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7210) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7211) all_54_4 = e3
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (7211) imply:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7212) all_52_1 = e3
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7163), (7212) imply:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7213) $false
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7213) is inconsistent.
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7214) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7214) gives:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7215) all_54_4 = e2
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (7215) imply:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7216) all_52_1 = e2
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7180), (7216) imply:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7217) $false
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7217) is inconsistent.
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7218) ~ (all_54_4 = e2)
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7219) all_54_4 = e1 | all_54_4 = e0
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7219) gives:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7220) all_54_4 = e1
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (7220) imply:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7221) all_52_1 = e1
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7143), (7221) imply:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7222) $false
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7222) is inconsistent.
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7223) all_54_4 = e0
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (7223) imply:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7224) all_52_1 = e0
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (7224) imply:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7225) ~ (all_52_3 = e0)
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7225) implies:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7226) ~ (all_52_3 = e0)
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7180), (7224) imply:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7227) ~ (e2 = e0)
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (36), (159), (164), (165), (167), (225),
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (371), (7000), (7007), (7180), (7183), (7191),
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7192), (7209), (7210), (7226), (function-axioms)
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #101.
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | (7228) all_57_13 = e2 & op(e0, e2) = e2
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (7182), (7228), (function-axioms) are
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #100.
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | (7229) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7229) gives:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | (7230) all_57_14 = e2 & op(e0, e1) = e2
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (7001), (7230), (function-axioms) are
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #512.
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | (7231) all_57_15 = e2 & op(e0, e0) = e2
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (7018), (7231), (function-axioms) are
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #107.
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | (7232) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7232) gives:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | (7233) all_57_7 = e2 & op(e1, e2) = e2
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (6998), (7233), (function-axioms) are
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #515.
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | (7234) all_57_13 = e2 & op(e0, e2) = e2
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (7182), (7234), (function-axioms) are
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #100.
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | (7235) all_57_10 = e2 & op(e2, e0) = e2
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | ALPHA: (7235) implies:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | (7236) op(e2, e0) = e2
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (7183), (7236), (function-axioms) are
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | (7237) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | BETA: splitting (7237) gives:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | (7238) all_57_11 = e2 & op(e1, e0) = e2
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | ALPHA: (7238) implies:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | (7239) all_57_11 = e2
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (215), (216), (7006),
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | (7169), (7239) are inconsistent by sub-proof #572.
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | (7240) all_57_15 = e2 & op(e0, e0) = e2
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (7018), (7240), (function-axioms) are
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #107.
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | (7241) all_54_5 = e1 | all_54_5 = e0
% 133.97/19.36 | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (7008), (7172), (7241) are inconsistent by
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | sub-proof #624.
% 133.97/19.36 | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | (7242) all_30_2 = e0
% 133.97/19.36 | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | COMBINE_EQS: (309), (7242) imply:
% 133.97/19.36 | | | | | | | | | | | | | | | | | (7243) all_8_2 = e0
% 133.97/19.36 | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | SIMP: (7243) implies:
% 133.97/19.36 | | | | | | | | | | | | | | | | | (7244) all_8_2 = e0
% 133.97/19.36 | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | REDUCE: (347), (7244) imply:
% 133.97/19.36 | | | | | | | | | | | | | | | | | (7245) ~ (all_52_1 = e0)
% 133.97/19.36 | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | REDUCE: (350), (7244) imply:
% 133.97/19.36 | | | | | | | | | | | | | | | | | (7246) ~ (all_52_4 = e0)
% 133.97/19.36 | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | REDUCE: (356), (7244) imply:
% 133.97/19.36 | | | | | | | | | | | | | | | | | (7247) ~ (all_52_9 = e0)
% 133.97/19.36 | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | REDUCE: (42), (7244) imply:
% 133.97/19.36 | | | | | | | | | | | | | | | | | (7248) op(e2, e2) = e0
% 133.97/19.36 | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 133.97/19.36 | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.36 | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | (7249) all_54_4 = e3
% 133.97/19.36 | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (7249) imply:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | (7250) all_52_1 = e3
% 133.97/19.36 | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | REDUCE: (7163), (7250) imply:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | (7251) $false
% 133.97/19.36 | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | CLOSE: (7251) is inconsistent.
% 133.97/19.36 | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | (7252) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 133.97/19.36 | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | BETA: splitting (7252) gives:
% 133.97/19.36 | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | (7253) all_54_4 = e2
% 133.97/19.36 | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (7253) imply:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | (7254) all_52_1 = e2
% 133.97/19.36 | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | REDUCE: (148), (7254) imply:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | (7255) ~ (all_52_3 = e2)
% 133.97/19.36 | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | SIMP: (7255) implies:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | (7256) ~ (all_52_3 = e2)
% 133.97/19.36 | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | REDUCE: (145), (7254) imply:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | (7257) ~ (all_52_13 = e2)
% 133.97/19.36 | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | SIMP: (7257) implies:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | (7258) ~ (all_52_13 = e2)
% 133.97/19.36 | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | (7259) all_54_12 = e3
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (7164), (7259) are inconsistent by
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | sub-proof #424.
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | (7260) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | BETA: splitting (7260) gives:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | (7261) all_54_12 = e2
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (7256), (7261) are inconsistent by
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | sub-proof #423.
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | (7262) ~ (all_54_12 = e2)
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | (7263) all_54_12 = e1 | all_54_12 = e0
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7263) gives:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | (7264) all_54_12 = e1
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (7145), (7264) are inconsistent by
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | sub-proof #99.
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | (7265) all_54_12 = e0
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (7265) imply:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | (7266) all_52_3 = e0
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | SIMP: (7266) implies:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | (7267) all_52_3 = e0
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (349), (7267) imply:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | (7268) ~ (all_4_2 = e0)
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | SIMP: (7268) implies:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | (7269) ~ (all_4_2 = e0)
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7256), (7267) imply:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | (7270) ~ (e2 = e0)
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7145), (7267) imply:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | (7271) ~ (e1 = e0)
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | (7272) all_54_15 = e3
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (7272) imply:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | (7273) all_4_2 = e3
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7273) implies:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | (7274) all_4_2 = e3
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (7274) imply:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | (7275) all_34_2 = e3
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (7274) imply:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | (7276) ~ (all_52_7 = e3)
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (7274) imply:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | (7277) op(e0, e0) = e3
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | (7278) ~ (all_34_2 = e3)
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7275), (7278) imply:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | (7279) $false
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7279) is inconsistent.
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | (7280) ( ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 &
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_34_0)) | ( ~ (all_34_1 = e1) & op(e3, e3)
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | = all_34_1 & $i(all_34_1))
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | (7281) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7281) gives:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (7282) all_57_4 = e0 & op(e3, e1) = e0
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7282) implies:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (7283) all_57_4 = e0
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7284) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7284) gives:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7285) all_57_1 = e3 & op(e3, e2) = e3
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7285) implies:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7286) all_57_1 = e3
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (236), (7146), (7280), (7283),
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7286), (function-axioms) are inconsistent by
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #550.
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7287) all_57_3 = e3 & op(e2, e2) = e3
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7287) implies:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7288) op(e2, e2) = e3
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7248), (7288), (function-axioms) are
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641.
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7289) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (7165), (7276), (7289),
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | #555.
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (7290) all_57_5 = e0 & op(e2, e1) = e0
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7247), (7290), (function-axioms) are
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #455.
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | (7291) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7291) gives:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (7292) all_57_8 = e0 & op(e1, e1) = e0
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7292) implies:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (7293) op(e1, e1) = e0
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7007), (7293), (function-axioms) are
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #98.
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (7294) all_57_14 = e0 & op(e0, e1) = e0
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7294) implies:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (7295) all_57_14 = e0
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7296) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7296) gives:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7297) all_57_12 = e1 & op(e0, e3) = e1
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7297) implies:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7298) all_57_12 = e1
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (235), (237),
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7146), (7298), (function-axioms) are inconsistent
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #583.
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7299) all_57_13 = e1 & op(e0, e2) = e1
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7299) implies:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7300) all_57_13 = e1
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7301) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7301) gives:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7302) all_57_9 = e2 & op(e3, e0) = e2
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7302) implies:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7303) all_57_9 = e2
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7304) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7304) gives:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7305) all_57_12 = e2 & op(e0, e3) = e2
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (7256), (7305), (function-axioms) are
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #97.
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7306) all_57_13 = e2 & op(e0, e2) = e2
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7306) implies:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7307) all_57_13 = e2
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7300), (7307) imply:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7308) e2 = e1
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7308) implies:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7309) e2 = e1
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7303), (7309) imply:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7310) all_57_9 = e1
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (236),
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (7146), (7246), (7310), (function-axioms)
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #686.
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7311) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7311) gives:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7312) all_57_14 = e2 & op(e0, e1) = e2
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (7001), (7312), (function-axioms) are
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #512.
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7313) all_57_15 = e2 & op(e0, e0) = e2
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7313) implies:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7314) op(e0, e0) = e2
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7277), (7314), (function-axioms) are
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #634.
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7315) all_57_10 = e2 & op(e2, e0) = e2
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7315) implies:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7316) op(e2, e0) = e2
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (7258), (7316), (function-axioms) are
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7317) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7317) gives:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7318) all_57_11 = e2 & op(e1, e0) = e2
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7318) implies:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7319) all_57_11 = e2
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (215), (216), (7006),
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7169), (7319) are inconsistent by sub-proof #572.
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7320) all_57_15 = e2 & op(e0, e0) = e2
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7320) implies:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7321) op(e0, e0) = e2
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7277), (7321), (function-axioms) are
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #634.
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7322) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7322) gives:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7323) all_57_14 = e1 & op(e0, e1) = e1
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7323) implies:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7324) all_57_14 = e1
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7295), (7324) are inconsistent by sub-proof
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #221.
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7325) all_57_15 = e1 & op(e0, e0) = e1
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7325) implies:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7326) op(e0, e0) = e1
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7277), (7326), (function-axioms) are
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #606.
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | (7327) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (371), (7018), (7269), (7327) are
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #746.
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | (7328) all_54_4 = e1 | all_54_4 = e0
% 133.97/19.36 | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (7143), (7245), (7328) are inconsistent by
% 133.97/19.36 | | | | | | | | | | | | | | | | | | | sub-proof #153.
% 133.97/19.36 | | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | (7329) all_57_7 = e3 & op(e1, e2) = e3
% 133.97/19.36 | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | ALPHA: (7329) implies:
% 133.97/19.36 | | | | | | | | | | | | | | | | (7330) op(e1, e2) = e3
% 133.97/19.36 | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | REF_CLOSE: (162), (7165), (7330), (function-axioms) are
% 133.97/19.36 | | | | | | | | | | | | | | | | inconsistent by sub-proof #654.
% 133.97/19.36 | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | (7331) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 133.97/19.36 | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 133.97/19.36 | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | BETA: splitting (7331) gives:
% 133.97/19.36 | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | Case 1:
% 133.97/19.36 | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | (7332) all_57_8 = e3 & op(e1, e1) = e3
% 133.97/19.36 | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | ALPHA: (7332) implies:
% 133.97/19.36 | | | | | | | | | | | | | | | | (7333) op(e1, e1) = e3
% 133.97/19.36 | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7007), (7333), (function-axioms) are
% 133.97/19.36 | | | | | | | | | | | | | | | | inconsistent by sub-proof #109.
% 133.97/19.36 | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | (7334) all_57_11 = e3 & op(e1, e0) = e3
% 133.97/19.36 | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | | REF_CLOSE: (160), (7166), (7334), (function-axioms) are
% 133.97/19.36 | | | | | | | | | | | | | | | | inconsistent by sub-proof #750.
% 133.97/19.36 | | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | (7335) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 133.97/19.36 | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | REF_CLOSE: (7148), (7151), (7159), (7160), (7335) are
% 133.97/19.36 | | | | | | | | | | | | | | inconsistent by sub-proof #96.
% 133.97/19.36 | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | (7336) ~ (all_32_1 = e2) & op(e1, e1) = all_32_1 &
% 133.97/19.36 | | | | | | | | | | | | | $i(all_32_1)
% 133.97/19.36 | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | REF_CLOSE: (7007), (7336), (function-axioms) are inconsistent
% 133.97/19.36 | | | | | | | | | | | | | by sub-proof #95.
% 133.97/19.36 | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | End of split
% 133.97/19.36 | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | (7337) all_20_2 = e2
% 133.97/19.36 | | | | | | | | | | | (7338) ( ~ (all_20_0 = e3) & op(e2, e0) = all_20_0 &
% 133.97/19.36 | | | | | | | | | | | $i(all_20_0)) | ( ~ (all_20_1 = e1) & op(e2, e2)
% 133.97/19.36 | | | | | | | | | | | = all_20_1 & $i(all_20_1))
% 133.97/19.36 | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | COMBINE_EQS: (318), (7337) imply:
% 133.97/19.36 | | | | | | | | | | | (7339) all_4_2 = e2
% 133.97/19.36 | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | SIMP: (7339) implies:
% 133.97/19.36 | | | | | | | | | | | (7340) all_4_2 = e2
% 133.97/19.36 | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | REDUCE: (349), (7340) imply:
% 133.97/19.36 | | | | | | | | | | | (7341) ~ (all_52_3 = e2)
% 133.97/19.36 | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | REDUCE: (368), (7340) imply:
% 133.97/19.36 | | | | | | | | | | | (7342) ~ (all_52_12 = e2)
% 133.97/19.36 | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | REDUCE: (36), (7340) imply:
% 133.97/19.36 | | | | | | | | | | | (7343) op(e0, e0) = e2
% 133.97/19.36 | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | BETA: splitting (235) gives:
% 133.97/19.36 | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | Case 1:
% 133.97/19.36 | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | (7344) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 133.97/19.36 | | | | | | | | | | | | & op(e2, e3) = e2)
% 133.97/19.36 | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | BETA: splitting (7344) gives:
% 133.97/19.36 | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | Case 1:
% 133.97/19.36 | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | (7345) all_57_0 = e2 & op(e3, e3) = e2
% 133.97/19.36 | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | ALPHA: (7345) implies:
% 133.97/19.36 | | | | | | | | | | | | | (7346) op(e3, e3) = e2
% 133.97/19.36 | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | REF_CLOSE: (45), (7016), (7346), (function-axioms) are
% 133.97/19.36 | | | | | | | | | | | | | inconsistent by sub-proof #536.
% 133.97/19.36 | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | (7347) all_57_2 = e2 & op(e2, e3) = e2
% 133.97/19.36 | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | ALPHA: (7347) implies:
% 133.97/19.36 | | | | | | | | | | | | | (7348) all_57_2 = e2
% 133.97/19.36 | | | | | | | | | | | | | (7349) op(e2, e3) = e2
% 133.97/19.36 | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | BETA: splitting (236) gives:
% 133.97/19.36 | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | Case 1:
% 133.97/19.36 | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | (7350) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 133.97/19.36 | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 133.97/19.36 | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | BETA: splitting (7350) gives:
% 133.97/19.36 | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | Case 1:
% 133.97/19.36 | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | (7351) all_57_0 = e2 & op(e3, e3) = e2
% 133.97/19.36 | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | ALPHA: (7351) implies:
% 133.97/19.36 | | | | | | | | | | | | | | | (7352) op(e3, e3) = e2
% 133.97/19.36 | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | REF_CLOSE: (45), (7016), (7352), (function-axioms) are
% 133.97/19.36 | | | | | | | | | | | | | | | inconsistent by sub-proof #536.
% 133.97/19.36 | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | Case 2:
% 133.97/19.36 | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | (7353) all_57_1 = e2 & op(e3, e2) = e2
% 133.97/19.36 | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | ALPHA: (7353) implies:
% 133.97/19.36 | | | | | | | | | | | | | | | (7354) op(e3, e2) = e2
% 133.97/19.36 | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 133.97/19.36 | | | | | | | | | | | | | | | e3, e2, simplifying with (167), (7349) gives:
% 133.97/19.36 | | | | | | | | | | | | | | | (7355) all_52_1 = e2
% 133.97/19.36 | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e2,
% 133.97/19.36 | | | | | | | | | | | | | | | e2, e3, simplifying with (170), (7354) gives:
% 133.97/19.36 | | | | | | | | | | | | | | | (7356) all_52_4 = e2
% 133.97/19.36 | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | REDUCE: (146), (7355) imply:
% 133.97/19.36 | | | | | | | | | | | | | | | (7357) ~ (all_52_9 = e2)
% 133.97/19.36 | | | | | | | | | | | | | | |
% 133.97/19.36 | | | | | | | | | | | | | | | REDUCE: (134), (7356) imply:
% 133.97/19.37 | | | | | | | | | | | | | | | (7358) ~ (all_52_8 = e2)
% 133.97/19.37 | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | REDUCE: (342), (7356) imply:
% 133.97/19.37 | | | | | | | | | | | | | | | (7359) ~ (all_10_2 = e2)
% 133.97/19.37 | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | REDUCE: (350), (7356) imply:
% 133.97/19.37 | | | | | | | | | | | | | | | (7360) ~ (all_8_2 = e2)
% 133.97/19.37 | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | SIMP: (7360) implies:
% 133.97/19.37 | | | | | | | | | | | | | | | (7361) ~ (all_8_2 = e2)
% 133.97/19.37 | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 133.97/19.37 | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | Case 1:
% 133.97/19.37 | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | (7362) all_54_5 = e3
% 133.97/19.37 | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (7362) imply:
% 133.97/19.37 | | | | | | | | | | | | | | | | (7363) all_8_2 = e3
% 133.97/19.37 | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | REDUCE: (7011), (7363) imply:
% 133.97/19.37 | | | | | | | | | | | | | | | | (7364) $false
% 133.97/19.37 | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | CLOSE: (7364) is inconsistent.
% 133.97/19.37 | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | Case 2:
% 133.97/19.37 | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | (7365) ~ (all_54_5 = e3)
% 133.97/19.37 | | | | | | | | | | | | | | | | (7366) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 133.97/19.37 | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | BETA: splitting (7366) gives:
% 133.97/19.37 | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.37 | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | (7367) all_54_5 = e2
% 133.97/19.37 | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (7367) imply:
% 133.97/19.37 | | | | | | | | | | | | | | | | | (7368) all_8_2 = e2
% 133.97/19.37 | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | REDUCE: (7361), (7368) imply:
% 133.97/19.37 | | | | | | | | | | | | | | | | | (7369) $false
% 133.97/19.37 | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | CLOSE: (7369) is inconsistent.
% 133.97/19.37 | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.37 | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | (7370) ~ (all_54_5 = e2)
% 133.97/19.37 | | | | | | | | | | | | | | | | | (7371) all_54_5 = e1 | all_54_5 = e0
% 133.97/19.37 | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | BETA: splitting (7371) gives:
% 133.97/19.37 | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.37 | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | (7372) all_54_5 = e1
% 133.97/19.37 | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (7372) imply:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | (7373) all_8_2 = e1
% 133.97/19.37 | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | REDUCE: (7008), (7373) imply:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | (7374) $false
% 133.97/19.37 | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | CLOSE: (7374) is inconsistent.
% 133.97/19.37 | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.37 | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | (7375) all_54_5 = e0
% 133.97/19.37 | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (7375) imply:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | (7376) all_8_2 = e0
% 133.97/19.37 | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | REDUCE: (356), (7376) imply:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | (7377) ~ (all_52_9 = e0)
% 133.97/19.37 | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | REDUCE: (7011), (7376) imply:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | (7378) ~ (e3 = e0)
% 133.97/19.37 | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | REDUCE: (7361), (7376) imply:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | (7379) ~ (e2 = e0)
% 133.97/19.37 | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | REDUCE: (7008), (7376) imply:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | (7380) ~ (e1 = e0)
% 133.97/19.37 | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | REDUCE: (42), (7376) imply:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | (7381) op(e2, e2) = e0
% 133.97/19.37 | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (79), (117),
% 133.97/19.37 | | | | | | | | | | | | | | | | | | (123), (164), (165), (169), (198), (206), (224),
% 133.97/19.37 | | | | | | | | | | | | | | | | | | (226), (231), (237), (260), (312), (6999), (7000),
% 133.97/19.37 | | | | | | | | | | | | | | | | | | (7007), (7009), (7014), (7016), (7338), (7343),
% 133.97/19.37 | | | | | | | | | | | | | | | | | | (7348), (7349), (7354), (7377), (7381),
% 133.97/19.37 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.97/19.37 | | | | | | | | | | | | | | | | | | #90.
% 133.97/19.37 | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | End of split
% 133.97/19.37 | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | End of split
% 133.97/19.37 | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | End of split
% 133.97/19.37 | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | End of split
% 133.97/19.37 | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | Case 2:
% 133.97/19.37 | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | (7382) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 133.97/19.37 | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 133.97/19.37 | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | BETA: splitting (7382) gives:
% 133.97/19.37 | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | Case 1:
% 133.97/19.37 | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | (7383) all_57_4 = e2 & op(e3, e1) = e2
% 133.97/19.37 | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | REF_CLOSE: (169), (6999), (7383), (function-axioms) are
% 133.97/19.37 | | | | | | | | | | | | | | | inconsistent by sub-proof #442.
% 133.97/19.37 | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | Case 2:
% 133.97/19.37 | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | (7384) all_57_9 = e2 & op(e3, e0) = e2
% 133.97/19.37 | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | REF_CLOSE: (168), (7342), (7384), (function-axioms) are
% 133.97/19.37 | | | | | | | | | | | | | | | inconsistent by sub-proof #460.
% 133.97/19.37 | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | End of split
% 133.97/19.37 | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | End of split
% 133.97/19.37 | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | End of split
% 133.97/19.37 | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | Case 2:
% 133.97/19.37 | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | (7385) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 133.97/19.37 | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 133.97/19.37 | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | BETA: splitting (7385) gives:
% 133.97/19.37 | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | Case 1:
% 133.97/19.37 | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | (7386) all_57_6 = e2 & op(e1, e3) = e2
% 133.97/19.37 | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | REF_CLOSE: (163), (6997), (7386), (function-axioms) are
% 133.97/19.37 | | | | | | | | | | | | | inconsistent by sub-proof #341.
% 133.97/19.37 | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | Case 2:
% 133.97/19.37 | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | (7387) all_57_12 = e2 & op(e0, e3) = e2
% 133.97/19.37 | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | REF_CLOSE: (159), (7341), (7387), (function-axioms) are
% 133.97/19.37 | | | | | | | | | | | | | inconsistent by sub-proof #97.
% 133.97/19.37 | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | End of split
% 133.97/19.37 | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | End of split
% 133.97/19.37 | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | End of split
% 133.97/19.37 | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | Case 2:
% 133.97/19.37 | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | (7388) all_16_2 = e2
% 133.97/19.37 | | | | | | | | | | (7389) ( ~ (all_16_0 = e1) & op(e2, e3) = all_16_0 &
% 133.97/19.37 | | | | | | | | | | $i(all_16_0)) | ( ~ (all_16_1 = e0) & op(e2, e2)
% 133.97/19.37 | | | | | | | | | | = all_16_1 & $i(all_16_1))
% 133.97/19.37 | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | COMBINE_EQS: (327), (7388) imply:
% 133.97/19.37 | | | | | | | | | | (7390) all_10_2 = e2
% 133.97/19.37 | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | SIMP: (7390) implies:
% 133.97/19.37 | | | | | | | | | | (7391) all_10_2 = e2
% 133.97/19.37 | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | REDUCE: (336), (7391) imply:
% 133.97/19.37 | | | | | | | | | | (7392) ~ (all_52_1 = e2)
% 133.97/19.37 | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | REDUCE: (346), (7391) imply:
% 133.97/19.37 | | | | | | | | | | (7393) ~ (all_52_12 = e2)
% 133.97/19.37 | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | REDUCE: (45), (7391) imply:
% 133.97/19.37 | | | | | | | | | | (7394) op(e3, e3) = e2
% 133.97/19.37 | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | BETA: splitting (61) gives:
% 133.97/19.37 | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | Case 1:
% 133.97/19.37 | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | (7395) ~ (all_20_2 = e2)
% 133.97/19.37 | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | REDUCE: (318), (7395) imply:
% 133.97/19.37 | | | | | | | | | | | (7396) ~ (all_4_2 = e2)
% 133.97/19.37 | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | BETA: splitting (213) gives:
% 133.97/19.37 | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | Case 1:
% 133.97/19.37 | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | (7397) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 133.97/19.37 | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 133.97/19.37 | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | BETA: splitting (7397) gives:
% 133.97/19.37 | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | Case 1:
% 133.97/19.37 | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | (7398) all_57_9 = e2 & op(e3, e0) = e2
% 133.97/19.37 | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | REF_CLOSE: (168), (7393), (7398), (function-axioms) are
% 133.97/19.37 | | | | | | | | | | | | | inconsistent by sub-proof #460.
% 133.97/19.37 | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | Case 2:
% 133.97/19.37 | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | (7399) all_57_10 = e2 & op(e2, e0) = e2
% 133.97/19.37 | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | ALPHA: (7399) implies:
% 133.97/19.37 | | | | | | | | | | | | | (7400) all_57_10 = e2
% 133.97/19.37 | | | | | | | | | | | | | (7401) op(e2, e0) = e2
% 133.97/19.37 | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | BETA: splitting (210) gives:
% 133.97/19.37 | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | Case 1:
% 133.97/19.37 | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | (7402) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 133.97/19.37 | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 133.97/19.37 | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | BETA: splitting (7402) gives:
% 133.97/19.37 | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | Case 1:
% 133.97/19.37 | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | (7403) all_57_12 = e2 & op(e0, e3) = e2
% 133.97/19.37 | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | ALPHA: (7403) implies:
% 133.97/19.37 | | | | | | | | | | | | | | | (7404) all_57_12 = e2
% 133.97/19.37 | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 133.97/19.37 | | | | | | | | | | | | | | | (7394), (7404), (function-axioms) are inconsistent
% 133.97/19.37 | | | | | | | | | | | | | | | by sub-proof #290.
% 133.97/19.37 | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | Case 2:
% 133.97/19.37 | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | (7405) all_57_13 = e2 & op(e0, e2) = e2
% 133.97/19.37 | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | ALPHA: (7405) implies:
% 133.97/19.37 | | | | | | | | | | | | | | | (7406) all_57_13 = e2
% 133.97/19.37 | | | | | | | | | | | | | | | (7407) op(e0, e2) = e2
% 133.97/19.37 | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e2,
% 133.97/19.37 | | | | | | | | | | | | | | | e2, e0, simplifying with (158), (7407) gives:
% 133.97/19.37 | | | | | | | | | | | | | | | (7408) all_52_7 = e2
% 133.97/19.37 | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 133.97/19.37 | | | | | | | | | | | | | | | e2, e0, e2, simplifying with (164), (7401) gives:
% 133.97/19.37 | | | | | | | | | | | | | | | (7409) all_52_13 = e2
% 133.97/19.37 | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | REDUCE: (140), (7408) imply:
% 133.97/19.37 | | | | | | | | | | | | | | | (7410) ~ (all_52_3 = e2)
% 133.97/19.37 | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | REDUCE: (358), (7409) imply:
% 133.97/19.37 | | | | | | | | | | | | | | | (7411) ~ (all_8_2 = e2)
% 133.97/19.37 | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | SIMP: (7411) implies:
% 133.97/19.37 | | | | | | | | | | | | | | | (7412) ~ (all_8_2 = e2)
% 133.97/19.37 | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | REDUCE: (369), (7409) imply:
% 133.97/19.37 | | | | | | | | | | | | | | | (7413) ~ (all_4_2 = e2)
% 133.97/19.37 | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 133.97/19.37 | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | Case 1:
% 133.97/19.37 | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | (7414) all_54_5 = e3
% 133.97/19.37 | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (7414) imply:
% 133.97/19.37 | | | | | | | | | | | | | | | | (7415) all_8_2 = e3
% 133.97/19.37 | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | REDUCE: (7011), (7415) imply:
% 133.97/19.37 | | | | | | | | | | | | | | | | (7416) $false
% 133.97/19.37 | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | CLOSE: (7416) is inconsistent.
% 133.97/19.37 | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | Case 2:
% 133.97/19.37 | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | (7417) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 133.97/19.37 | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | BETA: splitting (7417) gives:
% 133.97/19.37 | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.37 | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | (7418) all_54_5 = e2
% 133.97/19.37 | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (7418) imply:
% 133.97/19.37 | | | | | | | | | | | | | | | | | (7419) all_8_2 = e2
% 133.97/19.37 | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | REDUCE: (7412), (7419) imply:
% 133.97/19.37 | | | | | | | | | | | | | | | | | (7420) $false
% 133.97/19.37 | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | CLOSE: (7420) is inconsistent.
% 133.97/19.37 | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.37 | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | (7421) ~ (all_54_5 = e2)
% 133.97/19.37 | | | | | | | | | | | | | | | | | (7422) all_54_5 = e1 | all_54_5 = e0
% 133.97/19.37 | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | BETA: splitting (7422) gives:
% 133.97/19.37 | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.37 | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | (7423) all_54_5 = e1
% 133.97/19.37 | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (7423) imply:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | (7424) all_8_2 = e1
% 133.97/19.37 | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | REDUCE: (7008), (7424) imply:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | (7425) $false
% 133.97/19.37 | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | CLOSE: (7425) is inconsistent.
% 133.97/19.37 | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.37 | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | (7426) all_54_5 = e0
% 133.97/19.37 | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (7426) imply:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | (7427) all_8_2 = e0
% 133.97/19.37 | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | REDUCE: (347), (7427) imply:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | (7428) ~ (all_52_1 = e0)
% 133.97/19.37 | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | REDUCE: (7412), (7427) imply:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | (7429) ~ (e2 = e0)
% 133.97/19.37 | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | REDUCE: (7008), (7427) imply:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | (7430) ~ (e1 = e0)
% 133.97/19.37 | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | REDUCE: (42), (7427) imply:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | (7431) op(e2, e2) = e0
% 133.97/19.37 | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | BETA: splitting (7389) gives:
% 133.97/19.37 | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | (7432) ~ (all_16_0 = e1) & op(e2, e3) = all_16_0 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | $i(all_16_0)
% 133.97/19.37 | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | ALPHA: (7432) implies:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | (7433) ~ (all_16_0 = e1)
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | (7434) op(e2, e3) = all_16_0
% 133.97/19.37 | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | all_16_0, e3, e2, simplifying with (167), (7434)
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | gives:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | (7435) all_52_1 = all_16_0
% 133.97/19.37 | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (7435) imply:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | (7436) all_54_4 = all_16_0
% 133.97/19.37 | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | REDUCE: (149), (7435) imply:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | (7437) ~ (all_52_2 = all_16_0)
% 133.97/19.37 | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | SIMP: (7437) implies:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | (7438) ~ (all_52_2 = all_16_0)
% 133.97/19.37 | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | REDUCE: (7392), (7435) imply:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | (7439) ~ (all_16_0 = e2)
% 133.97/19.37 | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | REDUCE: (7428), (7435) imply:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | (7440) ~ (all_16_0 = e0)
% 133.97/19.37 | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | (7441) all_54_4 = e3
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7436), (7441) imply:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | (7442) all_16_0 = e3
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | SIMP: (7442) implies:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | (7443) all_16_0 = e3
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | REDUCE: (7438), (7443) imply:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | (7444) ~ (all_52_2 = e3)
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | (7445) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7431), (7433), (7434), (7445),
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | #415.
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | (7446) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7446) gives:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | (7447) all_57_5 = e1 & op(e2, e1) = e1
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7447) implies:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | (7448) all_57_5 = e1
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | (7449) op(e2, e1) = e1
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | (7450) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7450) gives:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | (7451) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7451) gives:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | (7452) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7452) implies:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | (7453) ~ (all_56_19 = e1)
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | (7454) op(e2, e1) = all_56_19
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7449), (7453), (7454), (function-axioms) are
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #106.
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | (7455) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7455) implies:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | (7456) op(e3, e3) = e1
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7394), (7456), (function-axioms) are
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743.
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | (7457) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7457) gives:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | (7458) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3,
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7458) implies:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | (7459) ~ (all_56_15 = e2)
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | (7460) op(e0, e2) = all_56_15
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7407), (7459), (7460), (function-axioms) are
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #609.
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | (7461) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2,
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7461) implies:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | (7462) op(e2, e2) = e3
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7431), (7462), (function-axioms) are
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641.
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | (7463) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7463) gives:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | (7464) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (7000), (7007), (7464),
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | #108.
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | (7465) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7465) gives:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | (7466) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7466) implies:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | (7467) ~ (all_56_15 = e2)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | (7468) op(e0, e2) = all_56_15
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7407), (7467), (7468), (function-axioms) are
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #609.
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | (7469) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7469) gives:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (7470) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7470) implies:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (7471) ~ (all_56_19 = e1)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (7472) op(e2, e1) = all_56_19
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7449), (7471), (7472), (function-axioms) are
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #106.
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (7473) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7473) implies:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (7474) op(e0, e0) = all_56_31
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (7475) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7476) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7476) gives:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7477) all_57_2 = e3 & op(e2, e3) = e3
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7477) implies:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7478) all_57_2 = e3
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7479) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7479) gives:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7480) all_57_12 = e1 & op(e0, e3) = e1
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7480) implies:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7481) all_57_12 = e1
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7482) op(e0, e3) = e1
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7483) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (167), (7394), (7428), (7483),
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #89.
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7484) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7484) gives:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7485) all_57_6 = e0 & op(e1, e3) = e0
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7485) implies:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7486) op(e1, e3) = e0
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31, e0, e0, simplifying with (36), (7474)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7487) all_56_31 = all_4_2
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e1,
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (159), (7482) gives:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7488) all_52_3 = e1
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e0,
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (163), (7486) gives:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7489) all_52_2 = e0
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7444), (7489) imply:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7490) ~ (e3 = e0)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (349), (7488) imply:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7491) ~ (all_4_2 = e1)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7410), (7488) imply:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7492) ~ (e2 = e1)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7475) gives:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7493) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27))
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7493) gives:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7494) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7494) implies:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7495) all_56_31 = e3
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7496) ~ (all_56_25 = e0)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7497) op(e3, e0) = all_56_25
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7487), (7495) imply:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7498) all_4_2 = e3
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (7498) imply:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7499) op(e0, e0) = e3
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7500) all_57_15 = e0 & op(e0, e0) = e0
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7500) implies:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7501) op(e0, e0) = e0
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (7474), (7475), (7501),
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #710.
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7502) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7502) implies:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7503) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7504) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7504) gives:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7505) all_57_6 = e3 & op(e1, e3) = e3
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (7444), (7505), (function-axioms) are
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #761.
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7506) all_57_7 = e3 & op(e1, e2) = e3
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7506) implies:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7507) all_57_7 = e3
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7508) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7508) gives:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7509) all_57_4 = e3 & op(e3, e1) = e3
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7509) implies:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7510) op(e3, e1) = e3
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7511) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7511) gives:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7512) all_57_1 = e1 & op(e3, e2) = e1
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7512) implies:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7513) op(e3, e2) = e1
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7514) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7394), (7513), (7514),
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #333.
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7515) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7515) gives:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7516) all_57_4 = e0 & op(e3, e1) = e0
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7516) implies:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7517) op(e3, e1) = e0
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (169), (7510), (7517), (function-axioms) are
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #600.
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7518) all_57_9 = e0 & op(e3, e0) = e0
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7518) implies:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7519) op(e3, e0) = e0
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7496), (7497), (7519), (function-axioms) are
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #642.
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7520) all_57_3 = e1 & op(e2, e2) = e1
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7520) implies:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7521) op(e2, e2) = e1
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7431), (7521), (function-axioms) are
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675.
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7522) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7522) gives:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7523) all_57_7 = e1 & op(e1, e2) = e1
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7523) implies:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7524) all_57_7 = e1
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7507), (7524) are inconsistent by sub-proof
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #390.
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7525) all_57_13 = e1 & op(e0, e2) = e1
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7406), (7525) are inconsistent by sub-proof
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #248.
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7526) all_57_5 = e3 & op(e2, e1) = e3
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (224), (7400), (7431), (7478),
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7526), (function-axioms) are inconsistent by
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #87.
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7527) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7527) gives:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7528) all_57_8 = e3 & op(e1, e1) = e3
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7528) implies:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7529) op(e1, e1) = e3
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7007), (7529), (function-axioms) are
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #109.
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7530) all_57_14 = e3 & op(e0, e1) = e3
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7530) implies:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7531) all_57_14 = e3
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (7406), (7481), (7503), (7531) are
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #399.
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7532) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7532) gives:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7533) all_57_8 = e3 & op(e1, e1) = e3
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7533) implies:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7534) op(e1, e1) = e3
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7007), (7534), (function-axioms) are
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #109.
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7535) all_57_11 = e3 & op(e1, e0) = e3
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7535) implies:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7536) all_57_11 = e3
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7537) all_57_15 = e0 & op(e0, e0) = e0
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7537) implies:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7538) op(e0, e0) = e0
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7499), (7538), (function-axioms) are
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #715.
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7502) implies:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7539) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7539) gives:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7540) all_57_9 = e0 & op(e3, e0) = e0
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7540) implies:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7541) all_57_9 = e0
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7542) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7542) gives:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7543) all_57_9 = e1 & op(e3, e0) = e1
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7543) implies:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7544) all_57_9 = e1
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7541), (7544) are inconsistent by sub-proof
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #383.
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7545) all_57_10 = e1 & op(e2, e0) = e1
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7400), (7545) are inconsistent by sub-proof
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #270.
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7546) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7546) gives:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7547) all_57_11 = e1 & op(e1, e0) = e1
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7536), (7547) are inconsistent by sub-proof
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #296.
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7548) all_57_15 = e1 & op(e0, e0) = e1
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7548) implies:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7549) op(e0, e0) = e1
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7499), (7549), (function-axioms) are
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #606.
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7550) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7550) gives:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7551) all_57_10 = e0 & op(e2, e0) = e0
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7551) implies:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7552) op(e2, e0) = e0
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7401), (7552), (function-axioms) are
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #451.
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7553) all_57_11 = e0 & op(e1, e0) = e0
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7536), (7553) are inconsistent by sub-proof
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #129.
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7554) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7554) implies:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7555) ~ (all_56_19 = e1)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7556) op(e2, e1) = all_56_19
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7449), (7555), (7556), (function-axioms) are
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #106.
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7557) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (371), (7007), (7487), (7557),
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #86.
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7558) all_57_12 = e0 & op(e0, e3) = e0
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7558) implies:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7559) all_57_12 = e0
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7481), (7559) are inconsistent by sub-proof
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #581.
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7560) all_57_13 = e1 & op(e0, e2) = e1
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7560) implies:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7561) all_57_13 = e1
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7406), (7561) are inconsistent by sub-proof
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #567.
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7562) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7562) gives:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7563) all_57_14 = e1 & op(e0, e1) = e1
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7563) implies:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7564) all_57_14 = e1
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7565) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7565) gives:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7566) all_57_4 = e3 & op(e3, e1) = e3
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7566) implies:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7567) all_57_4 = e3
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7568) op(e3, e1) = e3
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (169), (219), (220),
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7006), (7448), (7564), (7567), (7568),
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #82.
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7569) all_57_5 = e3 & op(e2, e1) = e3
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (224), (7400), (7431), (7478),
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7569), (function-axioms) are inconsistent by
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #87.
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7570) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (7007), (7564), (7570),
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #81.
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7571) all_57_15 = e1 & op(e0, e0) = e1
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7571) implies:
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7572) op(e0, e0) = e1
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (371), (7572), (function-axioms) are
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #354.
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7573) all_57_3 = e3 & op(e2, e2) = e3
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7573) implies:
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7574) op(e2, e2) = e3
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7431), (7574), (function-axioms) are
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641.
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7575) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7575) gives:
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7576) all_57_5 = e3 & op(e2, e1) = e3
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7576) implies:
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7577) all_57_5 = e3
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7448), (7577) imply:
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7578) e3 = e1
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (7578) imply:
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7579) $false
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7579) is inconsistent.
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7580) all_57_10 = e3 & op(e2, e0) = e3
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7580) implies:
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7581) op(e2, e0) = e3
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (164), (7401), (7581), (function-axioms) are
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #546.
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | (7582) all_57_10 = e1 & op(e2, e0) = e1
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7400), (7582) are inconsistent by sub-proof
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | #270.
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | (7583) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7433), (7436), (7439), (7440), (7583) are
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #381.
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.39 | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.39 | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | (7584) ~ (all_16_1 = e0) & op(e2, e2) = all_16_1 &
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | $i(all_16_1)
% 133.97/19.39 | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7431), (7584), (function-axioms) are inconsistent
% 133.97/19.39 | | | | | | | | | | | | | | | | | | | by sub-proof #380.
% 133.97/19.39 | | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.39 | | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | End of split
% 133.97/19.39 | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | End of split
% 133.97/19.39 | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | End of split
% 133.97/19.39 | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | End of split
% 133.97/19.39 | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | Case 2:
% 133.97/19.39 | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | (7585) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 133.97/19.39 | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 133.97/19.39 | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | BETA: splitting (7585) gives:
% 133.97/19.39 | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | Case 1:
% 133.97/19.39 | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | (7586) all_57_14 = e2 & op(e0, e1) = e2
% 133.97/19.39 | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | REF_CLOSE: (157), (7001), (7586), (function-axioms) are
% 133.97/19.39 | | | | | | | | | | | | | | | inconsistent by sub-proof #512.
% 133.97/19.39 | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | Case 2:
% 133.97/19.39 | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | (7587) all_57_15 = e2 & op(e0, e0) = e2
% 133.97/19.39 | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | REF_CLOSE: (36), (7396), (7587), (function-axioms) are
% 133.97/19.39 | | | | | | | | | | | | | | | inconsistent by sub-proof #107.
% 133.97/19.39 | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | End of split
% 133.97/19.39 | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | End of split
% 133.97/19.39 | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | End of split
% 133.97/19.39 | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | Case 2:
% 133.97/19.39 | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | (7588) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 133.97/19.39 | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 133.97/19.39 | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | BETA: splitting (7588) gives:
% 133.97/19.39 | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | Case 1:
% 133.97/19.39 | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | (7589) all_57_11 = e2 & op(e1, e0) = e2
% 133.97/19.39 | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | REF_CLOSE: (160), (7002), (7589), (function-axioms) are
% 133.97/19.39 | | | | | | | | | | | | | inconsistent by sub-proof #514.
% 133.97/19.39 | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | Case 2:
% 133.97/19.39 | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | (7590) all_57_15 = e2 & op(e0, e0) = e2
% 133.97/19.39 | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | REF_CLOSE: (36), (7396), (7590), (function-axioms) are
% 133.97/19.39 | | | | | | | | | | | | | inconsistent by sub-proof #107.
% 133.97/19.39 | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | End of split
% 133.97/19.39 | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | End of split
% 133.97/19.39 | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | Case 2:
% 133.97/19.39 | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | (7591) all_20_2 = e2
% 133.97/19.39 | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | COMBINE_EQS: (318), (7591) imply:
% 133.97/19.39 | | | | | | | | | | | (7592) all_4_2 = e2
% 133.97/19.39 | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | REDUCE: (369), (7592) imply:
% 133.97/19.39 | | | | | | | | | | | (7593) ~ (all_52_13 = e2)
% 133.97/19.39 | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | REDUCE: (36), (7592) imply:
% 133.97/19.39 | | | | | | | | | | | (7594) op(e0, e0) = e2
% 133.97/19.39 | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | BETA: splitting (225) gives:
% 133.97/19.39 | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | Case 1:
% 133.97/19.39 | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | (7595) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 133.97/19.39 | | | | | | | | | | | | & op(e2, e2) = e2)
% 133.97/19.39 | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | BETA: splitting (7595) gives:
% 133.97/19.39 | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | Case 1:
% 133.97/19.39 | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | (7596) all_57_2 = e2 & op(e2, e3) = e2
% 133.97/19.39 | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | ALPHA: (7596) implies:
% 133.97/19.39 | | | | | | | | | | | | | (7597) op(e2, e3) = e2
% 133.97/19.39 | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | REF_CLOSE: (167), (7392), (7597), (function-axioms) are
% 133.97/19.39 | | | | | | | | | | | | | inconsistent by sub-proof #779.
% 133.97/19.39 | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | Case 2:
% 133.97/19.39 | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | (7598) all_57_3 = e2 & op(e2, e2) = e2
% 133.97/19.39 | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | ALPHA: (7598) implies:
% 133.97/19.39 | | | | | | | | | | | | | (7599) op(e2, e2) = e2
% 133.97/19.39 | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, e2,
% 133.97/19.39 | | | | | | | | | | | | | e2, e2, simplifying with (42), (7599) gives:
% 133.97/19.39 | | | | | | | | | | | | | (7600) all_8_2 = e2
% 133.97/19.39 | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | REDUCE: (7011), (7600) imply:
% 133.97/19.39 | | | | | | | | | | | | | (7601) ~ (e3 = e2)
% 133.97/19.39 | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.97/19.39 | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | Case 1:
% 133.97/19.39 | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | (7602) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.97/19.39 | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.97/19.39 | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.97/19.39 | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.97/19.39 | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.97/19.39 | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.97/19.39 | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.97/19.39 | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.97/19.39 | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.97/19.39 | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.97/19.39 | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.97/19.39 | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.97/19.39 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.97/19.39 | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.97/19.39 | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.97/19.39 | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.97/19.39 | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.97/19.39 | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.39 | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.39 | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.97/19.39 | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.97/19.39 | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.97/19.39 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.39 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.39 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.39 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.97/19.39 | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.39 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.97/19.39 | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (42), (7011), (7394), (7599), (7602),
% 133.97/19.39 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.97/19.39 | | | | | | | | | | | | | | #80.
% 133.97/19.39 | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | Case 2:
% 133.97/19.39 | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | (7603) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.97/19.39 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.39 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.39 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.39 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.97/19.39 | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.39 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.97/19.39 | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.97/19.39 | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.97/19.39 | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.97/19.39 | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.97/19.39 | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.97/19.39 | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.97/19.39 | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.97/19.39 | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.97/19.39 | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.97/19.39 | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.97/19.39 | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.97/19.39 | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.97/19.39 | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.97/19.39 | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.97/19.39 | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.97/19.39 | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.97/19.39 | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.97/19.39 | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.97/19.39 | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.97/19.39 | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.97/19.39 | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.97/19.39 | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.97/19.39 | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.97/19.39 | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.97/19.39 | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.39 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.97/19.39 | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.97/19.39 | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.39 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.97/19.39 | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.97/19.39 | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.97/19.39 | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.97/19.39 | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.97/19.39 | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.97/19.39 | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.97/19.39 | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.97/19.39 | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.97/19.39 | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.97/19.39 | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.97/19.39 | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.97/19.39 | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.97/19.39 | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.97/19.39 | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.97/19.39 | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.97/19.39 | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.97/19.39 | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.97/19.39 | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.97/19.39 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.97/19.39 | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.97/19.39 | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.97/19.39 | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | BETA: splitting (7603) gives:
% 133.97/19.39 | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | Case 1:
% 133.97/19.39 | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | (7604) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.97/19.39 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.39 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.39 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.39 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.97/19.39 | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.39 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.97/19.39 | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.97/19.39 | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.97/19.39 | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.97/19.39 | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.97/19.39 | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.97/19.39 | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.97/19.39 | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.97/19.39 | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (7000), (7007), (7604),
% 133.97/19.39 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.97/19.39 | | | | | | | | | | | | | | | #108.
% 133.97/19.39 | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | Case 2:
% 133.97/19.39 | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | (7605) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.97/19.39 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.97/19.39 | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 133.97/19.39 | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.39 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.39 | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.97/19.39 | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.97/19.39 | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.97/19.39 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.97/19.39 | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.97/19.39 | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.97/19.39 | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.97/19.39 | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.97/19.39 | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.97/19.39 | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.97/19.39 | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.97/19.39 | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.97/19.39 | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.97/19.39 | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.97/19.39 | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.97/19.39 | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.97/19.39 | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.97/19.39 | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.97/19.39 | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.97/19.39 | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.97/19.39 | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.97/19.39 | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.97/19.39 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.97/19.39 | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.97/19.39 | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.97/19.39 | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.97/19.39 | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.97/19.39 | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.97/19.39 | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.39 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.39 | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.97/19.39 | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.97/19.39 | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.97/19.39 | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.97/19.39 | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.97/19.39 | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.97/19.39 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.97/19.39 | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.97/19.39 | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.97/19.39 | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | BETA: splitting (7605) gives:
% 133.97/19.39 | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | Case 1:
% 133.97/19.39 | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | (7606) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.97/19.39 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.97/19.39 | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 133.97/19.39 | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.97/19.39 | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 133.97/19.39 | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.97/19.39 | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 133.97/19.39 | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | ALPHA: (7606) implies:
% 133.97/19.39 | | | | | | | | | | | | | | | | (7607) op(e2, e0) = e2
% 133.97/19.39 | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | REF_CLOSE: (164), (7593), (7607), (function-axioms) are
% 133.97/19.39 | | | | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 133.97/19.39 | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | Case 2:
% 133.97/19.39 | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | (7608) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.97/19.39 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.97/19.39 | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.97/19.39 | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.97/19.39 | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.97/19.39 | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.97/19.39 | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.97/19.39 | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.97/19.39 | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.97/19.39 | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.97/19.39 | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.97/19.39 | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.97/19.39 | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.97/19.39 | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.97/19.39 | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.97/19.39 | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.97/19.39 | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.97/19.39 | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.97/19.39 | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.97/19.39 | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.97/19.39 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.97/19.39 | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.97/19.39 | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.97/19.39 | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.97/19.39 | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.97/19.39 | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.97/19.39 | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.39 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.39 | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.97/19.39 | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.97/19.39 | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.97/19.39 | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.97/19.39 | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.97/19.39 | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.97/19.39 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.97/19.39 | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.97/19.39 | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.97/19.39 | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | BETA: splitting (7608) gives:
% 133.97/19.39 | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.39 | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | (7609) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.97/19.39 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 133.97/19.39 | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.97/19.39 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.97/19.39 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 133.97/19.39 | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.97/19.39 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 133.97/19.39 | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | ALPHA: (7609) implies:
% 133.97/19.39 | | | | | | | | | | | | | | | | | (7610) ~ (all_56_11 = e2)
% 133.97/19.39 | | | | | | | | | | | | | | | | | (7611) op(e2, e2) = all_56_11
% 133.97/19.39 | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | REF_CLOSE: (7599), (7610), (7611), (function-axioms) are
% 133.97/19.39 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #531.
% 133.97/19.39 | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.39 | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | (7612) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.97/19.39 | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.97/19.39 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 133.97/19.39 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.97/19.39 | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 133.97/19.39 | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.97/19.39 | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.39 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 133.97/19.39 | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 133.97/19.39 | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.97/19.39 | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.97/19.39 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.97/19.39 | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.97/19.39 | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.97/19.39 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 133.97/19.39 | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.97/19.39 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.97/19.39 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.97/19.39 | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.39 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.39 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 133.97/19.39 | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 133.97/19.39 | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 133.97/19.39 | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 133.97/19.39 | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 133.97/19.39 | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.97/19.39 | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 133.97/19.39 | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 133.97/19.39 | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 133.97/19.39 | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | ALPHA: (7612) implies:
% 133.97/19.39 | | | | | | | | | | | | | | | | | (7613) op(e0, e0) = all_56_31
% 133.97/19.39 | | | | | | | | | | | | | | | | | (7614) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.97/19.39 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.39 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.39 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.39 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 133.97/19.39 | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 133.97/19.39 | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 133.97/19.39 | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 133.97/19.39 | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 133.97/19.39 | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 133.97/19.39 | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 133.97/19.39 | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 133.97/19.39 | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 133.97/19.39 | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.97/19.39 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.97/19.39 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 133.97/19.39 | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.97/19.39 | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.39 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 133.97/19.39 | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 133.97/19.39 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.97/19.39 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 133.97/19.39 | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 133.97/19.39 | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 133.97/19.39 | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 133.97/19.39 | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.97/19.39 | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (39), (91), (157), (190), (246), (332),
% 133.97/19.39 | | | | | | | | | | | | | | | | | (364), (7001), (7594), (7599), (7613), (7614),
% 133.97/19.39 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.97/19.39 | | | | | | | | | | | | | | | | | #523.
% 133.97/19.39 | | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | | End of split
% 133.97/19.39 | | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | | End of split
% 133.97/19.39 | | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | End of split
% 133.97/19.39 | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | End of split
% 133.97/19.39 | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | End of split
% 133.97/19.39 | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | Case 2:
% 133.97/19.39 | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | (7615) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 133.97/19.39 | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 133.97/19.39 | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | REF_CLOSE: (164), (165), (7000), (7593), (7615),
% 133.97/19.39 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.97/19.39 | | | | | | | | | | | | #625.
% 133.97/19.39 | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | End of split
% 133.97/19.39 | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | End of split
% 133.97/19.39 | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | End of split
% 133.97/19.39 | | | | | | | | |
% 133.97/19.39 | | | | | | | | End of split
% 133.97/19.39 | | | | | | | |
% 133.97/19.39 | | | | | | | Case 2:
% 133.97/19.39 | | | | | | | |
% 133.97/19.39 | | | | | | | | (7616) all_14_2 = e3
% 133.97/19.39 | | | | | | | |
% 133.97/19.39 | | | | | | | | COMBINE_EQS: (329), (7616) imply:
% 133.97/19.39 | | | | | | | | (7617) all_8_2 = e3
% 133.97/19.39 | | | | | | | |
% 133.97/19.39 | | | | | | | | COMBINE_EQS: (322), (7617) imply:
% 133.97/19.39 | | | | | | | | (7618) all_22_2 = e3
% 133.97/19.39 | | | | | | | |
% 133.97/19.39 | | | | | | | | REDUCE: (347), (7617) imply:
% 133.97/19.39 | | | | | | | | (7619) ~ (all_52_1 = e3)
% 133.97/19.39 | | | | | | | |
% 133.97/19.39 | | | | | | | | REDUCE: (350), (7617) imply:
% 133.97/19.39 | | | | | | | | (7620) ~ (all_52_4 = e3)
% 133.97/19.39 | | | | | | | |
% 133.97/19.39 | | | | | | | | REDUCE: (352), (7617) imply:
% 133.97/19.39 | | | | | | | | (7621) ~ (all_52_6 = e3)
% 133.97/19.39 | | | | | | | |
% 133.97/19.39 | | | | | | | | REDUCE: (354), (7617) imply:
% 133.97/19.39 | | | | | | | | (7622) ~ (all_52_7 = e3)
% 133.97/19.39 | | | | | | | |
% 133.97/19.39 | | | | | | | | REDUCE: (356), (7617) imply:
% 133.97/19.39 | | | | | | | | (7623) ~ (all_52_9 = e3)
% 133.97/19.39 | | | | | | | |
% 133.97/19.39 | | | | | | | | REDUCE: (358), (7617) imply:
% 133.97/19.39 | | | | | | | | (7624) ~ (all_52_13 = e3)
% 133.97/19.39 | | | | | | | |
% 133.97/19.39 | | | | | | | | REDUCE: (42), (7617) imply:
% 133.97/19.39 | | | | | | | | (7625) op(e2, e2) = e3
% 133.97/19.39 | | | | | | | |
% 133.97/19.39 | | | | | | | | BETA: splitting (6995) gives:
% 133.97/19.39 | | | | | | | |
% 133.97/19.39 | | | | | | | | Case 1:
% 133.97/19.39 | | | | | | | | |
% 133.97/19.39 | | | | | | | | | (7626) ~ (all_6_0 = e0) & op(e2, e1) = all_6_0 &
% 133.97/19.39 | | | | | | | | | $i(all_6_0)
% 133.97/19.39 | | | | | | | | |
% 133.97/19.39 | | | | | | | | | ALPHA: (7626) implies:
% 133.97/19.39 | | | | | | | | | (7627) ~ (all_6_0 = e0)
% 133.97/19.39 | | | | | | | | | (7628) op(e2, e1) = all_6_0
% 133.97/19.39 | | | | | | | | |
% 133.97/19.39 | | | | | | | | | BETA: splitting (230) gives:
% 133.97/19.39 | | | | | | | | |
% 133.97/19.39 | | | | | | | | | Case 1:
% 133.97/19.39 | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | (7629) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 133.97/19.39 | | | | | | | | | | & op(e2, e2) = e3)
% 133.97/19.39 | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | BETA: splitting (7629) gives:
% 133.97/19.39 | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | Case 1:
% 133.97/19.39 | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | (7630) all_57_1 = e3 & op(e3, e2) = e3
% 133.97/19.39 | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | ALPHA: (7630) implies:
% 133.97/19.39 | | | | | | | | | | | (7631) op(e3, e2) = e3
% 133.97/19.39 | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | REF_CLOSE: (170), (7620), (7631), (function-axioms) are
% 133.97/19.39 | | | | | | | | | | | inconsistent by sub-proof #738.
% 133.97/19.39 | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | Case 2:
% 133.97/19.39 | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | (7632) all_57_3 = e3 & op(e2, e2) = e3
% 133.97/19.39 | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | ALPHA: (7632) implies:
% 133.97/19.39 | | | | | | | | | | | (7633) all_57_3 = e3
% 133.97/19.39 | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 133.97/19.39 | | | | | | | | | | | all_6_0, e1, e2, simplifying with (165), (7628)
% 133.97/19.39 | | | | | | | | | | | gives:
% 133.97/19.39 | | | | | | | | | | | (7634) all_52_9 = all_6_0
% 133.97/19.39 | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | COMBINE_EQS: (260), (7634) imply:
% 133.97/19.39 | | | | | | | | | | | (7635) all_54_6 = all_6_0
% 133.97/19.39 | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | REDUCE: (146), (7634) imply:
% 133.97/19.39 | | | | | | | | | | | (7636) ~ (all_52_1 = all_6_0)
% 133.97/19.39 | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | REDUCE: (123), (7634) imply:
% 133.97/19.39 | | | | | | | | | | | (7637) ~ (all_52_8 = all_6_0)
% 133.97/19.39 | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | REDUCE: (118), (7634) imply:
% 133.97/19.39 | | | | | | | | | | | (7638) ~ (all_52_11 = all_6_0)
% 133.97/19.39 | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | SIMP: (7638) implies:
% 133.97/19.39 | | | | | | | | | | | (7639) ~ (all_52_11 = all_6_0)
% 133.97/19.39 | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | REDUCE: (117), (7634) imply:
% 133.97/19.39 | | | | | | | | | | | (7640) ~ (all_52_13 = all_6_0)
% 133.97/19.39 | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | SIMP: (7640) implies:
% 133.97/19.39 | | | | | | | | | | | (7641) ~ (all_52_13 = all_6_0)
% 133.97/19.39 | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | REDUCE: (7623), (7634) imply:
% 133.97/19.39 | | | | | | | | | | | (7642) ~ (all_6_0 = e3)
% 133.97/19.39 | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | REDUCE: (7000), (7634) imply:
% 133.97/19.39 | | | | | | | | | | | (7643) ~ (all_6_0 = e2)
% 133.97/19.39 | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | BETA: splitting (198) gives:
% 133.97/19.39 | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | Case 1:
% 133.97/19.39 | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | (7644) all_54_6 = e3
% 133.97/19.39 | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | REF_CLOSE: (7635), (7642), (7644) are inconsistent by
% 133.97/19.39 | | | | | | | | | | | | sub-proof #79.
% 133.97/19.39 | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | Case 2:
% 133.97/19.39 | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | (7645) ~ (all_54_6 = e3)
% 133.97/19.39 | | | | | | | | | | | | (7646) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 133.97/19.39 | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | BETA: splitting (7646) gives:
% 133.97/19.39 | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | Case 1:
% 133.97/19.39 | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | (7647) all_54_6 = e2
% 133.97/19.39 | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | REF_CLOSE: (7635), (7643), (7647) are inconsistent by
% 133.97/19.39 | | | | | | | | | | | | | sub-proof #78.
% 133.97/19.39 | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | Case 2:
% 133.97/19.39 | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | (7648) ~ (all_54_6 = e2)
% 133.97/19.39 | | | | | | | | | | | | | (7649) all_54_6 = e1 | all_54_6 = e0
% 133.97/19.39 | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | BETA: splitting (7649) gives:
% 133.97/19.39 | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | Case 1:
% 133.97/19.39 | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | (7650) all_54_6 = e1
% 133.97/19.39 | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | COMBINE_EQS: (7635), (7650) imply:
% 133.97/19.39 | | | | | | | | | | | | | | (7651) all_6_0 = e1
% 133.97/19.39 | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | SIMP: (7651) implies:
% 133.97/19.39 | | | | | | | | | | | | | | (7652) all_6_0 = e1
% 133.97/19.39 | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | REDUCE: (7636), (7652) imply:
% 133.97/19.39 | | | | | | | | | | | | | | (7653) ~ (all_52_1 = e1)
% 133.97/19.39 | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | REDUCE: (7637), (7652) imply:
% 133.97/19.39 | | | | | | | | | | | | | | (7654) ~ (all_52_8 = e1)
% 133.97/19.39 | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | REDUCE: (7639), (7652) imply:
% 133.97/19.39 | | | | | | | | | | | | | | (7655) ~ (all_52_11 = e1)
% 133.97/19.39 | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | REDUCE: (7641), (7652) imply:
% 133.97/19.39 | | | | | | | | | | | | | | (7656) ~ (all_52_13 = e1)
% 133.97/19.39 | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | REDUCE: (7642), (7652) imply:
% 133.97/19.39 | | | | | | | | | | | | | | (7657) ~ (e3 = e1)
% 133.97/19.39 | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | REDUCE: (7643), (7652) imply:
% 133.97/19.39 | | | | | | | | | | | | | | (7658) ~ (e2 = e1)
% 133.97/19.39 | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 133.97/19.39 | | | | | | | | | | | | | |
% 133.97/19.39 | | | | | | | | | | | | | | Case 1:
% 133.97/19.39 | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | (7659) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 133.97/19.40 | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 133.97/19.40 | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | REF_CLOSE: (8), (167), (7625), (7653), (7659),
% 133.97/19.40 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.97/19.40 | | | | | | | | | | | | | | | #77.
% 133.97/19.40 | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | Case 2:
% 133.97/19.40 | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | (7660) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 133.97/19.40 | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 133.97/19.40 | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | BETA: splitting (7660) gives:
% 133.97/19.40 | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | Case 1:
% 133.97/19.40 | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | (7661) all_57_5 = e1 & op(e2, e1) = e1
% 133.97/19.40 | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | ALPHA: (7661) implies:
% 133.97/19.40 | | | | | | | | | | | | | | | | (7662) all_57_5 = e1
% 133.97/19.40 | | | | | | | | | | | | | | | | (7663) op(e2, e1) = e1
% 133.97/19.40 | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 133.97/19.40 | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.40 | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | (7664) ~ (all_16_2 = e2)
% 133.97/19.40 | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | REDUCE: (327), (7664) imply:
% 133.97/19.40 | | | | | | | | | | | | | | | | | (7665) ~ (all_10_2 = e2)
% 133.97/19.40 | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.40 | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | (7666) ~ (all_22_2 = e3)
% 133.97/19.40 | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | REDUCE: (7618), (7666) imply:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | (7667) $false
% 133.97/19.40 | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | CLOSE: (7667) is inconsistent.
% 133.97/19.40 | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.40 | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | (7668) ( ~ (all_22_0 = e0) & op(e3, e2) = all_22_0 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | $i(all_22_0)) | ( ~ (all_22_1 = e1) & op(e3, e3)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | = all_22_1 & $i(all_22_1))
% 133.97/19.40 | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | (7669) ~ (all_20_2 = e2)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | REDUCE: (318), (7669) imply:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | (7670) ~ (all_4_2 = e2)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | (7671) ~ (all_32_2 = e1)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | REDUCE: (312), (7671) imply:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | (7672) ~ (all_10_2 = e1)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (39), (45), (165), (168), (169), (202),
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | (204), (206), (270), (278), (344), (346), (361),
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | (371), (6999), (7000), (7007), (7009), (7625),
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | (7654), (7663), (7665), (7672), (function-axioms)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #104.
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | (7673) all_32_2 = e1
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | (7674) ( ~ (all_32_0 = e0) & op(e1, e3) = all_32_0 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | $i(all_32_0)) | ( ~ (all_32_1 = e2) & op(e1, e1)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | = all_32_1 & $i(all_32_1))
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (312), (7673) imply:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | (7675) all_10_2 = e1
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | SIMP: (7675) implies:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | (7676) all_10_2 = e1
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | REDUCE: (346), (7676) imply:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | (7677) ~ (all_52_12 = e1)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (7676) imply:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | (7678) op(e3, e3) = e1
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | (7679) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (7656), (7677), (7679),
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | #179.
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | (7680) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7680) gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | (7681) all_57_11 = e1 & op(e1, e0) = e1
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7681) implies:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | (7682) all_57_11 = e1
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | (7683) op(e1, e0) = e1
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7674) gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | (7684) ~ (all_32_0 = e0) & op(e1, e3) = all_32_0 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | $i(all_32_0)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7684) implies:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | (7685) ~ (all_32_0 = e0)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | (7686) op(e1, e3) = all_32_0
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | (7687) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7687) gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | (7688) all_57_6 = e3 & op(e1, e3) = e3
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7688) implies:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | (7689) all_57_6 = e3
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | (7690) op(e1, e3) = e3
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (7691) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7691) gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7692) all_57_12 = e1 & op(e0, e3) = e1
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7692) implies:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7693) all_57_12 = e1
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (235), (237),
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7678), (7693), (function-axioms) are inconsistent
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #583.
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7694) all_57_13 = e1 & op(e0, e2) = e1
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7694) implies:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7695) all_57_13 = e1
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7696) op(e0, e2) = e1
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7697) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7697) gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7698) all_57_1 = e2 & op(e3, e2) = e2
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7698) implies:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7699) all_57_1 = e2
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7700) op(e3, e2) = e2
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7701) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7701) gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7702) all_57_1 = e0 & op(e3, e2) = e0
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7699), (7702) are inconsistent by sub-proof
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #466.
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7703) all_57_3 = e0 & op(e2, e2) = e0
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7703) implies:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7704) op(e2, e2) = e0
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7625), (7704), (function-axioms) are
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641.
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7705) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7705) gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7706) all_57_7 = e0 & op(e1, e2) = e0
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7706) implies:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7707) op(e1, e2) = e0
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7708) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7708) gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7709) all_57_12 = e2 & op(e0, e3) = e2
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7709) implies:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7710) all_57_12 = e2
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7668) gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7711) ~ (all_22_0 = e0) & op(e3, e2) = all_22_0 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_22_0)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7711) implies:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7712) ~ (all_22_0 = e0)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7713) op(e3, e2) = all_22_0
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7714) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7714) gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7715) all_57_0 = e0 & op(e3, e3) = e0
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7715) implies:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7716) op(e3, e3) = e0
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7678), (7716), (function-axioms) are
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #717.
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7717) all_57_2 = e0 & op(e2, e3) = e0
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7717) implies:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7718) all_57_2 = e0
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7719) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7719) gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7720) all_57_2 = e2 & op(e2, e3) = e2
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7718), (7720) are inconsistent by sub-proof
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #680.
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7721) all_57_3 = e2 & op(e2, e2) = e2
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7721) implies:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7722) all_57_3 = e2
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (227), (228),
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230), (7621), (7699), (7722), (function-axioms)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #463.
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7723) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7723) gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7724) all_57_5 = e2 & op(e2, e1) = e2
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7724) implies:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7725) op(e2, e1) = e2
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7000), (7725), (function-axioms) are
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #770.
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7726) all_57_10 = e2 & op(e2, e0) = e2
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7726) implies:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7727) op(e2, e0) = e2
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e1,
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (158), (7696) gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7728) all_52_7 = e1
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e0, e1, simplifying with (160), (7683) gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7729) all_52_14 = e1
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e0,
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e1, simplifying with (162), (7707) gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7730) all_52_6 = e0
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e3,
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (163), (7690) gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7731) all_52_2 = e3
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2,
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_32_0, e3, e1, simplifying with (163), (7686)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7732) all_52_2 = all_32_0
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, e2, simplifying with (164), (7727) gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7733) all_52_13 = e2
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e2,
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (170), (7700) gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7734) all_52_4 = e2
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4,
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_22_0, e2, e3, simplifying with (170), (7713)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7735) all_52_4 = all_22_0
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7731), (7732) imply:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7736) all_32_0 = e3
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7734), (7735) imply:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7737) all_22_0 = e2
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7737) implies:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7738) all_22_0 = e2
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (7729), (7730) imply:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7739) ~ (e1 = e0)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7624), (7733) imply:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7740) ~ (e3 = e2)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7741) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7741) gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7742) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7690), (7710), (7742), (function-axioms) are
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #102.
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7743) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7743) gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7744) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3,
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7744) implies:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7745) op(e3, e3) = e0
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7678), (7745), (function-axioms) are
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #717.
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7746) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2,
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7746) implies:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7747) ~ (all_56_9 = e2)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7748) op(e3, e2) = all_56_9
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7700), (7747), (7748), (function-axioms) are
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #199.
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7749) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7749) gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7750) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (7000), (7007), (7750),
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #108.
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7751) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7751) gives:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7752) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7752) implies:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7753) op(e2, e2) = e0
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7625), (7753), (function-axioms) are
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641.
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7754) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7754) gives:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7755) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7755) implies:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7756) ~ (all_56_19 = e1)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7757) op(e2, e1) = all_56_19
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7663), (7756), (7757), (function-axioms) are
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #106.
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7758) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7758) implies:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7759) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7759) gives:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7760) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27))
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7663), (7700), (7760), (function-axioms) are
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #91.
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7761) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7761) gives:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7762) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7762) implies:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7763) op(e1, e1) = e0
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, e0, e1,
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, simplifying with (7007), (7763) gives:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7764) e2 = e0
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (7764) imply:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7765) $false
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7765) is inconsistent.
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7766) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7766) implies:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7767) ~ (all_56_5 = e3)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7768) op(e1, e3) = all_56_5
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7690), (7767), (7768), (function-axioms) are
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #724.
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7769) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7769) gives:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7770) all_57_6 = e0 & op(e1, e3) = e0
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7689), (7770) are inconsistent by sub-proof
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #576.
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7771) all_57_12 = e0 & op(e0, e3) = e0
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7710), (7771) are inconsistent by sub-proof
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #578.
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7772) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_22_1)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7678), (7772), (function-axioms) are inconsistent
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #305.
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7773) all_57_13 = e2 & op(e0, e2) = e2
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7773) implies:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7774) all_57_13 = e2
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (227), (228), (7633),
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7699), (7774) are inconsistent by sub-proof #301.
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7775) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7775) gives:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7776) all_57_14 = e2 & op(e0, e1) = e2
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (7001), (7776), (function-axioms) are
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #512.
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7777) all_57_15 = e2 & op(e0, e0) = e2
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (7670), (7777), (function-axioms) are
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #107.
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7778) all_57_13 = e0 & op(e0, e2) = e0
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7778) implies:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7779) all_57_13 = e0
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7695), (7779) are inconsistent by sub-proof
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #681.
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7780) all_57_3 = e2 & op(e2, e2) = e2
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7633), (7780) are inconsistent by sub-proof
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #375.
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7781) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7781) gives:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7782) all_57_7 = e2 & op(e1, e2) = e2
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7782) implies:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7783) all_57_7 = e2
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7668) gives:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7784) ~ (all_22_0 = e0) & op(e3, e2) = all_22_0 &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_22_0)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7784) implies:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7785) ~ (all_22_0 = e0)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7786) op(e3, e2) = all_22_0
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (227), (228),
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232), (236), (238), (7620), (7625), (7678),
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7783), (7785), (7786), (function-axioms) are
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #308.
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7787) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_22_1)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7678), (7787), (function-axioms) are inconsistent
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #305.
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7788) all_57_13 = e2 & op(e0, e2) = e2
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7788) implies:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7789) all_57_13 = e2
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7695), (7789) are inconsistent by sub-proof
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #567.
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | (7790) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7790) gives:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7791) all_57_14 = e1 & op(e0, e1) = e1
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7791) implies:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7792) all_57_14 = e1
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (169), (219),
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (220), (222), (7006), (7007), (7623), (7662),
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7792), (function-axioms) are inconsistent by
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #76.
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7793) all_57_15 = e1 & op(e0, e0) = e1
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7793) implies:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7794) op(e0, e0) = e1
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (371), (7794), (function-axioms) are
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #354.
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | (7795) all_57_7 = e3 & op(e1, e2) = e3
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7795) implies:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | (7796) op(e1, e2) = e3
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (7621), (7796), (function-axioms) are
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #654.
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | (7797) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7797) gives:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | (7798) all_57_8 = e3 & op(e1, e1) = e3
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7798) implies:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | (7799) op(e1, e1) = e3
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7007), (7799), (function-axioms) are
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #109.
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | (7800) all_57_11 = e3 & op(e1, e0) = e3
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7800) implies:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | (7801) all_57_11 = e3
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7682), (7801) are inconsistent by sub-proof
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | #167.
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | (7802) ~ (all_32_1 = e2) & op(e1, e1) = all_32_1 &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | $i(all_32_1)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7007), (7802), (function-axioms) are inconsistent
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #95.
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | (7803) all_57_15 = e1 & op(e0, e0) = e1
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7803) implies:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | (7804) op(e0, e0) = e1
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (371), (7804), (function-axioms) are
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #354.
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.41 | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | (7805) all_20_2 = e2
% 133.97/19.41 | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (318), (7805) imply:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | (7806) all_4_2 = e2
% 133.97/19.41 | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | SIMP: (7806) implies:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | (7807) all_4_2 = e2
% 133.97/19.41 | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (331), (7807) imply:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | (7808) all_26_2 = e2
% 133.97/19.41 | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | REDUCE: (368), (7807) imply:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | (7809) ~ (all_52_12 = e2)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | REDUCE: (369), (7807) imply:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | (7810) ~ (all_52_13 = e2)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | REDUCE: (36), (7807) imply:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | (7811) op(e0, e0) = e2
% 133.97/19.41 | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | (7812) ~ (all_26_2 = e2)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | REDUCE: (7808), (7812) imply:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | (7813) $false
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | CLOSE: (7813) is inconsistent.
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | (7814) ( ~ (all_26_0 = e1) & op(e2, e0) = all_26_0 &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | $i(all_26_0)) | ( ~ (all_26_1 = e3) & op(e2, e2)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | = all_26_1 & $i(all_26_1))
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | (7815) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7815) gives:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | (7816) all_57_1 = e2 & op(e3, e2) = e2
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7816) implies:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | (7817) all_57_1 = e2
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | (7818) op(e3, e2) = e2
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | (7819) all_54_7 = e3
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (7819) imply:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | (7820) all_52_13 = e3
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7624), (7820) imply:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | (7821) $false
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7821) is inconsistent.
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | (7822) ~ (all_54_7 = e3)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | (7823) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7823) gives:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | (7824) all_54_7 = e2
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (7824) imply:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | (7825) all_52_13 = e2
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7810), (7825) imply:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | (7826) $false
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7826) is inconsistent.
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | (7827) ~ (all_54_7 = e2)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | (7828) all_54_7 = e1 | all_54_7 = e0
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7828) gives:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | (7829) all_54_7 = e1
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (7829) imply:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | (7830) all_52_13 = e1
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7656), (7830) imply:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | (7831) $false
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7831) is inconsistent.
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | (7832) all_54_7 = e0
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (7832) imply:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | (7833) all_52_13 = e0
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7624), (7833) imply:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | (7834) ~ (e3 = e0)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7810), (7833) imply:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | (7835) ~ (e2 = e0)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7656), (7833) imply:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | (7836) ~ (e1 = e0)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (7833) imply:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | (7837) op(e2, e0) = e0
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7814) gives:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | (7838) ~ (all_26_0 = e1) & op(e2, e0) = all_26_0 &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_26_0)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7838) implies:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | (7839) ~ (all_26_0 = e1)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | (7840) op(e2, e0) = all_26_0
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7841) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7841) gives:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7842) all_57_0 = e0 & op(e3, e3) = e0
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7842) implies:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7843) op(e3, e3) = e0
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (7009), (7843), (function-axioms) are
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #534.
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7844) all_57_1 = e0 & op(e3, e2) = e0
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7817), (7844) are inconsistent by sub-proof
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #466.
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7845) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7845) gives:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7846) all_57_4 = e0 & op(e3, e1) = e0
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7846) implies:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7847) all_57_4 = e0
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7848) op(e3, e1) = e0
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7849) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (165), (169), (7623), (7848), (7849),
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #420.
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7850) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7850) gives:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7851) all_57_8 = e3 & op(e1, e1) = e3
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7851) implies:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7852) op(e1, e1) = e3
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7007), (7852), (function-axioms) are
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #109.
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7853) all_57_14 = e3 & op(e0, e1) = e3
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7853) implies:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7854) op(e0, e1) = e3
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e1, e0, simplifying with (157), (7854) gives:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7855) all_52_11 = e3
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_26_0,
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e2, simplifying with (7837), (7840) gives:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7856) all_26_0 = e0
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e0,
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (169), (7848) gives:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7857) all_52_8 = e0
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e2,
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (170), (7818) gives:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7858) all_52_4 = e2
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (344), (7857) imply:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7859) ~ (all_10_2 = e0)
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7860) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7860) gives:
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7861) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7861) gives:
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7862) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7862) implies:
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7863) op(e3, e3) = e2
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (234),
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (7620), (7817), (7847), (7863),
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #238.
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7864) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7864) implies:
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7865) op(e3, e1) = e3
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (169), (7848), (7865), (function-axioms) are
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #600.
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7866) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7866) gives:
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7867) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3,
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7867) implies:
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7868) op(e3, e3) = e0
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (7009), (7868), (function-axioms) are
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #534.
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7869) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2,
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7869) implies:
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7870) ~ (all_56_9 = e2)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7871) op(e3, e2) = all_56_9
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7818), (7870), (7871), (function-axioms) are
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #199.
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7872) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7872) gives:
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7873) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (7000), (7007), (7873),
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #108.
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7874) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7874) gives:
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7875) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7875) implies:
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7876) op(e2, e2) = e0
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7625), (7876), (function-axioms) are
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641.
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7877) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7877) gives:
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7878) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7878) implies:
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7879) ~ (all_56_19 = e1)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7880) op(e2, e1) = all_56_19
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7663), (7879), (7880), (function-axioms) are
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #106.
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7881) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7881) implies:
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7882) op(e0, e0) = all_56_31
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7883) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (39), (91), (157), (190), (246), (332),
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (364), (7001), (7811), (7837), (7882), (7883),
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #273.
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7884) all_57_9 = e0 & op(e3, e0) = e0
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7884) implies:
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7885) all_57_9 = e0
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (208), (212),
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (214), (223), (224), (225), (7624), (7625),
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7633), (7811), (7837), (7885), (function-axioms)
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #291.
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (7886) ~ (all_26_1 = e3) & op(e2, e2) = all_26_1 &
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_26_1)
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7886) implies:
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (7887) ~ (all_26_1 = e3)
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (7888) op(e2, e2) = all_26_1
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7625), (7887), (7888), (function-axioms) are
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #334.
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | (7889) all_57_3 = e2 & op(e2, e2) = e2
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7633), (7889) are inconsistent by sub-proof
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | #375.
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | (7890) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7890) gives:
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | (7891) all_57_7 = e2 & op(e1, e2) = e2
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (6998), (7891), (function-axioms) are
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #515.
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | (7892) all_57_13 = e2 & op(e0, e2) = e2
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7892) implies:
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | (7893) all_57_13 = e2
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | (7894) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7894) gives:
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | (7895) all_57_0 = e2 & op(e3, e3) = e2
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7895) implies:
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | (7896) op(e3, e3) = e2
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (7665), (7896), (function-axioms) are
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #536.
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | (7897) all_57_1 = e2 & op(e3, e2) = e2
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7897) implies:
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | (7898) all_57_1 = e2
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (227), (228), (7633),
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | (7893), (7898) are inconsistent by sub-proof #301.
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | (7899) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7899) gives:
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | (7900) all_57_4 = e2 & op(e3, e1) = e2
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (6999), (7900), (function-axioms) are
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #442.
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | (7901) all_57_9 = e2 & op(e3, e0) = e2
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (7809), (7901), (function-axioms) are
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #460.
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.42 | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.42 | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | End of split
% 134.25/19.42 | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.42 | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | (7902) all_16_2 = e2
% 134.25/19.42 | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | COMBINE_EQS: (327), (7902) imply:
% 134.25/19.42 | | | | | | | | | | | | | | | | | (7903) all_10_2 = e2
% 134.25/19.42 | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | SIMP: (7903) implies:
% 134.25/19.42 | | | | | | | | | | | | | | | | | (7904) all_10_2 = e2
% 134.25/19.42 | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | REDUCE: (336), (7904) imply:
% 134.25/19.42 | | | | | | | | | | | | | | | | | (7905) ~ (all_52_1 = e2)
% 134.25/19.42 | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | REDUCE: (45), (7904) imply:
% 134.25/19.42 | | | | | | | | | | | | | | | | | (7906) op(e3, e3) = e2
% 134.25/19.42 | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 134.25/19.42 | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.42 | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | (7907) all_54_4 = e3
% 134.25/19.42 | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (7907) imply:
% 134.25/19.42 | | | | | | | | | | | | | | | | | | (7908) all_52_1 = e3
% 134.25/19.42 | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | REDUCE: (7619), (7908) imply:
% 134.25/19.42 | | | | | | | | | | | | | | | | | | (7909) $false
% 134.25/19.42 | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | CLOSE: (7909) is inconsistent.
% 134.25/19.42 | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.42 | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | (7910) ~ (all_54_4 = e3)
% 134.25/19.42 | | | | | | | | | | | | | | | | | | (7911) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 134.25/19.42 | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | BETA: splitting (7911) gives:
% 134.25/19.42 | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.42 | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | (7912) all_54_4 = e2
% 134.25/19.42 | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (7912) imply:
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | (7913) all_52_1 = e2
% 134.25/19.42 | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | REDUCE: (7905), (7913) imply:
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | (7914) $false
% 134.25/19.42 | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | CLOSE: (7914) is inconsistent.
% 134.25/19.42 | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.42 | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | (7915) ~ (all_54_4 = e2)
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | (7916) all_54_4 = e1 | all_54_4 = e0
% 134.25/19.42 | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 134.25/19.42 | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | (7917) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | BETA: splitting (7917) gives:
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | (7918) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (170), (7620), (7906), (7918),
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | #254.
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | (7919) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (167), (7905), (7906), (7919),
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | #443.
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | (7920) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | BETA: splitting (7920) gives:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | (7921) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (7000), (7007), (7921),
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | #108.
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | (7922) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7922) gives:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | (7923) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7923) implies:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | (7924) op(e2, e2) = e0
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7625), (7924), (function-axioms) are
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641.
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | (7925) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7925) gives:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | (7926) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7926) implies:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | (7927) ~ (all_56_19 = e1)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | (7928) op(e2, e1) = all_56_19
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7663), (7927), (7928), (function-axioms) are
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #106.
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | (7929) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7929) implies:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | (7930) op(e0, e0) = all_56_31
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | (7931) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7916) gives:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | (7932) all_54_4 = e1
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (7932) imply:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | (7933) all_52_1 = e1
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7653), (7933) imply:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | (7934) $false
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7934) is inconsistent.
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | (7935) all_54_4 = e0
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (7935) imply:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | (7936) all_52_1 = e0
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (7936) imply:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | (7937) ~ (all_52_3 = e0)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7937) implies:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | (7938) ~ (all_52_3 = e0)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (7936) imply:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | (7939) ~ (all_52_13 = e0)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7939) implies:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | (7940) ~ (all_52_13 = e0)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7619), (7936) imply:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | (7941) ~ (e3 = e0)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7653), (7936) imply:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | (7942) ~ (e1 = e0)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7931) gives:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | (7943) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27))
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7943) gives:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (7944) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7944) implies:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (7945) op(e0, e3) = e0
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (7938), (7945), (function-axioms) are
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #219.
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (7946) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7946) implies:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (7947) all_56_31 = e2
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7930), (7947) imply:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (7948) op(e0, e0) = e2
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7949) all_54_7 = e3
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (7624), (7949) are inconsistent by
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #338.
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7950) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7950) gives:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7951) all_54_7 = e2
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (7951) imply:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7952) all_52_13 = e2
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7952) implies:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7953) all_52_13 = e2
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (7953) imply:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7954) ~ (all_4_2 = e2)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7954) implies:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7955) ~ (all_4_2 = e2)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (7930), (7948), (7955), (function-axioms)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #427.
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7956) all_54_7 = e1 | all_54_7 = e0
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (7656), (7940), (7956) are inconsistent by
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #313.
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | (7957) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7957) gives:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (7958) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7958) implies:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (7959) ~ (all_56_15 = e2)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (7960) op(e0, e2) = all_56_15
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7961) all_54_7 = e3
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (7624), (7961) are inconsistent by
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #338.
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7962) ~ (all_54_7 = e3)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7963) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7963) gives:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7964) all_54_7 = e2
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (7964) imply:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7965) all_52_13 = e2
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7965) implies:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7966) all_52_13 = e2
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (7966) imply:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7967) ~ (all_4_2 = e2)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7967) implies:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7968) ~ (all_4_2 = e2)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7624), (7966) imply:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7969) ~ (e3 = e2)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7970) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7970) gives:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7971) all_57_12 = e2 & op(e0, e3) = e2
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7971) implies:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7972) all_57_12 = e2
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7906), (7972), (function-axioms) are inconsistent
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #290.
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7973) all_57_13 = e2 & op(e0, e2) = e2
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7973) implies:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7974) op(e0, e2) = e2
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7959), (7960), (7974), (function-axioms) are
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #609.
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7975) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7975) gives:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7976) all_57_14 = e2 & op(e0, e1) = e2
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (7001), (7976), (function-axioms) are
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #512.
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7977) all_57_15 = e2 & op(e0, e0) = e2
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7977) implies:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7978) op(e0, e0) = e2
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (7930), (7968), (7978), (function-axioms)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #427.
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7979) all_54_7 = e1 | all_54_7 = e0
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (7656), (7940), (7979) are inconsistent by
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #313.
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (7980) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7980) implies:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (7981) all_56_31 = e1
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7930), (7981) imply:
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (7982) op(e0, e0) = e1
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (371), (7982), (function-axioms) are
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #354.
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.43 | | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.43 | | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | | End of split
% 134.25/19.43 | | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | End of split
% 134.25/19.43 | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | Case 2:
% 134.25/19.43 | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | (7983) all_57_10 = e1 & op(e2, e0) = e1
% 134.25/19.43 | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | ALPHA: (7983) implies:
% 134.25/19.43 | | | | | | | | | | | | | | | | (7984) op(e2, e0) = e1
% 134.25/19.43 | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | | REF_CLOSE: (164), (7656), (7984), (function-axioms) are
% 134.25/19.43 | | | | | | | | | | | | | | | | inconsistent by sub-proof #180.
% 134.25/19.43 | | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | | End of split
% 134.25/19.43 | | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | End of split
% 134.25/19.43 | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | Case 2:
% 134.25/19.43 | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | (7985) all_54_6 = e0
% 134.25/19.43 | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | | REF_CLOSE: (7627), (7635), (7985) are inconsistent by
% 134.25/19.43 | | | | | | | | | | | | | | sub-proof #75.
% 134.25/19.43 | | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | | End of split
% 134.25/19.43 | | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | | End of split
% 134.25/19.43 | | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | | End of split
% 134.25/19.43 | | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | End of split
% 134.25/19.43 | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | Case 2:
% 134.25/19.43 | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | (7986) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 134.25/19.43 | | | | | | | | | | e3 & op(e0, e2) = e3)
% 134.25/19.43 | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | | REF_CLOSE: (158), (162), (7621), (7622), (7986),
% 134.25/19.43 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.25/19.43 | | | | | | | | | | #555.
% 134.25/19.43 | | | | | | | | | |
% 134.25/19.43 | | | | | | | | | End of split
% 134.25/19.43 | | | | | | | | |
% 134.25/19.43 | | | | | | | | Case 2:
% 134.25/19.43 | | | | | | | | |
% 134.25/19.43 | | | | | | | | | (7987) ~ (all_6_1 = e3) & op(e2, e2) = all_6_1 &
% 134.25/19.43 | | | | | | | | | $i(all_6_1)
% 134.25/19.43 | | | | | | | | |
% 134.25/19.43 | | | | | | | | | REF_CLOSE: (7625), (7987), (function-axioms) are inconsistent
% 134.25/19.43 | | | | | | | | | by sub-proof #74.
% 134.25/19.43 | | | | | | | | |
% 134.25/19.43 | | | | | | | | End of split
% 134.25/19.43 | | | | | | | |
% 134.25/19.43 | | | | | | | End of split
% 134.25/19.43 | | | | | | |
% 134.25/19.43 | | | | | | Case 2:
% 134.25/19.43 | | | | | | |
% 134.25/19.43 | | | | | | | (7988) all_10_2 = e0
% 134.25/19.43 | | | | | | |
% 134.25/19.43 | | | | | | | COMBINE_EQS: (319), (7988) imply:
% 134.25/19.43 | | | | | | | (7989) all_24_2 = e0
% 134.25/19.43 | | | | | | |
% 134.25/19.43 | | | | | | | REDUCE: (336), (7988) imply:
% 134.25/19.43 | | | | | | | (7990) ~ (all_52_1 = e0)
% 134.25/19.43 | | | | | | |
% 134.25/19.43 | | | | | | | REDUCE: (338), (7988) imply:
% 134.25/19.43 | | | | | | | (7991) ~ (all_52_2 = e0)
% 134.25/19.43 | | | | | | |
% 134.25/19.43 | | | | | | | REDUCE: (340), (7988) imply:
% 134.25/19.43 | | | | | | | (7992) ~ (all_52_3 = e0)
% 134.25/19.43 | | | | | | |
% 134.25/19.43 | | | | | | | REDUCE: (342), (7988) imply:
% 134.25/19.43 | | | | | | | (7993) ~ (all_52_4 = e0)
% 134.25/19.43 | | | | | | |
% 134.25/19.43 | | | | | | | REDUCE: (344), (7988) imply:
% 134.25/19.43 | | | | | | | (7994) ~ (all_52_8 = e0)
% 134.25/19.43 | | | | | | |
% 134.25/19.43 | | | | | | | REDUCE: (346), (7988) imply:
% 134.25/19.43 | | | | | | | (7995) ~ (all_52_12 = e0)
% 134.25/19.43 | | | | | | |
% 134.25/19.44 | | | | | | | REDUCE: (45), (7988) imply:
% 134.25/19.44 | | | | | | | (7996) op(e3, e3) = e0
% 134.25/19.44 | | | | | | |
% 134.25/19.44 | | | | | | | BETA: splitting (52) gives:
% 134.25/19.44 | | | | | | |
% 134.25/19.44 | | | | | | | Case 1:
% 134.25/19.44 | | | | | | | |
% 134.25/19.44 | | | | | | | | (7997) ~ (all_14_2 = e3)
% 134.25/19.44 | | | | | | | |
% 134.25/19.44 | | | | | | | | REDUCE: (329), (7997) imply:
% 134.25/19.44 | | | | | | | | (7998) ~ (all_8_2 = e3)
% 134.25/19.44 | | | | | | | |
% 134.25/19.44 | | | | | | | | BETA: splitting (58) gives:
% 134.25/19.44 | | | | | | | |
% 134.25/19.44 | | | | | | | | Case 1:
% 134.25/19.44 | | | | | | | | |
% 134.25/19.44 | | | | | | | | | (7999) ~ (all_18_2 = e2)
% 134.25/19.44 | | | | | | | | |
% 134.25/19.44 | | | | | | | | | REDUCE: (6996), (7999) imply:
% 134.25/19.44 | | | | | | | | | (8000) $false
% 134.25/19.44 | | | | | | | | |
% 134.25/19.44 | | | | | | | | | CLOSE: (8000) is inconsistent.
% 134.25/19.44 | | | | | | | | |
% 134.25/19.44 | | | | | | | | Case 2:
% 134.25/19.44 | | | | | | | | |
% 134.25/19.44 | | | | | | | | | (8001) ( ~ (all_18_0 = e3) & op(e2, e1) = all_18_0 &
% 134.25/19.44 | | | | | | | | | $i(all_18_0)) | ( ~ (all_18_1 = e0) & op(e2, e2) =
% 134.25/19.44 | | | | | | | | | all_18_1 & $i(all_18_1))
% 134.25/19.44 | | | | | | | | |
% 134.25/19.44 | | | | | | | | | BETA: splitting (61) gives:
% 134.25/19.44 | | | | | | | | |
% 134.25/19.44 | | | | | | | | | Case 1:
% 134.25/19.44 | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | (8002) ~ (all_20_2 = e2)
% 134.25/19.44 | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | REDUCE: (318), (8002) imply:
% 134.25/19.44 | | | | | | | | | | (8003) ~ (all_4_2 = e2)
% 134.25/19.44 | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | BETA: splitting (76) gives:
% 134.25/19.44 | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | Case 1:
% 134.25/19.44 | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | (8004) ~ (all_30_2 = e0)
% 134.25/19.44 | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | REDUCE: (309), (8004) imply:
% 134.25/19.44 | | | | | | | | | | | (8005) ~ (all_8_2 = e0)
% 134.25/19.44 | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | BETA: splitting (199) gives:
% 134.25/19.44 | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | Case 1:
% 134.25/19.44 | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | (8006) all_54_5 = e3
% 134.25/19.44 | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | REF_CLOSE: (267), (7998), (8006) are inconsistent by
% 134.25/19.44 | | | | | | | | | | | | sub-proof #554.
% 134.25/19.44 | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | Case 2:
% 134.25/19.44 | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | (8007) ~ (all_54_5 = e3)
% 134.25/19.44 | | | | | | | | | | | | (8008) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 134.25/19.44 | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | BETA: splitting (8008) gives:
% 134.25/19.44 | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | Case 1:
% 134.25/19.44 | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | (8009) all_54_5 = e2
% 134.25/19.44 | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | COMBINE_EQS: (267), (8009) imply:
% 134.25/19.44 | | | | | | | | | | | | | (8010) all_8_2 = e2
% 134.25/19.44 | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | SIMP: (8010) implies:
% 134.25/19.44 | | | | | | | | | | | | | (8011) all_8_2 = e2
% 134.25/19.44 | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | REDUCE: (347), (8011) imply:
% 134.25/19.44 | | | | | | | | | | | | | (8012) ~ (all_52_1 = e2)
% 134.25/19.44 | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | REDUCE: (350), (8011) imply:
% 134.25/19.44 | | | | | | | | | | | | | (8013) ~ (all_52_4 = e2)
% 134.25/19.44 | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | REDUCE: (358), (8011) imply:
% 134.25/19.44 | | | | | | | | | | | | | (8014) ~ (all_52_13 = e2)
% 134.25/19.44 | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | REDUCE: (7998), (8011) imply:
% 134.25/19.44 | | | | | | | | | | | | | (8015) ~ (e3 = e2)
% 134.25/19.44 | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | BETA: splitting (235) gives:
% 134.25/19.44 | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | Case 1:
% 134.25/19.44 | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | (8016) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 134.25/19.44 | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 134.25/19.44 | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | BETA: splitting (8016) gives:
% 134.25/19.44 | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | Case 1:
% 134.25/19.44 | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | (8017) all_57_0 = e2 & op(e3, e3) = e2
% 134.25/19.44 | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | ALPHA: (8017) implies:
% 134.25/19.44 | | | | | | | | | | | | | | | (8018) op(e3, e3) = e2
% 134.25/19.44 | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | REF_CLOSE: (5), (7996), (8018), (function-axioms) are
% 134.25/19.44 | | | | | | | | | | | | | | | inconsistent by sub-proof #495.
% 134.25/19.44 | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | Case 2:
% 134.25/19.44 | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | (8019) all_57_2 = e2 & op(e2, e3) = e2
% 134.25/19.44 | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | ALPHA: (8019) implies:
% 134.25/19.44 | | | | | | | | | | | | | | | (8020) op(e2, e3) = e2
% 134.25/19.44 | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | REF_CLOSE: (167), (8012), (8020), (function-axioms) are
% 134.25/19.44 | | | | | | | | | | | | | | | inconsistent by sub-proof #779.
% 134.25/19.44 | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | End of split
% 134.25/19.44 | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | Case 2:
% 134.25/19.44 | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | (8021) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 134.25/19.44 | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 134.25/19.44 | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | BETA: splitting (8021) gives:
% 134.25/19.44 | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | Case 1:
% 134.25/19.44 | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | (8022) all_57_6 = e2 & op(e1, e3) = e2
% 134.25/19.44 | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | REF_CLOSE: (163), (6997), (8022), (function-axioms) are
% 134.25/19.44 | | | | | | | | | | | | | | | inconsistent by sub-proof #341.
% 134.25/19.44 | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | Case 2:
% 134.25/19.44 | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | (8023) all_57_12 = e2 & op(e0, e3) = e2
% 134.25/19.44 | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | ALPHA: (8023) implies:
% 134.25/19.44 | | | | | | | | | | | | | | | (8024) all_57_12 = e2
% 134.25/19.44 | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 134.25/19.44 | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | Case 1:
% 134.25/19.44 | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | (8025) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 134.25/19.44 | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 134.25/19.44 | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | BETA: splitting (8025) gives:
% 134.25/19.44 | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.44 | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | (8026) all_57_0 = e2 & op(e3, e3) = e2
% 134.25/19.44 | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | ALPHA: (8026) implies:
% 134.25/19.44 | | | | | | | | | | | | | | | | | (8027) op(e3, e3) = e2
% 134.25/19.44 | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 134.25/19.44 | | | | | | | | | | | | | | | | | (8024), (8027), (function-axioms) are inconsistent
% 134.25/19.44 | | | | | | | | | | | | | | | | | by sub-proof #290.
% 134.25/19.44 | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.44 | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | (8028) all_57_1 = e2 & op(e3, e2) = e2
% 134.25/19.44 | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (8013), (8028), (function-axioms) are
% 134.25/19.44 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #396.
% 134.25/19.44 | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | End of split
% 134.25/19.44 | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | Case 2:
% 134.25/19.44 | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | (8029) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 134.25/19.44 | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 134.25/19.44 | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | BETA: splitting (8029) gives:
% 134.25/19.44 | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.44 | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | (8030) all_57_4 = e2 & op(e3, e1) = e2
% 134.25/19.44 | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (6999), (8030), (function-axioms) are
% 134.25/19.44 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #442.
% 134.25/19.44 | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.44 | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | (8031) all_57_9 = e2 & op(e3, e0) = e2
% 134.25/19.44 | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | ALPHA: (8031) implies:
% 134.25/19.44 | | | | | | | | | | | | | | | | | (8032) op(e3, e0) = e2
% 134.25/19.44 | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 134.25/19.44 | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.44 | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | (8033) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 134.25/19.44 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 134.25/19.44 | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | BETA: splitting (8033) gives:
% 134.25/19.44 | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.44 | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | (8034) all_57_2 = e2 & op(e2, e3) = e2
% 134.25/19.44 | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | ALPHA: (8034) implies:
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | (8035) op(e2, e3) = e2
% 134.25/19.44 | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (8012), (8035), (function-axioms) are
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #779.
% 134.25/19.44 | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.44 | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | (8036) all_57_3 = e2 & op(e2, e2) = e2
% 134.25/19.44 | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | ALPHA: (8036) implies:
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | (8037) all_57_3 = e2
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | (8038) op(e2, e2) = e2
% 134.25/19.44 | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 134.25/19.44 | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | (8039) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | BETA: splitting (8039) gives:
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | (8040) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8040) gives:
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | (8041) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8041) implies:
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | (8042) op(e3, e3) = e2
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | (8024), (8042), (function-axioms) are inconsistent
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #290.
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | (8043) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8043) implies:
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | (8044) op(e3, e3) = e1
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7996), (8044), (function-axioms) are
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #717.
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | (8045) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (42), (168), (7998), (8032), (8045),
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | #110.
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | (8046) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | BETA: splitting (8046) gives:
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | (8047) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (7000), (7007), (8047),
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | #108.
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | (8048) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8048) gives:
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | (8049) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8049) implies:
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | (8050) op(e2, e0) = e2
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8014), (8050), (function-axioms) are
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | (8051) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8051) gives:
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | (8052) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8052) implies:
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | (8053) ~ (all_56_11 = e2)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | (8054) op(e2, e2) = all_56_11
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8038), (8053), (8054), (function-axioms) are
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #531.
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | (8055) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8055) implies:
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | (8056) op(e0, e0) = all_56_31
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | (8057) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (36), (159), (164), (165), (167), (225),
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | (371), (7000), (7007), (7992), (8012), (8014),
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | (8037), (8038), (8056), (8057), (function-axioms)
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #101.
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.44 | | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.44 | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.44 | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | (8058) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 134.25/19.44 | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 134.25/19.44 | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (165), (7000), (8014), (8058),
% 134.25/19.44 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.25/19.44 | | | | | | | | | | | | | | | | | | #625.
% 134.25/19.44 | | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | | End of split
% 134.25/19.44 | | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | | End of split
% 134.25/19.44 | | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | | End of split
% 134.25/19.44 | | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | | End of split
% 134.25/19.44 | | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | End of split
% 134.25/19.44 | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | Case 2:
% 134.25/19.44 | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | (8059) all_54_5 = e1 | all_54_5 = e0
% 134.25/19.44 | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | REF_CLOSE: (267), (7008), (8005), (8059) are inconsistent by
% 134.25/19.44 | | | | | | | | | | | | | sub-proof #624.
% 134.25/19.44 | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | End of split
% 134.25/19.44 | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | End of split
% 134.25/19.44 | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | Case 2:
% 134.25/19.44 | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | (8060) all_30_2 = e0
% 134.25/19.44 | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | COMBINE_EQS: (309), (8060) imply:
% 134.25/19.44 | | | | | | | | | | | (8061) all_8_2 = e0
% 134.25/19.44 | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | SIMP: (8061) implies:
% 134.25/19.44 | | | | | | | | | | | (8062) all_8_2 = e0
% 134.25/19.44 | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | COMBINE_EQS: (301), (8062) imply:
% 134.25/19.44 | | | | | | | | | | | (8063) all_42_2 = e0
% 134.25/19.44 | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | REDUCE: (352), (8062) imply:
% 134.25/19.44 | | | | | | | | | | | (8064) ~ (all_52_6 = e0)
% 134.25/19.44 | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | REDUCE: (356), (8062) imply:
% 134.25/19.44 | | | | | | | | | | | (8065) ~ (all_52_9 = e0)
% 134.25/19.44 | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | REDUCE: (42), (8062) imply:
% 134.25/19.44 | | | | | | | | | | | (8066) op(e2, e2) = e0
% 134.25/19.44 | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | BETA: splitting (215) gives:
% 134.25/19.44 | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | Case 1:
% 134.25/19.44 | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | (8067) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 134.25/19.44 | | | | | | | | | | | | & op(e1, e2) = e0)
% 134.25/19.44 | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | BETA: splitting (8067) gives:
% 134.25/19.44 | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | Case 1:
% 134.25/19.44 | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | (8068) all_57_6 = e0 & op(e1, e3) = e0
% 134.25/19.44 | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | REF_CLOSE: (163), (7991), (8068), (function-axioms) are
% 134.25/19.44 | | | | | | | | | | | | | inconsistent by sub-proof #73.
% 134.25/19.44 | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | Case 2:
% 134.25/19.44 | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | (8069) all_57_7 = e0 & op(e1, e2) = e0
% 134.25/19.44 | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | | REF_CLOSE: (162), (8064), (8069), (function-axioms) are
% 134.25/19.44 | | | | | | | | | | | | | inconsistent by sub-proof #505.
% 134.25/19.44 | | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | End of split
% 134.25/19.44 | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | Case 2:
% 134.25/19.44 | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | (8070) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 134.25/19.44 | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 134.25/19.44 | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | BETA: splitting (8070) gives:
% 134.25/19.44 | | | | | | | | | | | |
% 134.25/19.44 | | | | | | | | | | | | Case 1:
% 134.25/19.44 | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | (8071) all_57_8 = e0 & op(e1, e1) = e0
% 134.25/19.45 | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | REF_CLOSE: (5), (7006), (8071) are inconsistent by sub-proof
% 134.25/19.45 | | | | | | | | | | | | | #573.
% 134.25/19.45 | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | Case 2:
% 134.25/19.45 | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | (8072) all_57_11 = e0 & op(e1, e0) = e0
% 134.25/19.45 | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | ALPHA: (8072) implies:
% 134.25/19.45 | | | | | | | | | | | | | (8073) op(e1, e0) = e0
% 134.25/19.45 | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | BETA: splitting (219) gives:
% 134.25/19.45 | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | (8074) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 134.25/19.45 | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 134.25/19.45 | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | BETA: splitting (8074) gives:
% 134.25/19.45 | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | (8075) all_57_4 = e0 & op(e3, e1) = e0
% 134.25/19.45 | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | REF_CLOSE: (169), (7994), (8075), (function-axioms) are
% 134.25/19.45 | | | | | | | | | | | | | | | inconsistent by sub-proof #224.
% 134.25/19.45 | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | Case 2:
% 134.25/19.45 | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | (8076) all_57_5 = e0 & op(e2, e1) = e0
% 134.25/19.45 | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | REF_CLOSE: (165), (8065), (8076), (function-axioms) are
% 134.25/19.45 | | | | | | | | | | | | | | | inconsistent by sub-proof #455.
% 134.25/19.45 | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | End of split
% 134.25/19.45 | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | Case 2:
% 134.25/19.45 | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | (8077) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 134.25/19.45 | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 134.25/19.45 | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | BETA: splitting (8077) gives:
% 134.25/19.45 | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | (8078) all_57_8 = e0 & op(e1, e1) = e0
% 134.25/19.45 | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | REF_CLOSE: (5), (7006), (8078) are inconsistent by sub-proof
% 134.25/19.45 | | | | | | | | | | | | | | | #83.
% 134.25/19.45 | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | Case 2:
% 134.25/19.45 | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | (8079) all_57_14 = e0 & op(e0, e1) = e0
% 134.25/19.45 | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | ALPHA: (8079) implies:
% 134.25/19.45 | | | | | | | | | | | | | | | (8080) all_57_14 = e0
% 134.25/19.45 | | | | | | | | | | | | | | | (8081) op(e0, e1) = e0
% 134.25/19.45 | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | BETA: splitting (8001) gives:
% 134.25/19.45 | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | (8082) ~ (all_18_0 = e3) & op(e2, e1) = all_18_0 &
% 134.25/19.45 | | | | | | | | | | | | | | | | $i(all_18_0)
% 134.25/19.45 | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | ALPHA: (8082) implies:
% 134.25/19.45 | | | | | | | | | | | | | | | | (8083) ~ (all_18_0 = e3)
% 134.25/19.45 | | | | | | | | | | | | | | | | (8084) op(e2, e1) = all_18_0
% 134.25/19.45 | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 134.25/19.45 | | | | | | | | | | | | | | | | e0, e1, e0, simplifying with (157), (8081) gives:
% 134.25/19.45 | | | | | | | | | | | | | | | | (8085) all_52_11 = e0
% 134.25/19.45 | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 134.25/19.45 | | | | | | | | | | | | | | | | e0, e0, e1, simplifying with (160), (8073) gives:
% 134.25/19.45 | | | | | | | | | | | | | | | | (8086) all_52_14 = e0
% 134.25/19.45 | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 134.25/19.45 | | | | | | | | | | | | | | | | all_18_0, e1, e2, simplifying with (165), (8084)
% 134.25/19.45 | | | | | | | | | | | | | | | | gives:
% 134.25/19.45 | | | | | | | | | | | | | | | | (8087) all_52_9 = all_18_0
% 134.25/19.45 | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (8087) imply:
% 134.25/19.45 | | | | | | | | | | | | | | | | (8088) all_54_6 = all_18_0
% 134.25/19.45 | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | REDUCE: (125), (8085) imply:
% 134.25/19.45 | | | | | | | | | | | | | | | | (8089) ~ (all_52_7 = e0)
% 134.25/19.45 | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | REDUCE: (123), (8087) imply:
% 134.25/19.45 | | | | | | | | | | | | | | | | (8090) ~ (all_52_8 = all_18_0)
% 134.25/19.45 | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | REDUCE: (117), (8087) imply:
% 134.25/19.45 | | | | | | | | | | | | | | | | (8091) ~ (all_52_13 = all_18_0)
% 134.25/19.45 | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | SIMP: (8091) implies:
% 134.25/19.45 | | | | | | | | | | | | | | | | (8092) ~ (all_52_13 = all_18_0)
% 134.25/19.45 | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | REDUCE: (7000), (8087) imply:
% 134.25/19.45 | | | | | | | | | | | | | | | | (8093) ~ (all_18_0 = e2)
% 134.25/19.45 | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | REDUCE: (8065), (8087) imply:
% 134.25/19.45 | | | | | | | | | | | | | | | | (8094) ~ (all_18_0 = e0)
% 134.25/19.45 | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | REDUCE: (110), (8086) imply:
% 134.25/19.45 | | | | | | | | | | | | | | | | (8095) ~ (all_52_13 = e0)
% 134.25/19.45 | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | REDUCE: (370), (8086) imply:
% 134.25/19.45 | | | | | | | | | | | | | | | | (8096) ~ (all_4_2 = e0)
% 134.25/19.45 | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | SIMP: (8096) implies:
% 134.25/19.45 | | | | | | | | | | | | | | | | (8097) ~ (all_4_2 = e0)
% 134.25/19.45 | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | REDUCE: (7002), (8086) imply:
% 134.25/19.45 | | | | | | | | | | | | | | | | (8098) ~ (e2 = e0)
% 134.25/19.45 | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 134.25/19.45 | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | (8099) all_54_6 = e3
% 134.25/19.45 | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | COMBINE_EQS: (8088), (8099) imply:
% 134.25/19.45 | | | | | | | | | | | | | | | | | (8100) all_18_0 = e3
% 134.25/19.45 | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | REDUCE: (8083), (8100) imply:
% 134.25/19.45 | | | | | | | | | | | | | | | | | (8101) $false
% 134.25/19.45 | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | CLOSE: (8101) is inconsistent.
% 134.25/19.45 | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.45 | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | (8102) ~ (all_54_6 = e3)
% 134.25/19.45 | | | | | | | | | | | | | | | | | (8103) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 134.25/19.45 | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | BETA: splitting (8103) gives:
% 134.25/19.45 | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | (8104) all_54_6 = e2
% 134.25/19.45 | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8088), (8104) imply:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | (8105) all_18_0 = e2
% 134.25/19.45 | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | REDUCE: (8093), (8105) imply:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | (8106) $false
% 134.25/19.45 | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | CLOSE: (8106) is inconsistent.
% 134.25/19.45 | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.45 | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | (8107) ~ (all_54_6 = e2)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | (8108) all_54_6 = e1 | all_54_6 = e0
% 134.25/19.45 | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | BETA: splitting (8108) gives:
% 134.25/19.45 | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | (8109) all_54_6 = e1
% 134.25/19.45 | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8088), (8109) imply:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | (8110) all_18_0 = e1
% 134.25/19.45 | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | REDUCE: (8090), (8110) imply:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | (8111) ~ (all_52_8 = e1)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | REDUCE: (8093), (8110) imply:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | (8112) ~ (e2 = e1)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | (8113) all_54_2 = e3
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (8113) imply:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | (8114) all_52_8 = e3
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | SIMP: (8114) implies:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | (8115) all_52_8 = e3
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (8115) imply:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | (8116) ~ (all_52_4 = e3)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (8115) imply:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | (8117) ~ (all_52_12 = e3)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | SIMP: (8117) implies:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | (8118) ~ (all_52_12 = e3)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | (8119) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (170), (7996), (8116), (8119),
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | #197.
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | (8120) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8120) gives:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | (8121) all_57_4 = e3 & op(e3, e1) = e3
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8121) implies:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | (8122) all_57_4 = e3
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | (8123) op(e3, e1) = e3
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | (8124) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8124) gives:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | (8125) all_57_4 = e1 & op(e3, e1) = e1
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8122), (8125) are inconsistent by sub-proof
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | #382.
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | (8126) all_57_5 = e1 & op(e2, e1) = e1
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8126) implies:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | (8127) all_57_5 = e1
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | (8128) all_54_15 = e3
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (8128) imply:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | (8129) all_4_2 = e3
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8129) implies:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | (8130) all_4_2 = e3
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (8130) imply:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | (8131) ~ (all_52_7 = e3)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (8130) imply:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | (8132) ~ (all_52_13 = e3)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (8130) imply:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | (8133) op(e0, e0) = e3
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | (8134) ~ (all_42_2 = e0)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8063), (8134) imply:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | (8135) $false
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8135) is inconsistent.
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | (8136) ( ~ (all_42_0 = e1) & op(e0, e2) = all_42_0 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_42_0)) | ( ~ (all_42_1 = e3) & op(e0, e0)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_42_1 & $i(all_42_1))
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8136) gives:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8137) ~ (all_42_0 = e1) & op(e0, e2) = all_42_0 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_42_0)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8137) implies:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8138) ~ (all_42_0 = e1)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8139) op(e0, e2) = all_42_0
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8140) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8140) gives:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8141) all_57_2 = e3 & op(e2, e3) = e3
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8141) implies:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8142) all_57_2 = e3
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8143) op(e2, e3) = e3
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8144) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8144) gives:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8145) all_57_0 = e2 & op(e3, e3) = e2
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8145) implies:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8146) op(e3, e3) = e2
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7996), (8146), (function-axioms) are
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495.
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8147) all_57_2 = e2 & op(e2, e3) = e2
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8142), (8147) are inconsistent by sub-proof
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #454.
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8148) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8148) gives:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8149) all_57_6 = e2 & op(e1, e3) = e2
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (6997), (8149), (function-axioms) are
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #341.
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8150) all_57_12 = e2 & op(e0, e3) = e2
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8150) implies:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8151) all_57_12 = e2
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8152) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8152) gives:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8153) all_57_2 = e2 & op(e2, e3) = e2
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8142), (8153) are inconsistent by sub-proof
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #454.
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8154) all_57_3 = e2 & op(e2, e2) = e2
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8154) implies:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8155) all_57_3 = e2
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (158), (162), (170), (227), (7993), (8064),
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8089), (8155), (function-axioms) are inconsistent
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #503.
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8156) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8156) gives:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8157) all_57_5 = e2 & op(e2, e1) = e2
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8157) implies:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8158) op(e2, e1) = e2
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7000), (8158), (function-axioms) are
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #770.
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8159) all_57_10 = e2 & op(e2, e0) = e2
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8159) implies:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8160) all_57_10 = e2
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8161) all_54_6 = e3
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8088), (8161) imply:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8162) all_18_0 = e3
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8083), (8162) imply:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8163) $false
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8163) is inconsistent.
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8103) gives:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8164) all_54_6 = e2
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8088), (8164) imply:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8165) all_18_0 = e2
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8093), (8165) imply:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8166) $false
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8166) is inconsistent.
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8108) gives:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8092), (8110) imply:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8167) ~ (all_52_13 = e1)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8083), (8110) imply:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8168) ~ (e3 = e1)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8169) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8169) gives:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8170) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8170) gives:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8171) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8171) implies:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8172) op(e3, e3) = e2
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8151), (8172), (function-axioms) are inconsistent
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #290.
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8173) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8173) implies:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8174) op(e3, e3) = e1
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (168), (169), (170), (232), (7993),
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7995), (8123), (8174), (function-axioms) are
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #599.
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8175) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (8066), (8118), (8175),
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #622.
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8176) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8176) gives:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8177) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8177) gives:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8178) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8178) implies:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8179) ~ (all_56_9 = e2)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8180) op(e3, e2) = all_56_9
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8181) all_54_7 = e3
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (8132), (8181) are inconsistent by
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #338.
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8182) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8182) gives:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8183) all_54_7 = e2
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (8183) imply:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8184) all_52_13 = e2
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8184) implies:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8185) all_52_13 = e2
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (8185) imply:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8186) ~ (all_52_12 = e2)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8187) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8187) gives:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8188) all_57_0 = e2 & op(e3, e3) = e2
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8188) implies:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8189) all_57_0 = e2
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (231), (233), (8142),
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8151), (8189) are inconsistent by sub-proof #133.
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8190) all_57_1 = e2 & op(e3, e2) = e2
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8190) implies:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8191) op(e3, e2) = e2
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8179), (8180), (8191), (function-axioms) are
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #199.
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8192) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8192) gives:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8193) all_57_4 = e2 & op(e3, e1) = e2
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (6999), (8193), (function-axioms) are
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #442.
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8194) all_57_9 = e2 & op(e3, e0) = e2
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (8186), (8194), (function-axioms) are
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #460.
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8195) all_54_7 = e1 | all_54_7 = e0
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (8095), (8167), (8195) are inconsistent by
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #313.
% 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8196) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2,
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8196) implies:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8197) op(e2, e1) = e2
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7000), (8197), (function-axioms) are
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #770.
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8198) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8198) gives:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8199) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8199) implies:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8200) op(e0, e2) = all_56_15
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (113), (133), (158), (170), (197),
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (201), (223), (224), (228), (230), (259), (269),
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7995), (8066), (8095), (8116), (8118), (8131),
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8132), (8138), (8139), (8142), (8160), (8167),
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8200), (function-axioms) are inconsistent by
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #72.
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8201) ~ (all_54_2 = e3)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (270), (8201) imply:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8202) ~ (all_52_8 = e3)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (8123), (8202), (function-axioms) are
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #705.
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8203) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8203) gives:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8204) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8204) implies:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8205) ~ (all_56_3 = e3)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8206) op(e2, e3) = all_56_3
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8143), (8205), (8206), (function-axioms) are
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #347.
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8207) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8207) implies:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8208) op(e0, e0) = all_56_31
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8209) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8209) gives:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8210) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27))
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8210) gives:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8211) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8211) implies:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8212) op(e0, e3) = e0
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (7992), (8212), (function-axioms) are
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #219.
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8213) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8213) implies:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8214) op(e0, e2) = e0
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (8089), (8214), (function-axioms) are
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #545.
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8215) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8215) gives:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8216) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8216) implies:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8217) op(e0, e2) = all_56_15
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (113), (133), (158), (170), (197),
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (201), (223), (224), (228), (230), (259), (269),
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7995), (8066), (8095), (8116), (8118), (8131),
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8132), (8138), (8139), (8142), (8160), (8167),
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8217), (function-axioms) are inconsistent by
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #72.
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8218) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8218) implies:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8219) all_56_31 = e1
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8208), (8219) imply:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8220) op(e0, e0) = e1
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8133), (8220), (function-axioms) are
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #606.
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8221) ~ (all_54_2 = e3)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (270), (8221) imply:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8222) ~ (all_52_8 = e3)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (8123), (8222), (function-axioms) are
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #705.
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8223) all_54_6 = e0
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8088), (8223) imply:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8224) all_18_0 = e0
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8094), (8224) imply:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8225) $false
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8225) is inconsistent.
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8226) all_57_3 = e3 & op(e2, e2) = e3
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8226) implies:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8227) op(e2, e2) = e3
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8066), (8227), (function-axioms) are
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641.
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8228) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8228) gives:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8229) all_57_5 = e3 & op(e2, e1) = e3
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8229) implies:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8230) all_57_5 = e3
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8127), (8230) are inconsistent by sub-proof
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #88.
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8231) all_57_10 = e3 & op(e2, e0) = e3
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8132), (8231), (function-axioms) are
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749.
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8232) ~ (all_42_1 = e3) & op(e0, e0) = all_42_1 &
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_42_1)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8133), (8232), (function-axioms) are inconsistent
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #602.
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | (8233) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (371), (8003), (8097), (8233) are
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #746.
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | (8234) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8234) gives:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | (8235) all_57_8 = e1 & op(e1, e1) = e1
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7006), (8235) are inconsistent by sub-proof
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | #574.
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | (8236) all_57_14 = e1 & op(e0, e1) = e1
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8236) implies:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | (8237) all_57_14 = e1
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8080), (8237) are inconsistent by sub-proof
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | #221.
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | (8238) all_57_9 = e3 & op(e3, e0) = e3
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8238) implies:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | (8239) op(e3, e0) = e3
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (8118), (8239), (function-axioms) are
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #733.
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | (8240) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (6999), (7994), (8111), (8240) are
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #71.
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | (8241) all_54_6 = e0
% 134.25/19.46 | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8088), (8241) imply:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | (8242) all_18_0 = e0
% 134.25/19.46 | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | REDUCE: (8094), (8242) imply:
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | (8243) $false
% 134.25/19.46 | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | | CLOSE: (8243) is inconsistent.
% 134.25/19.46 | | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | Case 2:
% 134.25/19.46 | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | (8244) ~ (all_18_1 = e0) & op(e2, e2) = all_18_1 &
% 134.25/19.46 | | | | | | | | | | | | | | | | $i(all_18_1)
% 134.25/19.46 | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | ALPHA: (8244) implies:
% 134.25/19.46 | | | | | | | | | | | | | | | | (8245) ~ (all_18_1 = e0)
% 134.25/19.46 | | | | | | | | | | | | | | | | (8246) op(e2, e2) = all_18_1
% 134.25/19.46 | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_18_1,
% 134.25/19.46 | | | | | | | | | | | | | | | | e2, e2, simplifying with (8066), (8246) gives:
% 134.25/19.46 | | | | | | | | | | | | | | | | (8247) all_18_1 = e0
% 134.25/19.46 | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | REDUCE: (8245), (8247) imply:
% 134.25/19.46 | | | | | | | | | | | | | | | | (8248) $false
% 134.25/19.46 | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | CLOSE: (8248) is inconsistent.
% 134.25/19.46 | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | End of split
% 134.25/19.46 | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | Case 2:
% 134.25/19.46 | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | (8249) all_20_2 = e2
% 134.25/19.46 | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | COMBINE_EQS: (318), (8249) imply:
% 134.25/19.46 | | | | | | | | | | (8250) all_4_2 = e2
% 134.25/19.46 | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | REDUCE: (349), (8250) imply:
% 134.25/19.46 | | | | | | | | | | (8251) ~ (all_52_3 = e2)
% 134.25/19.46 | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | REDUCE: (368), (8250) imply:
% 134.25/19.46 | | | | | | | | | | (8252) ~ (all_52_12 = e2)
% 134.25/19.46 | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | REDUCE: (36), (8250) imply:
% 134.25/19.46 | | | | | | | | | | (8253) op(e0, e0) = e2
% 134.25/19.46 | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | BETA: splitting (67) gives:
% 134.25/19.46 | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | Case 1:
% 134.25/19.46 | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | (8254) ~ (all_24_2 = e0)
% 134.25/19.46 | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | REDUCE: (7989), (8254) imply:
% 134.25/19.46 | | | | | | | | | | | (8255) $false
% 134.25/19.46 | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | CLOSE: (8255) is inconsistent.
% 134.25/19.46 | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | Case 2:
% 134.25/19.46 | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | (8256) ( ~ (all_24_0 = e1) & op(e0, e3) = all_24_0 &
% 134.25/19.46 | | | | | | | | | | | $i(all_24_0)) | ( ~ (all_24_1 = e2) & op(e0, e0)
% 134.25/19.46 | | | | | | | | | | | = all_24_1 & $i(all_24_1))
% 134.25/19.46 | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | BETA: splitting (8256) gives:
% 134.25/19.46 | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | Case 1:
% 134.25/19.46 | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | (8257) ~ (all_24_0 = e1) & op(e0, e3) = all_24_0 &
% 134.25/19.46 | | | | | | | | | | | | $i(all_24_0)
% 134.25/19.46 | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | ALPHA: (8257) implies:
% 134.25/19.46 | | | | | | | | | | | | (8258) ~ (all_24_0 = e1)
% 134.25/19.46 | | | | | | | | | | | | (8259) op(e0, e3) = all_24_0
% 134.25/19.46 | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | BETA: splitting (235) gives:
% 134.25/19.46 | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | Case 1:
% 134.25/19.46 | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | (8260) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 134.25/19.46 | | | | | | | | | | | | | & op(e2, e3) = e2)
% 134.25/19.46 | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | BETA: splitting (8260) gives:
% 134.25/19.46 | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | Case 1:
% 134.25/19.46 | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | (8261) all_57_0 = e2 & op(e3, e3) = e2
% 134.25/19.46 | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | ALPHA: (8261) implies:
% 134.25/19.46 | | | | | | | | | | | | | | (8262) op(e3, e3) = e2
% 134.25/19.46 | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | REF_CLOSE: (5), (7996), (8262), (function-axioms) are
% 134.25/19.46 | | | | | | | | | | | | | | inconsistent by sub-proof #495.
% 134.25/19.46 | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | Case 2:
% 134.25/19.46 | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | (8263) all_57_2 = e2 & op(e2, e3) = e2
% 134.25/19.46 | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | ALPHA: (8263) implies:
% 134.25/19.46 | | | | | | | | | | | | | | (8264) all_57_2 = e2
% 134.25/19.46 | | | | | | | | | | | | | | (8265) op(e2, e3) = e2
% 134.25/19.46 | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 134.25/19.46 | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | Case 1:
% 134.25/19.46 | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | (8266) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 134.25/19.46 | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 134.25/19.46 | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | BETA: splitting (8266) gives:
% 134.25/19.46 | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | Case 1:
% 134.25/19.46 | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | (8267) all_57_0 = e2 & op(e3, e3) = e2
% 134.25/19.46 | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | ALPHA: (8267) implies:
% 134.25/19.46 | | | | | | | | | | | | | | | | (8268) op(e3, e3) = e2
% 134.25/19.46 | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7996), (8268), (function-axioms) are
% 134.25/19.46 | | | | | | | | | | | | | | | | inconsistent by sub-proof #495.
% 134.25/19.46 | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | Case 2:
% 134.25/19.46 | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | (8269) all_57_1 = e2 & op(e3, e2) = e2
% 134.25/19.46 | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | ALPHA: (8269) implies:
% 134.25/19.46 | | | | | | | | | | | | | | | | (8270) all_57_1 = e2
% 134.25/19.46 | | | | | | | | | | | | | | | | (8271) op(e3, e2) = e2
% 134.25/19.46 | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 134.25/19.46 | | | | | | | | | | | | | | | | all_24_0, e3, e0, simplifying with (159), (8259)
% 134.25/19.46 | | | | | | | | | | | | | | | | gives:
% 134.25/19.46 | | | | | | | | | | | | | | | | (8272) all_52_3 = all_24_0
% 134.25/19.46 | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 134.25/19.46 | | | | | | | | | | | | | | | | e3, e2, simplifying with (167), (8265) gives:
% 134.25/19.46 | | | | | | | | | | | | | | | | (8273) all_52_1 = e2
% 134.25/19.46 | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e2,
% 134.25/19.46 | | | | | | | | | | | | | | | | e2, e3, simplifying with (170), (8271) gives:
% 134.25/19.46 | | | | | | | | | | | | | | | | (8274) all_52_4 = e2
% 134.25/19.46 | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (8272) imply:
% 134.25/19.46 | | | | | | | | | | | | | | | | (8275) all_54_12 = all_24_0
% 134.25/19.46 | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | REDUCE: (146), (8273) imply:
% 134.25/19.46 | | | | | | | | | | | | | | | | (8276) ~ (all_52_9 = e2)
% 134.25/19.46 | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | REDUCE: (145), (8273) imply:
% 134.25/19.46 | | | | | | | | | | | | | | | | (8277) ~ (all_52_13 = e2)
% 134.25/19.46 | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | SIMP: (8277) implies:
% 134.25/19.46 | | | | | | | | | | | | | | | | (8278) ~ (all_52_13 = e2)
% 134.25/19.46 | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | REDUCE: (144), (8272) imply:
% 134.25/19.46 | | | | | | | | | | | | | | | | (8279) ~ (all_52_2 = all_24_0)
% 134.25/19.46 | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | REDUCE: (140), (8272) imply:
% 134.25/19.46 | | | | | | | | | | | | | | | | (8280) ~ (all_52_7 = all_24_0)
% 134.25/19.46 | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | SIMP: (8280) implies:
% 134.25/19.46 | | | | | | | | | | | | | | | | (8281) ~ (all_52_7 = all_24_0)
% 134.25/19.46 | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | REDUCE: (139), (8272) imply:
% 134.25/19.46 | | | | | | | | | | | | | | | | (8282) ~ (all_52_11 = all_24_0)
% 134.25/19.46 | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | SIMP: (8282) implies:
% 134.25/19.46 | | | | | | | | | | | | | | | | (8283) ~ (all_52_11 = all_24_0)
% 134.25/19.46 | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | REDUCE: (8251), (8272) imply:
% 134.25/19.46 | | | | | | | | | | | | | | | | (8284) ~ (all_24_0 = e2)
% 134.25/19.46 | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | REDUCE: (7992), (8272) imply:
% 134.25/19.46 | | | | | | | | | | | | | | | | (8285) ~ (all_24_0 = e0)
% 134.25/19.46 | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 134.25/19.46 | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.46 | | | | | | | | | | | | | | | | |
% 134.25/19.46 | | | | | | | | | | | | | | | | | (8286) all_54_12 = e3
% 134.25/19.47 | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | COMBINE_EQS: (8275), (8286) imply:
% 134.25/19.47 | | | | | | | | | | | | | | | | | (8287) all_24_0 = e3
% 134.25/19.47 | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | SIMP: (8287) implies:
% 134.25/19.47 | | | | | | | | | | | | | | | | | (8288) all_24_0 = e3
% 134.25/19.47 | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | REDUCE: (8279), (8288) imply:
% 134.25/19.47 | | | | | | | | | | | | | | | | | (8289) ~ (all_52_2 = e3)
% 134.25/19.47 | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | REDUCE: (8281), (8288) imply:
% 134.25/19.47 | | | | | | | | | | | | | | | | | (8290) ~ (all_52_7 = e3)
% 134.25/19.47 | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | REDUCE: (8283), (8288) imply:
% 134.25/19.47 | | | | | | | | | | | | | | | | | (8291) ~ (all_52_11 = e3)
% 134.25/19.47 | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 134.25/19.47 | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.47 | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | (8292) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 134.25/19.47 | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 134.25/19.47 | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (7996), (8264), (8292),
% 134.25/19.47 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.25/19.47 | | | | | | | | | | | | | | | | | | #70.
% 134.25/19.47 | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.47 | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | (8293) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 134.25/19.47 | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | BETA: splitting (8293) gives:
% 134.25/19.47 | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | (8294) all_57_6 = e3 & op(e1, e3) = e3
% 134.25/19.47 | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (8289), (8294), (function-axioms) are
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #761.
% 134.25/19.47 | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | (8295) all_57_12 = e3 & op(e0, e3) = e3
% 134.25/19.47 | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | ALPHA: (8295) implies:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | (8296) all_57_12 = e3
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | (8297) op(e0, e3) = e3
% 134.25/19.47 | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | (8298) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7996), (8265), (8298),
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | #69.
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | (8299) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | BETA: splitting (8299) gives:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | (8300) all_57_6 = e1 & op(e1, e3) = e1
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | ALPHA: (8300) implies:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | (8301) all_57_6 = e1
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | (8302) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8302) gives:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | (8303) all_57_1 = e3 & op(e3, e2) = e3
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8303) implies:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | (8304) all_57_1 = e3
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8270), (8304) imply:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | (8305) e3 = e2
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8305) implies:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | (8306) e3 = e2
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8296), (8306) imply:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | (8307) all_57_12 = e2
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (208), (209),
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | (211), (8253), (8291), (8307), (function-axioms)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #458.
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | (8308) all_57_3 = e3 & op(e2, e2) = e3
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8308) implies:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | (8309) op(e2, e2) = e3
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (7998), (8309), (function-axioms) are
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #228.
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | (8310) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8310) gives:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | (8311) all_57_7 = e3 & op(e1, e2) = e3
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8311) implies:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | (8312) all_57_7 = e3
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | (8313) op(e1, e2) = e3
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | (8314) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8314) gives:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | (8315) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8315) gives:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (8316) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8316) implies:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (8317) op(e3, e3) = e2
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (231), (8264), (8296), (8301),
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (8317), (function-axioms) are inconsistent by
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #491.
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (8318) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8318) implies:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (8319) op(e3, e3) = e1
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7996), (8319), (function-axioms) are
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #717.
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | (8320) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (7998), (8297), (8320), (function-axioms)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #68.
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | (8321) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8321) gives:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | (8322) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (7000), (7007), (8322),
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | #108.
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | (8323) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8323) gives:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (8324) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8324) implies:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (8325) op(e2, e0) = e2
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8278), (8325), (function-axioms) are
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (8326) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8326) gives:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8327) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8327) implies:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8328) ~ (all_56_11 = e2)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8329) op(e1, e2) = e1
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8330) op(e2, e2) = all_56_11
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8331) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8331) gives:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8332) all_57_1 = e0 & op(e3, e2) = e0
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (7993), (8332), (function-axioms) are
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #693.
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8333) all_57_3 = e0 & op(e2, e2) = e0
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8333) implies:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8334) op(e2, e2) = e0
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8001) gives:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, e3, e2,
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, simplifying with (8313), (8329) gives:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8335) e3 = e1
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8296), (8335) imply:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8336) all_57_12 = e1
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (157), (158), (211), (8253), (8290),
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8291), (8336), (function-axioms) are inconsistent
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #123.
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8337) ~ (all_18_1 = e0) & op(e2, e2) = all_18_1 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_18_1)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8334), (8337), (function-axioms) are inconsistent
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #103.
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8338) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8338) gives:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8339) all_57_7 = e0 & op(e1, e2) = e0
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8312), (8339) are inconsistent by sub-proof
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #147.
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8340) all_57_13 = e0 & op(e0, e2) = e0
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8340) implies:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8341) op(e0, e2) = e0
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (158), (199), (267), (354), (7008), (7998),
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8328), (8330), (8341), (function-axioms) are
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #227.
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8342) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8342) implies:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8343) op(e0, e0) = all_56_31
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8344) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (157), (158),
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (199), (208), (209), (211), (267), (354), (7008),
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7998), (8253), (8291), (8296), (8297), (8343),
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8344), (function-axioms) are inconsistent by
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #208.
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | (8345) all_57_13 = e3 & op(e0, e2) = e3
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (8290), (8345), (function-axioms) are
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #556.
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | (8346) all_57_12 = e1 & op(e0, e3) = e1
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | ALPHA: (8346) implies:
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | (8347) all_57_12 = e1
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (157), (158), (211), (8253), (8290),
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | (8291), (8347), (function-axioms) are inconsistent
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | by sub-proof #123.
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.47 | | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.47 | | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | End of split
% 134.25/19.47 | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.47 | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | (8348) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 134.25/19.47 | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | | REF_CLOSE: (8258), (8275), (8284), (8285), (8348) are
% 134.25/19.47 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #205.
% 134.25/19.47 | | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | End of split
% 134.25/19.47 | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | End of split
% 134.25/19.47 | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | Case 2:
% 134.25/19.47 | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | (8349) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 134.25/19.47 | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 134.25/19.47 | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | BETA: splitting (8349) gives:
% 134.25/19.47 | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | Case 1:
% 134.25/19.47 | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | (8350) all_57_4 = e2 & op(e3, e1) = e2
% 134.25/19.47 | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | REF_CLOSE: (169), (6999), (8350), (function-axioms) are
% 134.25/19.47 | | | | | | | | | | | | | | | | inconsistent by sub-proof #442.
% 134.25/19.47 | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | Case 2:
% 134.25/19.47 | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | (8351) all_57_9 = e2 & op(e3, e0) = e2
% 134.25/19.47 | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | | REF_CLOSE: (168), (8252), (8351), (function-axioms) are
% 134.25/19.47 | | | | | | | | | | | | | | | | inconsistent by sub-proof #460.
% 134.25/19.47 | | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | | End of split
% 134.25/19.47 | | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | | End of split
% 134.25/19.47 | | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | | End of split
% 134.25/19.47 | | | | | | | | | | | | |
% 134.25/19.47 | | | | | | | | | | | | Case 2:
% 134.25/19.47 | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | (8352) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 134.25/19.48 | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 134.25/19.48 | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | BETA: splitting (8352) gives:
% 134.25/19.48 | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | (8353) all_57_6 = e2 & op(e1, e3) = e2
% 134.25/19.48 | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | REF_CLOSE: (163), (6997), (8353), (function-axioms) are
% 134.25/19.48 | | | | | | | | | | | | | | inconsistent by sub-proof #341.
% 134.25/19.48 | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | Case 2:
% 134.25/19.48 | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | (8354) all_57_12 = e2 & op(e0, e3) = e2
% 134.25/19.48 | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | REF_CLOSE: (159), (8251), (8354), (function-axioms) are
% 134.25/19.48 | | | | | | | | | | | | | | inconsistent by sub-proof #97.
% 134.25/19.48 | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | End of split
% 134.25/19.48 | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | End of split
% 134.25/19.48 | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | Case 2:
% 134.25/19.48 | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | (8355) ~ (all_24_1 = e2) & op(e0, e0) = all_24_1 &
% 134.25/19.48 | | | | | | | | | | | | $i(all_24_1)
% 134.25/19.48 | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | REF_CLOSE: (8253), (8355), (function-axioms) are inconsistent
% 134.25/19.48 | | | | | | | | | | | | by sub-proof #204.
% 134.25/19.48 | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | End of split
% 134.25/19.48 | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | End of split
% 134.25/19.48 | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | End of split
% 134.25/19.48 | | | | | | | | |
% 134.25/19.48 | | | | | | | | End of split
% 134.25/19.48 | | | | | | | |
% 134.25/19.48 | | | | | | | Case 2:
% 134.25/19.48 | | | | | | | |
% 134.25/19.48 | | | | | | | | (8356) all_14_2 = e3
% 134.25/19.48 | | | | | | | | (8357) ( ~ (all_14_0 = e1) & op(e3, e2) = all_14_0 &
% 134.25/19.48 | | | | | | | | $i(all_14_0)) | ( ~ (all_14_1 = e0) & op(e3, e3) =
% 134.25/19.48 | | | | | | | | all_14_1 & $i(all_14_1))
% 134.25/19.48 | | | | | | | |
% 134.25/19.48 | | | | | | | | COMBINE_EQS: (329), (8356) imply:
% 134.25/19.48 | | | | | | | | (8358) all_8_2 = e3
% 134.25/19.48 | | | | | | | |
% 134.25/19.48 | | | | | | | | SIMP: (8358) implies:
% 134.25/19.48 | | | | | | | | (8359) all_8_2 = e3
% 134.25/19.48 | | | | | | | |
% 134.25/19.48 | | | | | | | | REDUCE: (347), (8359) imply:
% 134.25/19.48 | | | | | | | | (8360) ~ (all_52_1 = e3)
% 134.25/19.48 | | | | | | | |
% 134.25/19.48 | | | | | | | | REDUCE: (350), (8359) imply:
% 134.25/19.48 | | | | | | | | (8361) ~ (all_52_4 = e3)
% 134.25/19.48 | | | | | | | |
% 134.25/19.48 | | | | | | | | REDUCE: (352), (8359) imply:
% 134.25/19.48 | | | | | | | | (8362) ~ (all_52_6 = e3)
% 134.25/19.48 | | | | | | | |
% 134.25/19.48 | | | | | | | | REDUCE: (354), (8359) imply:
% 134.25/19.48 | | | | | | | | (8363) ~ (all_52_7 = e3)
% 134.25/19.48 | | | | | | | |
% 134.25/19.48 | | | | | | | | REDUCE: (356), (8359) imply:
% 134.25/19.48 | | | | | | | | (8364) ~ (all_52_9 = e3)
% 134.25/19.48 | | | | | | | |
% 134.25/19.48 | | | | | | | | REDUCE: (358), (8359) imply:
% 134.25/19.48 | | | | | | | | (8365) ~ (all_52_13 = e3)
% 134.25/19.48 | | | | | | | |
% 134.25/19.48 | | | | | | | | BETA: splitting (230) gives:
% 134.25/19.48 | | | | | | | |
% 134.25/19.48 | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | |
% 134.25/19.48 | | | | | | | | | (8366) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 &
% 134.25/19.48 | | | | | | | | | op(e2, e2) = e3)
% 134.25/19.48 | | | | | | | | |
% 134.25/19.48 | | | | | | | | | BETA: splitting (8366) gives:
% 134.25/19.48 | | | | | | | | |
% 134.25/19.48 | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | (8367) all_57_1 = e3 & op(e3, e2) = e3
% 134.25/19.48 | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | ALPHA: (8367) implies:
% 134.25/19.48 | | | | | | | | | | (8368) op(e3, e2) = e3
% 134.25/19.48 | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | REF_CLOSE: (170), (8361), (8368), (function-axioms) are
% 134.25/19.48 | | | | | | | | | | inconsistent by sub-proof #738.
% 134.25/19.48 | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | Case 2:
% 134.25/19.48 | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | (8369) all_57_3 = e3 & op(e2, e2) = e3
% 134.25/19.48 | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | ALPHA: (8369) implies:
% 134.25/19.48 | | | | | | | | | | (8370) all_57_3 = e3
% 134.25/19.48 | | | | | | | | | | (8371) op(e2, e2) = e3
% 134.25/19.48 | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | BETA: splitting (6995) gives:
% 134.25/19.48 | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | (8372) ~ (all_6_0 = e0) & op(e2, e1) = all_6_0 &
% 134.25/19.48 | | | | | | | | | | | $i(all_6_0)
% 134.25/19.48 | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | ALPHA: (8372) implies:
% 134.25/19.48 | | | | | | | | | | | (8373) ~ (all_6_0 = e0)
% 134.25/19.48 | | | | | | | | | | | (8374) op(e2, e1) = all_6_0
% 134.25/19.48 | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | BETA: splitting (8357) gives:
% 134.25/19.48 | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | (8375) ~ (all_14_0 = e1) & op(e3, e2) = all_14_0 &
% 134.25/19.48 | | | | | | | | | | | | $i(all_14_0)
% 134.25/19.48 | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | ALPHA: (8375) implies:
% 134.25/19.48 | | | | | | | | | | | | (8376) ~ (all_14_0 = e1)
% 134.25/19.48 | | | | | | | | | | | | (8377) op(e3, e2) = all_14_0
% 134.25/19.48 | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 134.25/19.48 | | | | | | | | | | | | all_6_0, e1, e2, simplifying with (165), (8374)
% 134.25/19.48 | | | | | | | | | | | | gives:
% 134.25/19.48 | | | | | | | | | | | | (8378) all_52_9 = all_6_0
% 134.25/19.48 | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4,
% 134.25/19.48 | | | | | | | | | | | | all_14_0, e2, e3, simplifying with (170), (8377)
% 134.25/19.48 | | | | | | | | | | | | gives:
% 134.25/19.48 | | | | | | | | | | | | (8379) all_52_4 = all_14_0
% 134.25/19.48 | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | COMBINE_EQS: (260), (8378) imply:
% 134.25/19.48 | | | | | | | | | | | | (8380) all_54_6 = all_6_0
% 134.25/19.48 | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | COMBINE_EQS: (271), (8379) imply:
% 134.25/19.48 | | | | | | | | | | | | (8381) all_54_1 = all_14_0
% 134.25/19.48 | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | REDUCE: (146), (8378) imply:
% 134.25/19.48 | | | | | | | | | | | | (8382) ~ (all_52_1 = all_6_0)
% 134.25/19.48 | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | REDUCE: (136), (8379) imply:
% 134.25/19.48 | | | | | | | | | | | | (8383) ~ (all_52_6 = all_14_0)
% 134.25/19.48 | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | SIMP: (8383) implies:
% 134.25/19.48 | | | | | | | | | | | | (8384) ~ (all_52_6 = all_14_0)
% 134.25/19.48 | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | REDUCE: (134), (8379) imply:
% 134.25/19.48 | | | | | | | | | | | | (8385) ~ (all_52_8 = all_14_0)
% 134.25/19.48 | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | SIMP: (8385) implies:
% 134.25/19.48 | | | | | | | | | | | | (8386) ~ (all_52_8 = all_14_0)
% 134.25/19.48 | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | REDUCE: (133), (8379) imply:
% 134.25/19.48 | | | | | | | | | | | | (8387) ~ (all_52_12 = all_14_0)
% 134.25/19.48 | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | SIMP: (8387) implies:
% 134.25/19.48 | | | | | | | | | | | | (8388) ~ (all_52_12 = all_14_0)
% 134.25/19.48 | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | REDUCE: (8361), (8379) imply:
% 134.25/19.48 | | | | | | | | | | | | (8389) ~ (all_14_0 = e3)
% 134.25/19.48 | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | REDUCE: (7993), (8379) imply:
% 134.25/19.48 | | | | | | | | | | | | (8390) ~ (all_14_0 = e0)
% 134.25/19.48 | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | REDUCE: (123), (8378) imply:
% 134.25/19.48 | | | | | | | | | | | | (8391) ~ (all_52_8 = all_6_0)
% 134.25/19.48 | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | REDUCE: (117), (8378) imply:
% 134.25/19.48 | | | | | | | | | | | | (8392) ~ (all_52_13 = all_6_0)
% 134.25/19.48 | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | SIMP: (8392) implies:
% 134.25/19.48 | | | | | | | | | | | | (8393) ~ (all_52_13 = all_6_0)
% 134.25/19.48 | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | REDUCE: (8364), (8378) imply:
% 134.25/19.48 | | | | | | | | | | | | (8394) ~ (all_6_0 = e3)
% 134.25/19.48 | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | REDUCE: (7000), (8378) imply:
% 134.25/19.48 | | | | | | | | | | | | (8395) ~ (all_6_0 = e2)
% 134.25/19.48 | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | BETA: splitting (203) gives:
% 134.25/19.48 | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | (8396) all_54_1 = e3
% 134.25/19.48 | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | COMBINE_EQS: (8381), (8396) imply:
% 134.25/19.48 | | | | | | | | | | | | | (8397) all_14_0 = e3
% 134.25/19.48 | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | REDUCE: (8389), (8397) imply:
% 134.25/19.48 | | | | | | | | | | | | | (8398) $false
% 134.25/19.48 | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | CLOSE: (8398) is inconsistent.
% 134.25/19.48 | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | Case 2:
% 134.25/19.48 | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | (8399) ~ (all_54_1 = e3)
% 134.25/19.48 | | | | | | | | | | | | | (8400) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 134.25/19.48 | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | BETA: splitting (219) gives:
% 134.25/19.48 | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | (8401) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 134.25/19.48 | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 134.25/19.48 | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | BETA: splitting (8401) gives:
% 134.25/19.48 | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | (8402) all_57_4 = e0 & op(e3, e1) = e0
% 134.25/19.48 | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | REF_CLOSE: (169), (7994), (8402), (function-axioms) are
% 134.25/19.48 | | | | | | | | | | | | | | | inconsistent by sub-proof #224.
% 134.25/19.48 | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | Case 2:
% 134.25/19.48 | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | (8403) all_57_5 = e0 & op(e2, e1) = e0
% 134.25/19.48 | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | ALPHA: (8403) implies:
% 134.25/19.48 | | | | | | | | | | | | | | | (8404) all_57_5 = e0
% 134.25/19.48 | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 134.25/19.48 | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | (8405) all_54_6 = e3
% 134.25/19.48 | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | REF_CLOSE: (8380), (8394), (8405) are inconsistent by
% 134.25/19.48 | | | | | | | | | | | | | | | | sub-proof #79.
% 134.25/19.48 | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | Case 2:
% 134.25/19.48 | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | (8406) ~ (all_54_6 = e3)
% 134.25/19.48 | | | | | | | | | | | | | | | | (8407) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 134.25/19.48 | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | BETA: splitting (8407) gives:
% 134.25/19.48 | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | (8408) all_54_6 = e2
% 134.25/19.48 | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | REF_CLOSE: (8380), (8395), (8408) are inconsistent by
% 134.25/19.48 | | | | | | | | | | | | | | | | | sub-proof #78.
% 134.25/19.48 | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.48 | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | (8409) all_54_6 = e1 | all_54_6 = e0
% 134.25/19.48 | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | BETA: splitting (8409) gives:
% 134.25/19.48 | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | (8410) all_54_6 = e1
% 134.25/19.48 | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8380), (8410) imply:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | (8411) all_6_0 = e1
% 134.25/19.48 | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | SIMP: (8411) implies:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | (8412) all_6_0 = e1
% 134.25/19.48 | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | REDUCE: (8382), (8412) imply:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | (8413) ~ (all_52_1 = e1)
% 134.25/19.48 | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | REDUCE: (8393), (8412) imply:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | (8414) ~ (all_52_13 = e1)
% 134.25/19.48 | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | REDUCE: (8394), (8412) imply:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | (8415) ~ (e3 = e1)
% 134.25/19.48 | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 134.25/19.48 | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | (8416) all_54_4 = e3
% 134.25/19.48 | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (8416) imply:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | (8417) all_52_1 = e3
% 134.25/19.48 | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | REDUCE: (8360), (8417) imply:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | (8418) $false
% 134.25/19.48 | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | CLOSE: (8418) is inconsistent.
% 134.25/19.48 | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | (8419) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 134.25/19.48 | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | BETA: splitting (8419) gives:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | (8420) all_54_4 = e2
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (8420) imply:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | (8421) all_52_1 = e2
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (8421) imply:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | (8422) ~ (all_52_13 = e2)
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | SIMP: (8422) implies:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | (8423) ~ (all_52_13 = e2)
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (8421) imply:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | (8424) op(e2, e3) = e2
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | (8425) all_54_7 = e3
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (8365), (8425) are inconsistent by
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | sub-proof #338.
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | (8426) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8426) gives:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | (8427) all_54_7 = e2
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (8423), (8427) are inconsistent by
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | sub-proof #337.
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | (8428) all_54_7 = e1 | all_54_7 = e0
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8428) gives:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | (8429) all_54_7 = e1
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (8414), (8429) are inconsistent by
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #314.
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | (8430) all_54_7 = e0
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (8430) imply:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | (8431) all_52_13 = e0
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8431) implies:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | (8432) all_52_13 = e0
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8414), (8432) imply:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | (8433) ~ (e1 = e0)
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (8432) imply:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | (8434) op(e2, e0) = e0
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | (8435) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (8371), (8424), (8435),
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | #292.
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | (8436) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8436) gives:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | (8437) all_57_5 = e1 & op(e2, e1) = e1
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8404), (8437) are inconsistent by sub-proof
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | #365.
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | (8438) all_57_10 = e1 & op(e2, e0) = e1
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8438) implies:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | (8439) op(e2, e0) = e1
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8434), (8439), (function-axioms) are
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #695.
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | (8440) all_54_4 = e1 | all_54_4 = e0
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (7990), (8413), (8440) are inconsistent by
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | sub-proof #153.
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.48 | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.48 | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.48 | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | (8441) all_54_6 = e0
% 134.25/19.48 | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8373), (8380), (8441) are inconsistent by
% 134.25/19.48 | | | | | | | | | | | | | | | | | | sub-proof #75.
% 134.25/19.48 | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | End of split
% 134.25/19.48 | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | End of split
% 134.25/19.48 | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | End of split
% 134.25/19.48 | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | End of split
% 134.25/19.48 | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | Case 2:
% 134.25/19.48 | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | (8442) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 134.25/19.48 | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 134.25/19.48 | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | BETA: splitting (8442) gives:
% 134.25/19.48 | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | (8443) all_57_8 = e0 & op(e1, e1) = e0
% 134.25/19.48 | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | REF_CLOSE: (5), (7006), (8443) are inconsistent by sub-proof
% 134.25/19.48 | | | | | | | | | | | | | | | #83.
% 134.25/19.48 | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | Case 2:
% 134.25/19.48 | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | (8444) all_57_14 = e0 & op(e0, e1) = e0
% 134.25/19.48 | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | ALPHA: (8444) implies:
% 134.25/19.48 | | | | | | | | | | | | | | | (8445) all_57_14 = e0
% 134.25/19.48 | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 134.25/19.48 | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | (8446) all_54_6 = e3
% 134.25/19.48 | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | REF_CLOSE: (8380), (8394), (8446) are inconsistent by
% 134.25/19.48 | | | | | | | | | | | | | | | | sub-proof #79.
% 134.25/19.48 | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | Case 2:
% 134.25/19.48 | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | (8447) ~ (all_54_6 = e3)
% 134.25/19.48 | | | | | | | | | | | | | | | | (8448) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 134.25/19.48 | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | BETA: splitting (8448) gives:
% 134.25/19.48 | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | (8449) all_54_6 = e2
% 134.25/19.48 | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | REF_CLOSE: (8380), (8395), (8449) are inconsistent by
% 134.25/19.48 | | | | | | | | | | | | | | | | | sub-proof #78.
% 134.25/19.48 | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.48 | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | (8450) ~ (all_54_6 = e2)
% 134.25/19.48 | | | | | | | | | | | | | | | | | (8451) all_54_6 = e1 | all_54_6 = e0
% 134.25/19.48 | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 134.25/19.48 | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | (8452) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 134.25/19.48 | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 134.25/19.48 | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | BETA: splitting (8452) gives:
% 134.25/19.48 | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | (8453) all_57_4 = e3 & op(e3, e1) = e3
% 134.25/19.48 | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | ALPHA: (8453) implies:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | (8454) all_57_4 = e3
% 134.25/19.48 | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | (8455) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (167), (7990), (8371), (8455),
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | #203.
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | (8456) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | BETA: splitting (8456) gives:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | (8457) all_57_5 = e0 & op(e2, e1) = e0
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | ALPHA: (8457) implies:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | (8458) all_57_5 = e0
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (220), (7006), (8445), (8454),
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | (8458) are inconsistent by sub-proof #84.
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | (8459) all_57_10 = e0 & op(e2, e0) = e0
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | ALPHA: (8459) implies:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | (8460) op(e2, e0) = e0
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | (8461) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8461) gives:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | (8462) all_57_2 = e2 & op(e2, e3) = e2
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8462) implies:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | (8463) all_57_2 = e2
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8400) gives:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | (8464) all_54_1 = e2
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8381), (8464) imply:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | (8465) all_14_0 = e2
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8388), (8465) imply:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | (8466) ~ (all_52_12 = e2)
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8389), (8465) imply:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | (8467) ~ (e3 = e2)
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | (8468) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8468) gives:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (8469) all_57_1 = e2 & op(e3, e2) = e2
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8469) implies:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (8470) all_57_1 = e2
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (8471) op(e3, e2) = e2
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8451) gives:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8472) all_54_6 = e1
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8380), (8472) imply:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8473) all_6_0 = e1
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8473) implies:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8474) all_6_0 = e1
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8391), (8474) imply:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8475) ~ (all_52_8 = e1)
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8394), (8474) imply:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8476) ~ (e3 = e1)
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8395), (8474) imply:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8477) ~ (e2 = e1)
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8478) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (168), (8460), (8466), (8478),
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #200.
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8479) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8479) gives:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8480) all_57_11 = e2 & op(e1, e0) = e2
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8480) implies:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8481) all_57_11 = e2
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (215), (216),
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218), (7006), (8362), (8481), (function-axioms)
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #571.
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8482) all_57_15 = e2 & op(e0, e0) = e2
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8482) implies:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8483) op(e0, e0) = e2
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8484) all_54_2 = e3
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (8484) imply:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8485) all_52_8 = e3
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8485) implies:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8486) all_52_8 = e3
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (8486) imply:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8487) ~ (all_52_11 = e3)
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8487) implies:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8488) ~ (all_52_11 = e3)
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (8486) imply:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8489) ~ (all_52_12 = e3)
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8489) implies:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8490) ~ (all_52_12 = e3)
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (169), (8486) imply:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8491) op(e3, e1) = e3
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8492) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (168), (169), (170), (232), (7993),
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7995), (8470), (8491), (8492), (function-axioms)
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #202.
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8493) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8493) gives:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8494) all_57_4 = e1 & op(e3, e1) = e1
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8454), (8494) are inconsistent by sub-proof
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #382.
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8495) all_57_9 = e1 & op(e3, e0) = e1
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8495) implies:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8496) all_57_9 = e1
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8497) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8497) gives:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8498) all_57_12 = e3 & op(e0, e3) = e3
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8498) implies:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8499) all_57_12 = e3
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8500) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8500) gives:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8501) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (231), (232),
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (236), (238), (7993), (8463), (8496),
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8499), (8501), (function-axioms) are inconsistent
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #116.
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8502) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (8471), (8490), (8502), (function-axioms)
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #198.
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8503) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8503) gives:
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8504) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (7000), (7007), (8504),
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #108.
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8505) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8505) gives:
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8506) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8506) implies:
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8507) op(e2, e2) = e0
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8371), (8507), (function-axioms) are
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641.
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8508) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (39), (91), (157), (190), (246), (332),
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (364), (7001), (8460), (8483), (8508),
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #67.
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8509) all_57_13 = e3 & op(e0, e2) = e3
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (8363), (8509), (function-axioms) are
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #556.
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8510) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (157), (8483), (8488), (8510),
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #459.
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8511) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (6999), (7994), (8475), (8511) are
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #71.
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8512) all_54_6 = e0
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8373), (8380), (8512) are inconsistent by
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #75.
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (8513) all_57_3 = e2 & op(e2, e2) = e2
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8513) implies:
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (8514) all_57_3 = e2
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8370), (8514) are inconsistent by sub-proof
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | #762.
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | (8515) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8515) gives:
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (8516) all_57_7 = e2 & op(e1, e2) = e2
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (6998), (8516), (function-axioms) are
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #515.
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (8517) all_57_13 = e2 & op(e0, e2) = e2
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (168), (169), (227),
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (236), (6999), (7996), (8370), (8466),
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (8517), (function-axioms) are inconsistent by
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #193.
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | (8518) all_54_1 = e1 | all_54_1 = e0
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8376), (8381), (8390), (8518) are inconsistent by
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #192.
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | (8519) all_57_3 = e2 & op(e2, e2) = e2
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8370), (8519) are inconsistent by sub-proof
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | #375.
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | (8520) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8520) gives:
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | (8521) all_57_5 = e2 & op(e2, e1) = e2
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8521) implies:
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | (8522) op(e2, e1) = e2
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7000), (8522), (function-axioms) are
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #770.
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | (8523) all_57_10 = e2 & op(e2, e0) = e2
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8523) implies:
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | (8524) op(e2, e0) = e2
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8460), (8524), (function-axioms) are
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #451.
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | | End of split
% 134.25/19.49 | | | | | | | | | | | | | | | | | | |
% 134.25/19.49 | | | | | | | | | | | | | | | | | | Case 2:
% 134.25/19.49 | | | | | | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | | | | | | (8525) all_57_5 = e3 & op(e2, e1) = e3
% 134.53/19.49 | | | | | | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (8364), (8525), (function-axioms) are
% 134.53/19.49 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547.
% 134.53/19.49 | | | | | | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.49 | | | | | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.49 | | | | | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | | | | | (8526) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 134.53/19.49 | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 134.53/19.49 | | | | | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | | | | | BETA: splitting (8526) gives:
% 134.53/19.49 | | | | | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.49 | | | | | | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | | | | | | (8527) all_57_8 = e3 & op(e1, e1) = e3
% 134.53/19.49 | | | | | | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | | | | | | ALPHA: (8527) implies:
% 134.53/19.49 | | | | | | | | | | | | | | | | | | | (8528) op(e1, e1) = e3
% 134.53/19.49 | | | | | | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7007), (8528), (function-axioms) are
% 134.53/19.49 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #109.
% 134.53/19.49 | | | | | | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.49 | | | | | | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | | | | | | (8529) all_57_14 = e3 & op(e0, e1) = e3
% 134.53/19.49 | | | | | | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | | | | | | ALPHA: (8529) implies:
% 134.53/19.49 | | | | | | | | | | | | | | | | | | | (8530) all_57_14 = e3
% 134.53/19.49 | | | | | | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8445), (8530) are inconsistent by sub-proof
% 134.53/19.49 | | | | | | | | | | | | | | | | | | | #400.
% 134.53/19.49 | | | | | | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.49 | | | | | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | | | | End of split
% 134.53/19.49 | | | | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | | | End of split
% 134.53/19.49 | | | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | | End of split
% 134.53/19.49 | | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | End of split
% 134.53/19.49 | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | End of split
% 134.53/19.49 | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | End of split
% 134.53/19.49 | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | Case 2:
% 134.53/19.49 | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | (8531) ~ (all_14_1 = e0) & op(e3, e3) = all_14_1 &
% 134.53/19.49 | | | | | | | | | | | | $i(all_14_1)
% 134.53/19.49 | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | REF_CLOSE: (7996), (8531), (function-axioms) are inconsistent
% 134.53/19.49 | | | | | | | | | | | | by sub-proof #191.
% 134.53/19.49 | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | End of split
% 134.53/19.49 | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | Case 2:
% 134.53/19.49 | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | (8532) ~ (all_6_1 = e3) & op(e2, e2) = all_6_1 &
% 134.53/19.49 | | | | | | | | | | | $i(all_6_1)
% 134.53/19.49 | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | REF_CLOSE: (8371), (8532), (function-axioms) are inconsistent
% 134.53/19.49 | | | | | | | | | | | by sub-proof #74.
% 134.53/19.49 | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | End of split
% 134.53/19.49 | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | End of split
% 134.53/19.49 | | | | | | | | |
% 134.53/19.49 | | | | | | | | Case 2:
% 134.53/19.49 | | | | | | | | |
% 134.53/19.49 | | | | | | | | | (8533) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3
% 134.53/19.49 | | | | | | | | | & op(e0, e2) = e3)
% 134.53/19.49 | | | | | | | | |
% 134.53/19.49 | | | | | | | | | REF_CLOSE: (158), (162), (8362), (8363), (8533),
% 134.53/19.49 | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.49 | | | | | | | | | #555.
% 134.53/19.49 | | | | | | | | |
% 134.53/19.49 | | | | | | | | End of split
% 134.53/19.49 | | | | | | | |
% 134.53/19.49 | | | | | | | End of split
% 134.53/19.49 | | | | | | |
% 134.53/19.49 | | | | | | End of split
% 134.53/19.49 | | | | | |
% 134.53/19.49 | | | | | Case 2:
% 134.53/19.49 | | | | | |
% 134.53/19.49 | | | | | | (8534) all_8_2 = e1
% 134.53/19.49 | | | | | |
% 134.53/19.49 | | | | | | REDUCE: (347), (8534) imply:
% 134.53/19.49 | | | | | | (8535) ~ (all_52_1 = e1)
% 134.53/19.49 | | | | | |
% 134.53/19.49 | | | | | | REDUCE: (350), (8534) imply:
% 134.53/19.49 | | | | | | (8536) ~ (all_52_4 = e1)
% 134.53/19.49 | | | | | |
% 134.53/19.49 | | | | | | REDUCE: (352), (8534) imply:
% 134.53/19.49 | | | | | | (8537) ~ (all_52_6 = e1)
% 134.53/19.49 | | | | | |
% 134.53/19.49 | | | | | | REDUCE: (354), (8534) imply:
% 134.53/19.49 | | | | | | (8538) ~ (all_52_7 = e1)
% 134.53/19.49 | | | | | |
% 134.53/19.49 | | | | | | REDUCE: (356), (8534) imply:
% 134.53/19.49 | | | | | | (8539) ~ (all_52_9 = e1)
% 134.53/19.49 | | | | | |
% 134.53/19.49 | | | | | | REDUCE: (358), (8534) imply:
% 134.53/19.49 | | | | | | (8540) ~ (all_52_13 = e1)
% 134.53/19.49 | | | | | |
% 134.53/19.49 | | | | | | BETA: splitting (224) gives:
% 134.53/19.49 | | | | | |
% 134.53/19.49 | | | | | | Case 1:
% 134.53/19.49 | | | | | | |
% 134.53/19.49 | | | | | | | (8541) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 &
% 134.53/19.49 | | | | | | | op(e2, e2) = e1)
% 134.53/19.49 | | | | | | |
% 134.53/19.49 | | | | | | | BETA: splitting (8541) gives:
% 134.53/19.49 | | | | | | |
% 134.53/19.49 | | | | | | | Case 1:
% 134.53/19.49 | | | | | | | |
% 134.53/19.49 | | | | | | | | (8542) all_57_2 = e1 & op(e2, e3) = e1
% 134.53/19.49 | | | | | | | |
% 134.53/19.49 | | | | | | | | REF_CLOSE: (167), (8535), (8542), (function-axioms) are
% 134.53/19.49 | | | | | | | | inconsistent by sub-proof #676.
% 134.53/19.49 | | | | | | | |
% 134.53/19.49 | | | | | | | Case 2:
% 134.53/19.49 | | | | | | | |
% 134.53/19.49 | | | | | | | | (8543) all_57_3 = e1 & op(e2, e2) = e1
% 134.53/19.49 | | | | | | | |
% 134.53/19.49 | | | | | | | | ALPHA: (8543) implies:
% 134.53/19.49 | | | | | | | | (8544) all_57_3 = e1
% 134.53/19.49 | | | | | | | | (8545) op(e2, e2) = e1
% 134.53/19.49 | | | | | | | |
% 134.53/19.49 | | | | | | | | BETA: splitting (46) gives:
% 134.53/19.49 | | | | | | | |
% 134.53/19.49 | | | | | | | | Case 1:
% 134.53/19.49 | | | | | | | | |
% 134.53/19.49 | | | | | | | | | (8546) ~ (all_10_2 = e0)
% 134.53/19.49 | | | | | | | | |
% 134.53/19.49 | | | | | | | | | BETA: splitting (55) gives:
% 134.53/19.49 | | | | | | | | |
% 134.53/19.49 | | | | | | | | | Case 1:
% 134.53/19.49 | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | (8547) ~ (all_16_2 = e2)
% 134.53/19.49 | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | REDUCE: (327), (8547) imply:
% 134.53/19.49 | | | | | | | | | | (8548) ~ (all_10_2 = e2)
% 134.53/19.49 | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | BETA: splitting (58) gives:
% 134.53/19.49 | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | Case 1:
% 134.53/19.49 | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | (8549) ~ (all_18_2 = e2)
% 134.53/19.49 | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | REDUCE: (6996), (8549) imply:
% 134.53/19.49 | | | | | | | | | | | (8550) $false
% 134.53/19.49 | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | CLOSE: (8550) is inconsistent.
% 134.53/19.49 | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | Case 2:
% 134.53/19.49 | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | (8551) ( ~ (all_18_0 = e3) & op(e2, e1) = all_18_0 &
% 134.53/19.49 | | | | | | | | | | | $i(all_18_0)) | ( ~ (all_18_1 = e0) & op(e2, e2)
% 134.53/19.49 | | | | | | | | | | | = all_18_1 & $i(all_18_1))
% 134.53/19.49 | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | BETA: splitting (61) gives:
% 134.53/19.49 | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | Case 1:
% 134.53/19.49 | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | (8552) ~ (all_20_2 = e2)
% 134.53/19.49 | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | REDUCE: (318), (8552) imply:
% 134.53/19.49 | | | | | | | | | | | | (8553) ~ (all_4_2 = e2)
% 134.53/19.49 | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | BETA: splitting (79) gives:
% 134.53/19.49 | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | Case 1:
% 134.53/19.49 | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | (8554) ~ (all_32_2 = e1)
% 134.53/19.49 | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | REDUCE: (312), (8554) imply:
% 134.53/19.49 | | | | | | | | | | | | | (8555) ~ (all_10_2 = e1)
% 134.53/19.49 | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | BETA: splitting (206) gives:
% 134.53/19.49 | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | Case 1:
% 134.53/19.49 | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | (8556) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 134.53/19.49 | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.49 | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 134.53/19.49 | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 134.53/19.49 | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.49 | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 134.53/19.49 | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.49 | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.53/19.49 | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.49 | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 134.53/19.49 | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 134.53/19.49 | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.49 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 134.53/19.49 | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 134.53/19.49 | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.53/19.49 | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.49 | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 134.53/19.49 | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.49 | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.49 | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.49 | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.49 | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.53/19.49 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.49 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.49 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.49 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 134.53/19.49 | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.49 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 134.53/19.49 | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | BETA: splitting (8556) gives:
% 134.53/19.49 | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | Case 1:
% 134.53/19.49 | | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | | (8557) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 134.53/19.49 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.49 | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 134.53/19.49 | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 134.53/19.49 | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.49 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 134.53/19.49 | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.49 | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.53/19.49 | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.49 | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 134.53/19.49 | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 134.53/19.49 | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.49 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 134.53/19.49 | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 134.53/19.49 | | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | | REF_CLOSE: (45), (204), (278), (8546), (8548), (8555),
% 134.53/19.49 | | | | | | | | | | | | | | | (8557), (function-axioms) are inconsistent by
% 134.53/19.49 | | | | | | | | | | | | | | | sub-proof #66.
% 134.53/19.49 | | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | Case 2:
% 134.53/19.49 | | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | | (8558) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.53/19.49 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.49 | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 134.53/19.49 | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.49 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.49 | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.49 | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.49 | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.53/19.49 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.49 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.49 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.49 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 134.53/19.49 | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.49 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 134.53/19.49 | | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | | BETA: splitting (8558) gives:
% 134.53/19.49 | | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | | Case 1:
% 134.53/19.49 | | | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | | | (8559) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.53/19.49 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 134.53/19.49 | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3,
% 134.53/19.49 | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.49 | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 134.53/19.49 | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.49 | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 134.53/19.49 | | | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | | | ALPHA: (8559) implies:
% 134.53/19.49 | | | | | | | | | | | | | | | | (8560) op(e3, e3) = e0
% 134.53/19.49 | | | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | | | REF_CLOSE: (45), (204), (278), (8546), (8548), (8555),
% 134.53/19.49 | | | | | | | | | | | | | | | | (8560), (function-axioms) are inconsistent by
% 134.53/19.49 | | | | | | | | | | | | | | | | sub-proof #772.
% 134.53/19.49 | | | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | | Case 2:
% 134.53/19.49 | | | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | | | (8561) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.53/19.49 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 134.53/19.49 | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.49 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.49 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2,
% 134.53/19.49 | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.49 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 134.53/19.49 | | | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | | | ALPHA: (8561) implies:
% 134.53/19.49 | | | | | | | | | | | | | | | | (8562) op(e2, e2) = e3
% 134.53/19.49 | | | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8545), (8562), (function-axioms) are
% 134.53/19.49 | | | | | | | | | | | | | | | | inconsistent by sub-proof #325.
% 134.53/19.49 | | | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | | End of split
% 134.53/19.49 | | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | End of split
% 134.53/19.49 | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | Case 2:
% 134.53/19.49 | | | | | | | | | | | | | |
% 134.53/19.49 | | | | | | | | | | | | | | (8563) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.53/19.49 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.49 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.49 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.49 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.53/19.49 | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.49 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.53/19.49 | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.53/19.49 | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.53/19.49 | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.53/19.49 | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.53/19.49 | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.53/19.49 | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.49 | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 134.53/19.49 | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 134.53/19.49 | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.49 | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 134.53/19.49 | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.49 | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 134.53/19.49 | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.49 | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 134.53/19.49 | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 134.53/19.49 | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.53/19.49 | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.49 | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 134.53/19.49 | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 134.53/19.49 | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.49 | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 134.53/19.49 | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 134.53/19.49 | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 134.53/19.49 | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 134.53/19.49 | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.49 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 134.53/19.49 | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 134.53/19.49 | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.49 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 134.53/19.49 | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 134.53/19.49 | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 134.53/19.49 | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.49 | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.49 | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 134.53/19.49 | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.49 | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 134.53/19.49 | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 134.53/19.49 | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 134.53/19.49 | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 134.53/19.49 | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 134.53/19.49 | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 134.53/19.49 | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.49 | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.49 | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.49 | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.49 | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.49 | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.49 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.49 | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.49 | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.49 | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | BETA: splitting (8563) gives:
% 134.53/19.50 | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | Case 1:
% 134.53/19.50 | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | (8564) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.53/19.50 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.50 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.50 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.50 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.53/19.50 | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.50 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.53/19.50 | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.53/19.50 | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.53/19.50 | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.53/19.50 | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.53/19.50 | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.53/19.50 | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.50 | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.53/19.50 | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (7000), (7007), (8564),
% 134.53/19.50 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.50 | | | | | | | | | | | | | | | #108.
% 134.53/19.50 | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | Case 2:
% 134.53/19.50 | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | (8565) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.53/19.50 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.50 | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 134.53/19.50 | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.50 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.50 | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.50 | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.50 | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.50 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.50 | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.53/19.50 | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.50 | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.53/19.50 | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.53/19.50 | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.50 | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.50 | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.53/19.50 | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.53/19.50 | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.50 | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.53/19.50 | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.53/19.50 | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.53/19.50 | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.53/19.50 | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.53/19.50 | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.53/19.50 | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.53/19.50 | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.53/19.50 | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.50 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.53/19.50 | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.53/19.50 | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.53/19.50 | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.50 | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.50 | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.50 | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.50 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.50 | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.53/19.50 | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.50 | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.50 | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.50 | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.50 | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.50 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.50 | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.50 | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.50 | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | BETA: splitting (8565) gives:
% 134.53/19.50 | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | Case 1:
% 134.53/19.50 | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | (8566) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.53/19.50 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 134.53/19.50 | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 134.53/19.50 | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.50 | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 134.53/19.50 | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.50 | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 134.53/19.50 | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | ALPHA: (8566) implies:
% 134.53/19.50 | | | | | | | | | | | | | | | | (8567) op(e2, e2) = e0
% 134.53/19.50 | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8545), (8567), (function-axioms) are
% 134.53/19.50 | | | | | | | | | | | | | | | | inconsistent by sub-proof #675.
% 134.53/19.50 | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | Case 2:
% 134.53/19.50 | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | (8568) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.50 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.50 | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.53/19.50 | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.50 | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.53/19.50 | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.53/19.50 | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.50 | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.50 | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.53/19.50 | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.53/19.50 | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.50 | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.53/19.50 | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.53/19.50 | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.53/19.50 | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.53/19.50 | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.53/19.50 | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.53/19.50 | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.53/19.50 | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.53/19.50 | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.50 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.53/19.50 | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.53/19.50 | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.53/19.50 | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.50 | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.50 | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.50 | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.50 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.50 | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.53/19.50 | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.50 | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.50 | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.50 | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.50 | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.50 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.50 | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.50 | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.50 | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | BETA: splitting (8568) gives:
% 134.53/19.50 | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.50 | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | (8569) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.50 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 134.53/19.50 | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 134.53/19.50 | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.50 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 134.53/19.50 | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | ALPHA: (8569) implies:
% 134.53/19.50 | | | | | | | | | | | | | | | | | (8570) op(e1, e2) = e1
% 134.53/19.50 | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (8537), (8570), (function-axioms) are
% 134.53/19.50 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #65.
% 134.53/19.50 | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.50 | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | (8571) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.50 | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.53/19.50 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 134.53/19.50 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.50 | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 134.53/19.50 | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 134.53/19.50 | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.50 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 134.53/19.50 | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 134.53/19.50 | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.53/19.50 | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.50 | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 134.53/19.50 | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.50 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 134.53/19.50 | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.50 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.50 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.50 | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.50 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 134.53/19.50 | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 134.53/19.50 | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 134.53/19.50 | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 134.53/19.50 | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 134.53/19.50 | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 134.53/19.50 | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 134.53/19.50 | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 134.53/19.50 | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 134.53/19.50 | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | ALPHA: (8571) implies:
% 134.53/19.50 | | | | | | | | | | | | | | | | | (8572) op(e0, e0) = all_56_31
% 134.53/19.50 | | | | | | | | | | | | | | | | | (8573) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.53/19.50 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.50 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 134.53/19.50 | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 134.53/19.50 | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 134.53/19.50 | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 134.53/19.50 | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 134.53/19.50 | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 134.53/19.50 | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 134.53/19.50 | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.50 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.50 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 134.53/19.50 | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.50 | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 134.53/19.50 | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 134.53/19.50 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.50 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 134.53/19.50 | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 134.53/19.50 | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 134.53/19.50 | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.50 | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.53/19.50 | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 134.53/19.50 | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.50 | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | (8574) all_54_0 = e3
% 134.53/19.50 | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (8574) imply:
% 134.53/19.50 | | | | | | | | | | | | | | | | | | (8575) all_10_2 = e3
% 134.53/19.50 | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | SIMP: (8575) implies:
% 134.53/19.50 | | | | | | | | | | | | | | | | | | (8576) all_10_2 = e3
% 134.53/19.50 | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | REDUCE: (45), (8576) imply:
% 134.53/19.50 | | | | | | | | | | | | | | | | | | (8577) op(e3, e3) = e3
% 134.53/19.50 | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 134.53/19.50 | | | | | | | | | | | | | | | | | | all_56_31, e0, e0, simplifying with (36), (8572)
% 134.53/19.50 | | | | | | | | | | | | | | | | | | gives:
% 134.53/19.50 | | | | | | | | | | | | | | | | | | (8578) all_56_31 = all_4_2
% 134.53/19.50 | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | BETA: splitting (8573) gives:
% 134.53/19.50 | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.50 | | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | (8579) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27))
% 134.53/19.50 | | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8553), (8577), (8578), (8579), (function-axioms)
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #764.
% 134.53/19.50 | | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.50 | | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | (8580) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.53/19.50 | | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (371), (7007), (8578), (8580),
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | #86.
% 134.53/19.50 | | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.50 | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.50 | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | (8581) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 134.53/19.50 | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (8546), (8548), (8555), (8581) are
% 134.53/19.50 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #777.
% 134.53/19.50 | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | End of split
% 134.53/19.50 | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | End of split
% 134.53/19.50 | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | End of split
% 134.53/19.50 | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | End of split
% 134.53/19.50 | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | End of split
% 134.53/19.50 | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | Case 2:
% 134.53/19.50 | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | (8582) all_32_2 = e1
% 134.53/19.50 | | | | | | | | | | | | | (8583) ( ~ (all_32_0 = e0) & op(e1, e3) = all_32_0 &
% 134.53/19.50 | | | | | | | | | | | | | $i(all_32_0)) | ( ~ (all_32_1 = e2) & op(e1, e1)
% 134.53/19.50 | | | | | | | | | | | | | = all_32_1 & $i(all_32_1))
% 134.53/19.50 | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | COMBINE_EQS: (312), (8582) imply:
% 134.53/19.50 | | | | | | | | | | | | | (8584) all_10_2 = e1
% 134.53/19.50 | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | SIMP: (8584) implies:
% 134.53/19.50 | | | | | | | | | | | | | (8585) all_10_2 = e1
% 134.53/19.50 | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | REDUCE: (338), (8585) imply:
% 134.53/19.50 | | | | | | | | | | | | | (8586) ~ (all_52_2 = e1)
% 134.53/19.50 | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | REDUCE: (346), (8585) imply:
% 134.53/19.50 | | | | | | | | | | | | | (8587) ~ (all_52_12 = e1)
% 134.53/19.50 | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | REDUCE: (8548), (8585) imply:
% 134.53/19.50 | | | | | | | | | | | | | (8588) ~ (e2 = e1)
% 134.53/19.50 | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | REDUCE: (45), (8585) imply:
% 134.53/19.50 | | | | | | | | | | | | | (8589) op(e3, e3) = e1
% 134.53/19.50 | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | BETA: splitting (8583) gives:
% 134.53/19.50 | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | Case 1:
% 134.53/19.50 | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | (8590) ~ (all_32_0 = e0) & op(e1, e3) = all_32_0 &
% 134.53/19.50 | | | | | | | | | | | | | | $i(all_32_0)
% 134.53/19.50 | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | ALPHA: (8590) implies:
% 134.53/19.50 | | | | | | | | | | | | | | (8591) ~ (all_32_0 = e0)
% 134.53/19.50 | | | | | | | | | | | | | | (8592) op(e1, e3) = all_32_0
% 134.53/19.50 | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 134.53/19.50 | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | Case 1:
% 134.53/19.50 | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | (8593) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 134.53/19.50 | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 134.53/19.50 | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (231), (235),
% 134.53/19.50 | | | | | | | | | | | | | | | (237), (8538), (8589), (8593), (function-axioms)
% 134.53/19.50 | | | | | | | | | | | | | | | are inconsistent by sub-proof #177.
% 134.53/19.50 | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | Case 2:
% 134.53/19.50 | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | (8594) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 134.53/19.50 | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 134.53/19.50 | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | BETA: splitting (8594) gives:
% 134.53/19.50 | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | Case 1:
% 134.53/19.50 | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | (8595) all_57_14 = e1 & op(e0, e1) = e1
% 134.53/19.50 | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | ALPHA: (8595) implies:
% 134.53/19.50 | | | | | | | | | | | | | | | | (8596) op(e0, e1) = e1
% 134.53/19.50 | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 134.53/19.50 | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.50 | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | (8597) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 134.53/19.50 | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 134.53/19.50 | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (8540), (8587), (8597),
% 134.53/19.50 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.50 | | | | | | | | | | | | | | | | | #179.
% 134.53/19.50 | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.50 | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | (8598) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 134.53/19.50 | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 134.53/19.50 | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | BETA: splitting (8598) gives:
% 134.53/19.50 | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.50 | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | (8599) all_57_11 = e1 & op(e1, e0) = e1
% 134.53/19.50 | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | ALPHA: (8599) implies:
% 134.53/19.50 | | | | | | | | | | | | | | | | | | (8600) op(e1, e0) = e1
% 134.53/19.50 | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 134.53/19.50 | | | | | | | | | | | | | | | | | | e1, e1, e0, simplifying with (157), (8596) gives:
% 134.53/19.50 | | | | | | | | | | | | | | | | | | (8601) all_52_11 = e1
% 134.53/19.50 | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 134.53/19.50 | | | | | | | | | | | | | | | | | | e1, e0, e1, simplifying with (160), (8600) gives:
% 134.53/19.50 | | | | | | | | | | | | | | | | | | (8602) all_52_14 = e1
% 134.53/19.50 | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2,
% 134.53/19.50 | | | | | | | | | | | | | | | | | | all_32_0, e3, e1, simplifying with (163), (8592)
% 134.53/19.50 | | | | | | | | | | | | | | | | | | gives:
% 134.53/19.50 | | | | | | | | | | | | | | | | | | (8603) all_52_2 = all_32_0
% 134.53/19.50 | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (8603) imply:
% 134.53/19.50 | | | | | | | | | | | | | | | | | | (8604) all_54_8 = all_32_0
% 134.53/19.50 | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | REDUCE: (144), (8603) imply:
% 134.53/19.50 | | | | | | | | | | | | | | | | | | (8605) ~ (all_52_3 = all_32_0)
% 134.53/19.50 | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | SIMP: (8605) implies:
% 134.53/19.50 | | | | | | | | | | | | | | | | | | (8606) ~ (all_52_3 = all_32_0)
% 134.53/19.50 | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | REDUCE: (143), (8603) imply:
% 134.53/19.50 | | | | | | | | | | | | | | | | | | (8607) ~ (all_52_6 = all_32_0)
% 134.53/19.50 | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | SIMP: (8607) implies:
% 134.53/19.50 | | | | | | | | | | | | | | | | | | (8608) ~ (all_52_6 = all_32_0)
% 134.53/19.50 | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | REDUCE: (6997), (8603) imply:
% 134.53/19.50 | | | | | | | | | | | | | | | | | | (8609) ~ (all_32_0 = e2)
% 134.53/19.50 | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | REDUCE: (8586), (8603) imply:
% 134.53/19.50 | | | | | | | | | | | | | | | | | | (8610) ~ (all_32_0 = e1)
% 134.53/19.50 | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | REDUCE: (139), (8601) imply:
% 134.53/19.50 | | | | | | | | | | | | | | | | | | (8611) ~ (all_52_3 = e1)
% 134.53/19.50 | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | REDUCE: (370), (8602) imply:
% 134.53/19.50 | | | | | | | | | | | | | | | | | | (8612) ~ (all_4_2 = e1)
% 134.53/19.50 | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 134.53/19.50 | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.50 | | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | (8613) all_54_8 = e3
% 134.53/19.50 | | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8604), (8613) imply:
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | (8614) all_32_0 = e3
% 134.53/19.50 | | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | REDUCE: (8606), (8614) imply:
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | (8615) ~ (all_52_3 = e3)
% 134.53/19.50 | | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | REDUCE: (8608), (8614) imply:
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | (8616) ~ (all_52_6 = e3)
% 134.53/19.50 | | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | REDUCE: (8592), (8614) imply:
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | (8617) op(e1, e3) = e3
% 134.53/19.50 | | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 134.53/19.50 | | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | (8618) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (8545), (8589), (8617), (8618),
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | #174.
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | (8619) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | BETA: splitting (8619) gives:
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | (8620) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (7000), (7007), (8620),
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | #108.
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.50 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | (8621) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8621) gives:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | (8622) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8622) implies:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | (8623) op(e2, e2) = e0
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8545), (8623), (function-axioms) are
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675.
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | (8624) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8624) gives:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | (8625) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8625) implies:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | (8626) op(e1, e2) = e1
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (8537), (8626), (function-axioms) are
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #65.
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | (8627) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8627) implies:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | (8628) op(e0, e0) = all_56_31
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | (8629) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | (8630) all_54_9 = e3
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (8616), (8630) are inconsistent by
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #64.
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | (8631) ~ (all_54_9 = e3)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | (8632) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8632) gives:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | (8633) all_54_9 = e2
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (6998), (8633) are inconsistent by
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #582.
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | (8634) ~ (all_54_9 = e2)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | (8635) all_54_9 = e1 | all_54_9 = e0
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8635) gives:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | (8636) all_54_9 = e1
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (8537), (8636) are inconsistent by
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #169.
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | (8637) all_54_9 = e0
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (8637) imply:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | (8638) all_52_6 = e0
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8638) implies:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | (8639) all_52_6 = e0
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (8639) imply:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | (8640) ~ (all_52_7 = e0)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8640) implies:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | (8641) ~ (all_52_7 = e0)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6998), (8639) imply:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | (8642) ~ (e2 = e0)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8629) gives:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8643) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27))
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8643) gives:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8644) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8644) implies:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8645) all_56_31 = e3
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8646) ~ (all_56_25 = e0)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8647) ~ (all_56_9 = e2)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8648) op(e0, e3) = e0
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8649) op(e3, e0) = all_56_25
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8650) op(e3, e2) = all_56_9
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8651) op(e3, e3) = all_56_1
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8628), (8645) imply:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8652) op(e0, e0) = e3
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e3,
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e0, simplifying with (36), (8652) gives:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8653) all_4_2 = e3
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e0,
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (159), (8648) gives:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8654) all_52_3 = e0
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_25, e0, e3, simplifying with (168), (8649)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8655) all_56_25 = all_52_12
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4,
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_9, e2, e3, simplifying with (170), (8650)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8656) all_56_9 = all_52_4
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_56_1,
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (8589), (8651) gives:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8657) all_56_1 = e1
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (8653) imply:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8658) all_34_2 = e3
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8647), (8656) imply:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8659) ~ (all_52_4 = e2)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (8653) imply:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8660) ~ (all_52_7 = e3)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8661) ~ (all_34_2 = e3)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8658), (8661) imply:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8662) $false
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8662) is inconsistent.
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8663) ( ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_34_0)) | ( ~ (all_34_1 = e1) & op(e3, e3)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_34_1 & $i(all_34_1))
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8664) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (159), (168), (170), (232), (236),
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8545), (8589), (8611), (8615), (8646), (8648),
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8649), (8650), (8651), (8659), (8663), (8664),
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #173.
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8665) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (8616), (8660), (8665),
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #555.
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8666) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27)
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8666) implies:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8667) op(e0, e2) = e0
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (8641), (8667), (function-axioms) are
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #545.
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8668) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8668) gives:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8669) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8669) implies:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8670) op(e1, e1) = e0
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7007), (8670), (function-axioms) are
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #98.
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8671) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8671) implies:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8672) ~ (all_56_5 = e3)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8673) op(e1, e3) = all_56_5
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8617), (8672), (8673), (function-axioms) are
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #724.
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.54 | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | (8674) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 134.53/19.54 | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8591), (8604), (8609), (8610), (8674) are
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #96.
% 134.53/19.54 | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.54 | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.54 | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | (8675) all_57_15 = e1 & op(e0, e0) = e1
% 134.53/19.54 | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | ALPHA: (8675) implies:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | (8676) op(e0, e0) = e1
% 134.53/19.54 | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (371), (8676), (function-axioms) are
% 134.53/19.54 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #354.
% 134.53/19.54 | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | End of split
% 134.53/19.54 | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | End of split
% 134.53/19.54 | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | Case 2:
% 134.53/19.54 | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | (8677) all_57_15 = e1 & op(e0, e0) = e1
% 134.53/19.54 | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | ALPHA: (8677) implies:
% 134.53/19.54 | | | | | | | | | | | | | | | | (8678) op(e0, e0) = e1
% 134.53/19.54 | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | REF_CLOSE: (36), (371), (8678), (function-axioms) are
% 134.53/19.54 | | | | | | | | | | | | | | | | inconsistent by sub-proof #354.
% 134.53/19.54 | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | End of split
% 134.53/19.54 | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | End of split
% 134.53/19.54 | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | Case 2:
% 134.53/19.54 | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | (8679) ~ (all_32_1 = e2) & op(e1, e1) = all_32_1 &
% 134.53/19.54 | | | | | | | | | | | | | | $i(all_32_1)
% 134.53/19.54 | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | REF_CLOSE: (7007), (8679), (function-axioms) are inconsistent
% 134.53/19.54 | | | | | | | | | | | | | | by sub-proof #95.
% 134.53/19.54 | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | End of split
% 134.53/19.54 | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | End of split
% 134.53/19.54 | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | Case 2:
% 134.53/19.54 | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | (8680) all_20_2 = e2
% 134.53/19.54 | | | | | | | | | | | | (8681) ( ~ (all_20_0 = e3) & op(e2, e0) = all_20_0 &
% 134.53/19.54 | | | | | | | | | | | | $i(all_20_0)) | ( ~ (all_20_1 = e1) & op(e2, e2)
% 134.53/19.54 | | | | | | | | | | | | = all_20_1 & $i(all_20_1))
% 134.53/19.54 | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | COMBINE_EQS: (318), (8680) imply:
% 134.53/19.54 | | | | | | | | | | | | (8682) all_4_2 = e2
% 134.53/19.54 | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | REDUCE: (368), (8682) imply:
% 134.53/19.54 | | | | | | | | | | | | (8683) ~ (all_52_12 = e2)
% 134.53/19.54 | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | REDUCE: (369), (8682) imply:
% 134.53/19.54 | | | | | | | | | | | | (8684) ~ (all_52_13 = e2)
% 134.53/19.54 | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | BETA: splitting (8681) gives:
% 134.53/19.54 | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | Case 1:
% 134.53/19.54 | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | (8685) ~ (all_20_0 = e3) & op(e2, e0) = all_20_0 &
% 134.53/19.54 | | | | | | | | | | | | | $i(all_20_0)
% 134.53/19.54 | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | ALPHA: (8685) implies:
% 134.53/19.54 | | | | | | | | | | | | | (8686) ~ (all_20_0 = e3)
% 134.53/19.54 | | | | | | | | | | | | | (8687) op(e2, e0) = all_20_0
% 134.53/19.54 | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | BETA: splitting (236) gives:
% 134.53/19.54 | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | Case 1:
% 134.53/19.54 | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | (8688) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 134.53/19.54 | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 134.53/19.54 | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | BETA: splitting (8688) gives:
% 134.53/19.54 | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | Case 1:
% 134.53/19.54 | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | (8689) all_57_0 = e2 & op(e3, e3) = e2
% 134.53/19.54 | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | ALPHA: (8689) implies:
% 134.53/19.54 | | | | | | | | | | | | | | | (8690) op(e3, e3) = e2
% 134.53/19.54 | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | REF_CLOSE: (45), (8548), (8690), (function-axioms) are
% 134.53/19.54 | | | | | | | | | | | | | | | inconsistent by sub-proof #536.
% 134.53/19.54 | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | Case 2:
% 134.53/19.54 | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | (8691) all_57_1 = e2 & op(e3, e2) = e2
% 134.53/19.54 | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | ALPHA: (8691) implies:
% 134.53/19.54 | | | | | | | | | | | | | | | (8692) op(e3, e2) = e2
% 134.53/19.54 | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 134.53/19.54 | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | Case 1:
% 134.53/19.54 | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | (8693) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 134.53/19.54 | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 134.53/19.54 | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | BETA: splitting (8693) gives:
% 134.53/19.54 | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.54 | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | (8694) all_57_2 = e2 & op(e2, e3) = e2
% 134.53/19.54 | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 134.53/19.54 | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.54 | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | (8695) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 134.53/19.54 | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (8683), (8684), (8695),
% 134.53/19.54 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.54 | | | | | | | | | | | | | | | | | | #440.
% 134.53/19.54 | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.54 | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | (8696) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 134.53/19.54 | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | BETA: splitting (8696) gives:
% 134.53/19.54 | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | (8697) all_57_11 = e2 & op(e1, e0) = e2
% 134.53/19.54 | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (7002), (8697), (function-axioms) are
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #514.
% 134.53/19.54 | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | (8698) all_57_15 = e2 & op(e0, e0) = e2
% 134.53/19.54 | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | ALPHA: (8698) implies:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | (8699) op(e0, e0) = e2
% 134.53/19.54 | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | ALPHA: (8694) implies:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | (8700) all_57_2 = e2
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | (8701) op(e2, e3) = e2
% 134.53/19.54 | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | all_20_0, e0, e2, simplifying with (164), (8687)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | gives:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | (8702) all_52_13 = all_20_0
% 134.53/19.54 | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | e3, e2, simplifying with (167), (8701) gives:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | (8703) all_52_1 = e2
% 134.53/19.54 | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e2,
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (170), (8692) gives:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | (8704) all_52_4 = e2
% 134.53/19.54 | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (8702) imply:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | (8705) all_54_7 = all_20_0
% 134.53/19.54 | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | REDUCE: (146), (8703) imply:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | (8706) ~ (all_52_9 = e2)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | REDUCE: (134), (8704) imply:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | (8707) ~ (all_52_8 = e2)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | REDUCE: (342), (8704) imply:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | (8708) ~ (all_10_2 = e2)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | REDUCE: (117), (8702) imply:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | (8709) ~ (all_52_9 = all_20_0)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | REDUCE: (8684), (8702) imply:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | (8710) ~ (all_20_0 = e2)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | REDUCE: (8540), (8702) imply:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | (8711) ~ (all_20_0 = e1)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | (8712) all_54_7 = e3
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8686), (8705), (8712) are inconsistent by
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | sub-proof #119.
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | (8713) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | BETA: splitting (8713) gives:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | (8714) all_54_7 = e2
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8705), (8710), (8714) are inconsistent by
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | sub-proof #63.
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | (8715) ~ (all_54_7 = e2)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | (8716) all_54_7 = e1 | all_54_7 = e0
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8716) gives:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | (8717) all_54_7 = e1
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8705), (8711), (8717) are inconsistent by
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | sub-proof #62.
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | (8718) all_54_7 = e0
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8705), (8718) imply:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | (8719) all_20_0 = e0
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | SIMP: (8719) implies:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | (8720) all_20_0 = e0
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8709), (8720) imply:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | (8721) ~ (all_52_9 = e0)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8710), (8720) imply:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | (8722) ~ (e2 = e0)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8711), (8720) imply:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | (8723) ~ (e1 = e0)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8687), (8720) imply:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | (8724) op(e2, e0) = e0
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | (8725) all_54_6 = e3
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (8725) imply:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | (8726) all_52_9 = e3
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8726) implies:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | (8727) all_52_9 = e3
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (8727) imply:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | (8728) ~ (all_52_8 = e3)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (8727) imply:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | (8729) op(e2, e1) = e3
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | (8730) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8730) gives:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | (8731) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (169), (8548), (8728), (8731),
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | #469.
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | (8732) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8732) gives:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (8733) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3,
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8733) implies:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (8734) op(e3, e3) = e0
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (8546), (8734), (function-axioms) are
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #534.
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (8735) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2,
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8735) implies:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (8736) op(e2, e2) = e3
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8545), (8736), (function-axioms) are
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #325.
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | (8737) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8737) gives:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | (8738) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8738) gives:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (8739) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8739) implies:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (8740) op(e1, e1) = e3
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7007), (8740), (function-axioms) are
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #109.
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (8741) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2,
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8729), (8741), (function-axioms) are
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #114.
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | (8742) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8742) gives:
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (8743) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8743) implies:
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (8744) op(e2, e2) = e0
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (79), (117),
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (123), (164), (165), (169), (198), (206), (224),
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (226), (231), (237), (260), (312), (6999), (7000),
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (7007), (8546), (8548), (8551), (8681), (8692),
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (8699), (8700), (8701), (8721), (8744),
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | #90.
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (8745) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (39), (91), (157), (190), (246), (332),
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (364), (7001), (8699), (8724), (8745),
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | #67.
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | (8746) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (7000), (8539), (8721), (8746) are
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #478.
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.55 | | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.55 | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | End of split
% 134.53/19.55 | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.55 | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | (8747) all_57_3 = e2 & op(e2, e2) = e2
% 134.53/19.55 | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | ALPHA: (8747) implies:
% 134.53/19.55 | | | | | | | | | | | | | | | | | (8748) all_57_3 = e2
% 134.53/19.55 | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8544), (8748) are inconsistent by sub-proof
% 134.53/19.55 | | | | | | | | | | | | | | | | | #728.
% 134.53/19.55 | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | End of split
% 134.53/19.55 | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | Case 2:
% 134.53/19.55 | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | (8749) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 134.53/19.55 | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 134.53/19.55 | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | REF_CLOSE: (164), (165), (7000), (8684), (8749),
% 134.53/19.55 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.55 | | | | | | | | | | | | | | | | #625.
% 134.53/19.55 | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | End of split
% 134.53/19.55 | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | End of split
% 134.53/19.55 | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | Case 2:
% 134.53/19.55 | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | (8750) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 134.53/19.55 | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 134.53/19.55 | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | BETA: splitting (8750) gives:
% 134.53/19.55 | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | Case 1:
% 134.53/19.55 | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | (8751) all_57_4 = e2 & op(e3, e1) = e2
% 134.53/19.55 | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | REF_CLOSE: (169), (6999), (8751), (function-axioms) are
% 134.53/19.55 | | | | | | | | | | | | | | | inconsistent by sub-proof #442.
% 134.53/19.55 | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | Case 2:
% 134.53/19.55 | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | (8752) all_57_9 = e2 & op(e3, e0) = e2
% 134.53/19.55 | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | REF_CLOSE: (168), (8683), (8752), (function-axioms) are
% 134.53/19.55 | | | | | | | | | | | | | | | inconsistent by sub-proof #460.
% 134.53/19.55 | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | End of split
% 134.53/19.55 | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | End of split
% 134.53/19.55 | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | Case 2:
% 134.53/19.55 | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | (8753) ~ (all_20_1 = e1) & op(e2, e2) = all_20_1 &
% 134.53/19.55 | | | | | | | | | | | | | $i(all_20_1)
% 134.53/19.55 | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | REF_CLOSE: (8545), (8753), (function-axioms) are inconsistent
% 134.53/19.55 | | | | | | | | | | | | | by sub-proof #113.
% 134.53/19.55 | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | End of split
% 134.53/19.55 | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | End of split
% 134.53/19.55 | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | End of split
% 134.53/19.55 | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | Case 2:
% 134.53/19.55 | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | (8754) all_16_2 = e2
% 134.53/19.55 | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | COMBINE_EQS: (327), (8754) imply:
% 134.53/19.55 | | | | | | | | | | (8755) all_10_2 = e2
% 134.53/19.55 | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | SIMP: (8755) implies:
% 134.53/19.55 | | | | | | | | | | (8756) all_10_2 = e2
% 134.53/19.55 | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | COMBINE_EQS: (299), (8756) imply:
% 134.53/19.55 | | | | | | | | | | (8757) all_38_2 = e2
% 134.53/19.55 | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | REDUCE: (336), (8756) imply:
% 134.53/19.55 | | | | | | | | | | (8758) ~ (all_52_1 = e2)
% 134.53/19.55 | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | REDUCE: (342), (8756) imply:
% 134.53/19.55 | | | | | | | | | | (8759) ~ (all_52_4 = e2)
% 134.53/19.55 | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | REDUCE: (45), (8756) imply:
% 134.53/19.55 | | | | | | | | | | (8760) op(e3, e3) = e2
% 134.53/19.55 | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | BETA: splitting (225) gives:
% 134.53/19.55 | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | Case 1:
% 134.53/19.55 | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | (8761) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 134.53/19.55 | | | | | | | | | | | & op(e2, e2) = e2)
% 134.53/19.55 | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | REF_CLOSE: (6), (167), (8544), (8758), (8761),
% 134.53/19.55 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.55 | | | | | | | | | | | #127.
% 134.53/19.55 | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | Case 2:
% 134.53/19.55 | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | (8762) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 134.53/19.55 | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 134.53/19.55 | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | BETA: splitting (8762) gives:
% 134.53/19.55 | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | Case 1:
% 134.53/19.55 | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | (8763) all_57_5 = e2 & op(e2, e1) = e2
% 134.53/19.55 | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | ALPHA: (8763) implies:
% 134.53/19.55 | | | | | | | | | | | | (8764) op(e2, e1) = e2
% 134.53/19.55 | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | REF_CLOSE: (165), (7000), (8764), (function-axioms) are
% 134.53/19.55 | | | | | | | | | | | | inconsistent by sub-proof #770.
% 134.53/19.55 | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | Case 2:
% 134.53/19.55 | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | (8765) all_57_10 = e2 & op(e2, e0) = e2
% 134.53/19.55 | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | ALPHA: (8765) implies:
% 134.53/19.55 | | | | | | | | | | | | (8766) op(e2, e0) = e2
% 134.53/19.55 | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | BETA: splitting (229) gives:
% 134.53/19.55 | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | Case 1:
% 134.53/19.55 | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | (8767) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 134.53/19.55 | | | | | | | | | | | | | & op(e2, e2) = e2)
% 134.53/19.55 | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | BETA: splitting (8767) gives:
% 134.53/19.55 | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | Case 1:
% 134.53/19.55 | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | (8768) all_57_1 = e2 & op(e3, e2) = e2
% 134.53/19.55 | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | REF_CLOSE: (170), (8759), (8768), (function-axioms) are
% 134.53/19.55 | | | | | | | | | | | | | | inconsistent by sub-proof #396.
% 134.53/19.55 | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | Case 2:
% 134.53/19.55 | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | (8769) all_57_3 = e2 & op(e2, e2) = e2
% 134.53/19.55 | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | ALPHA: (8769) implies:
% 134.53/19.55 | | | | | | | | | | | | | | (8770) all_57_3 = e2
% 134.53/19.55 | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | REF_CLOSE: (6), (8544), (8770) are inconsistent by sub-proof
% 134.53/19.55 | | | | | | | | | | | | | | #728.
% 134.53/19.55 | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | End of split
% 134.53/19.55 | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | Case 2:
% 134.53/19.55 | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | (8771) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 134.53/19.55 | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 134.53/19.55 | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | BETA: splitting (8771) gives:
% 134.53/19.55 | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | Case 1:
% 134.53/19.55 | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | (8772) all_57_7 = e2 & op(e1, e2) = e2
% 134.53/19.55 | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | REF_CLOSE: (162), (6998), (8772), (function-axioms) are
% 134.53/19.55 | | | | | | | | | | | | | | inconsistent by sub-proof #515.
% 134.53/19.55 | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | Case 2:
% 134.53/19.55 | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | (8773) all_57_13 = e2 & op(e0, e2) = e2
% 134.53/19.55 | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | ALPHA: (8773) implies:
% 134.53/19.55 | | | | | | | | | | | | | | (8774) op(e0, e2) = e2
% 134.53/19.55 | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 134.53/19.55 | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | Case 1:
% 134.53/19.55 | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | (8775) ~ (all_38_2 = e2)
% 134.53/19.55 | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | REDUCE: (8757), (8775) imply:
% 134.53/19.55 | | | | | | | | | | | | | | | (8776) $false
% 134.53/19.55 | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | CLOSE: (8776) is inconsistent.
% 134.53/19.55 | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | Case 2:
% 134.53/19.55 | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | (8777) ( ~ (all_38_0 = e0) & op(e2, e3) = all_38_0 &
% 134.53/19.55 | | | | | | | | | | | | | | | $i(all_38_0)) | ( ~ (all_38_1 = e1) & op(e2, e2)
% 134.53/19.55 | | | | | | | | | | | | | | | = all_38_1 & $i(all_38_1))
% 134.53/19.55 | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | BETA: splitting (8777) gives:
% 134.53/19.55 | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | Case 1:
% 134.53/19.55 | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | (8778) ~ (all_38_0 = e0) & op(e2, e3) = all_38_0 &
% 134.53/19.55 | | | | | | | | | | | | | | | | $i(all_38_0)
% 134.53/19.55 | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | ALPHA: (8778) implies:
% 134.53/19.55 | | | | | | | | | | | | | | | | (8779) ~ (all_38_0 = e0)
% 134.53/19.55 | | | | | | | | | | | | | | | | (8780) op(e2, e3) = all_38_0
% 134.53/19.55 | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e2,
% 134.53/19.55 | | | | | | | | | | | | | | | | e2, e0, simplifying with (158), (8774) gives:
% 134.53/19.55 | | | | | | | | | | | | | | | | (8781) all_52_7 = e2
% 134.53/19.55 | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 134.53/19.55 | | | | | | | | | | | | | | | | e2, e0, e2, simplifying with (164), (8766) gives:
% 134.53/19.55 | | | | | | | | | | | | | | | | (8782) all_52_13 = e2
% 134.53/19.55 | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 134.53/19.55 | | | | | | | | | | | | | | | | all_38_0, e3, e2, simplifying with (167), (8780)
% 134.53/19.55 | | | | | | | | | | | | | | | | gives:
% 134.53/19.55 | | | | | | | | | | | | | | | | (8783) all_52_1 = all_38_0
% 134.53/19.55 | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (8783) imply:
% 134.53/19.55 | | | | | | | | | | | | | | | | (8784) all_54_4 = all_38_0
% 134.53/19.55 | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | REDUCE: (146), (8783) imply:
% 134.53/19.55 | | | | | | | | | | | | | | | | (8785) ~ (all_52_9 = all_38_0)
% 134.53/19.55 | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | SIMP: (8785) implies:
% 134.53/19.55 | | | | | | | | | | | | | | | | (8786) ~ (all_52_9 = all_38_0)
% 134.53/19.55 | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | REDUCE: (8758), (8783) imply:
% 134.53/19.55 | | | | | | | | | | | | | | | | (8787) ~ (all_38_0 = e2)
% 134.53/19.55 | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | REDUCE: (8535), (8783) imply:
% 134.53/19.55 | | | | | | | | | | | | | | | | (8788) ~ (all_38_0 = e1)
% 134.53/19.55 | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | REDUCE: (369), (8782) imply:
% 134.53/19.55 | | | | | | | | | | | | | | | | (8789) ~ (all_4_2 = e2)
% 134.53/19.55 | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | SIMP: (8789) implies:
% 134.53/19.55 | | | | | | | | | | | | | | | | (8790) ~ (all_4_2 = e2)
% 134.53/19.55 | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 134.53/19.55 | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.55 | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | (8791) all_54_4 = e3
% 134.53/19.55 | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | COMBINE_EQS: (8784), (8791) imply:
% 134.53/19.55 | | | | | | | | | | | | | | | | | (8792) all_38_0 = e3
% 134.53/19.55 | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | SIMP: (8792) implies:
% 134.53/19.55 | | | | | | | | | | | | | | | | | (8793) all_38_0 = e3
% 134.53/19.55 | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | REDUCE: (8786), (8793) imply:
% 134.53/19.55 | | | | | | | | | | | | | | | | | (8794) ~ (all_52_9 = e3)
% 134.53/19.55 | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | REDUCE: (8780), (8793) imply:
% 134.53/19.55 | | | | | | | | | | | | | | | | | (8795) op(e2, e3) = e3
% 134.53/19.55 | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 134.53/19.55 | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.55 | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | (8796) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 134.53/19.55 | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 134.53/19.55 | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.55 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.55 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 134.53/19.55 | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | BETA: splitting (8796) gives:
% 134.53/19.55 | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.55 | | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | (8797) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 134.53/19.55 | | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8760), (8795), (8797), (function-axioms) are
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #335.
% 134.53/19.55 | | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.55 | | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | (8798) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 134.53/19.55 | | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8545), (8774), (8798), (function-axioms) are
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #157.
% 134.53/19.55 | | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.55 | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.55 | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | (8799) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.55 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.53/19.55 | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.53/19.55 | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.53/19.55 | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.53/19.55 | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.53/19.55 | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 134.53/19.55 | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 134.53/19.55 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.55 | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 134.53/19.55 | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 134.53/19.55 | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 134.53/19.55 | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 134.53/19.55 | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.53/19.55 | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 134.53/19.55 | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 134.53/19.55 | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 134.53/19.55 | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 134.53/19.55 | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 134.53/19.55 | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 134.53/19.55 | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 134.53/19.55 | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.55 | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.55 | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.55 | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.55 | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.55 | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | BETA: splitting (8799) gives:
% 134.53/19.55 | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.55 | | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | (8800) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.53/19.55 | | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (7000), (7007), (8800),
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | #108.
% 134.53/19.55 | | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.55 | | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | (8801) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.55 | | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | BETA: splitting (8801) gives:
% 134.53/19.55 | | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | (8802) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | ALPHA: (8802) implies:
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | (8803) op(e2, e2) = e0
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8545), (8803), (function-axioms) are
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675.
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.55 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | (8804) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | BETA: splitting (8804) gives:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | (8805) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | ALPHA: (8805) implies:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | (8806) ~ (all_56_3 = e3)
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | (8807) op(e2, e3) = all_56_3
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8795), (8806), (8807), (function-axioms) are
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #347.
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | (8808) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | ALPHA: (8808) implies:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | (8809) op(e0, e0) = all_56_31
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | (8810) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8810) gives:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | (8811) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27))
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8811) gives:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8812) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8812) implies:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8813) all_56_31 = e3
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8814) op(e3, e2) = all_56_9
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8815) op(e3, e3) = all_56_1
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8809), (8813) imply:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8816) op(e0, e0) = e3
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e3,
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | e0, e0, simplifying with (36), (8816) gives:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8817) all_4_2 = e3
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4,
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | all_56_9, e2, e3, simplifying with (170), (8814)
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | gives:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8818) all_56_9 = all_52_4
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_56_1,
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (8760), (8815) gives:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8819) all_56_1 = e2
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (8817) imply:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8820) all_44_2 = e3
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (367), (8817) imply:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8821) ~ (all_52_11 = e3)
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | (8822) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8822) gives:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | (8823) all_57_4 = e3 & op(e3, e1) = e3
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8823) implies:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | (8824) all_57_4 = e3
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (8825) ~ (all_44_2 = e3)
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8820), (8825) imply:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (8826) $false
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8826) is inconsistent.
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (8827) ( ~ (all_44_0 = e1) & op(e3, e0) = all_44_0 &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_44_0)) | ( ~ (all_44_1 = e2) & op(e3, e3)
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_44_1 & $i(all_44_1))
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (170), (234), (8536), (8760), (8824),
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (8827), (function-axioms) are inconsistent by
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #134.
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | (8828) all_57_5 = e3 & op(e2, e1) = e3
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (8794), (8828), (function-axioms) are
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547.
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | (8829) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8829) gives:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | (8830) all_57_8 = e3 & op(e1, e1) = e3
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8830) implies:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | (8831) op(e1, e1) = e3
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7007), (8831), (function-axioms) are
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #109.
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | (8832) all_57_14 = e3 & op(e0, e1) = e3
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (8821), (8832), (function-axioms) are
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #652.
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8833) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27)
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8833) implies:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8834) ~ (all_56_3 = e3)
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8835) op(e2, e3) = all_56_3
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8795), (8834), (8835), (function-axioms) are
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #347.
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | (8836) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8836) gives:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8837) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7)
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23)
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8837) implies:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8838) op(e1, e1) = e0
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7007), (8838), (function-axioms) are
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #98.
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8839) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8839) implies:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8840) all_56_31 = e1
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8809), (8840) imply:
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8841) op(e0, e0) = e1
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (371), (8841), (function-axioms) are
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #354.
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.56 | | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.56 | | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | End of split
% 134.53/19.56 | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.56 | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | (8842) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 134.53/19.56 | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | | REF_CLOSE: (8779), (8784), (8787), (8788), (8842) are
% 134.53/19.56 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #126.
% 134.53/19.56 | | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | End of split
% 134.53/19.56 | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | Case 2:
% 134.53/19.56 | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | (8843) ~ (all_38_1 = e1) & op(e2, e2) = all_38_1 &
% 134.53/19.56 | | | | | | | | | | | | | | | | $i(all_38_1)
% 134.53/19.56 | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | | REF_CLOSE: (8545), (8843), (function-axioms) are inconsistent
% 134.53/19.56 | | | | | | | | | | | | | | | | by sub-proof #125.
% 134.53/19.56 | | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | | End of split
% 134.53/19.56 | | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | End of split
% 134.53/19.56 | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | End of split
% 134.53/19.56 | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | End of split
% 134.53/19.56 | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | End of split
% 134.53/19.56 | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | End of split
% 134.53/19.56 | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | End of split
% 134.53/19.56 | | | | | | | | |
% 134.53/19.56 | | | | | | | | Case 2:
% 134.53/19.56 | | | | | | | | |
% 134.53/19.56 | | | | | | | | | (8844) all_10_2 = e0
% 134.53/19.56 | | | | | | | | |
% 134.53/19.56 | | | | | | | | | COMBINE_EQS: (319), (8844) imply:
% 134.53/19.56 | | | | | | | | | (8845) all_24_2 = e0
% 134.53/19.56 | | | | | | | | |
% 134.53/19.56 | | | | | | | | | REDUCE: (340), (8844) imply:
% 134.53/19.56 | | | | | | | | | (8846) ~ (all_52_3 = e0)
% 134.53/19.56 | | | | | | | | |
% 134.53/19.56 | | | | | | | | | REDUCE: (342), (8844) imply:
% 134.53/19.56 | | | | | | | | | (8847) ~ (all_52_4 = e0)
% 134.53/19.56 | | | | | | | | |
% 134.53/19.56 | | | | | | | | | REDUCE: (45), (8844) imply:
% 134.53/19.56 | | | | | | | | | (8848) op(e3, e3) = e0
% 134.53/19.56 | | | | | | | | |
% 134.53/19.56 | | | | | | | | | BETA: splitting (61) gives:
% 134.53/19.56 | | | | | | | | |
% 134.53/19.56 | | | | | | | | | Case 1:
% 134.53/19.56 | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | (8849) ~ (all_20_2 = e2)
% 134.53/19.56 | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | REDUCE: (318), (8849) imply:
% 134.53/19.56 | | | | | | | | | | (8850) ~ (all_4_2 = e2)
% 134.53/19.56 | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | BETA: splitting (206) gives:
% 134.53/19.56 | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | Case 1:
% 134.53/19.56 | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | (8851) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 134.53/19.56 | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.56 | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 134.53/19.56 | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 134.53/19.56 | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.56 | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 134.53/19.56 | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.56 | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.53/19.56 | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.56 | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 134.53/19.56 | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 134.53/19.56 | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.56 | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 134.53/19.56 | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 134.53/19.56 | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.53/19.56 | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.56 | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 134.53/19.56 | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.56 | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.56 | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.56 | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.56 | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.53/19.56 | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.56 | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.56 | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.56 | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 134.53/19.56 | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.56 | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 134.53/19.56 | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | BETA: splitting (8851) gives:
% 134.53/19.56 | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | Case 1:
% 134.53/19.56 | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | (8852) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 134.53/19.56 | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.56 | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 134.53/19.56 | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 134.53/19.56 | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.56 | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 134.53/19.56 | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.56 | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.53/19.56 | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.56 | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 134.53/19.56 | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 134.53/19.56 | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.56 | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 134.53/19.56 | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 134.53/19.56 | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | REF_CLOSE: (4), (5), (8848), (8852), (function-axioms) are
% 134.53/19.56 | | | | | | | | | | | | inconsistent by sub-proof #229.
% 134.53/19.56 | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | Case 2:
% 134.53/19.56 | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | (8853) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.53/19.56 | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.56 | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 134.53/19.56 | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.56 | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.56 | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.56 | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.56 | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.53/19.56 | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.56 | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.56 | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.56 | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 134.53/19.56 | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.56 | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 134.53/19.56 | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | BETA: splitting (8853) gives:
% 134.53/19.56 | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | Case 1:
% 134.53/19.56 | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | (8854) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.53/19.56 | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 134.53/19.56 | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3,
% 134.53/19.56 | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.56 | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 134.53/19.56 | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.56 | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 134.53/19.56 | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | ALPHA: (8854) implies:
% 134.53/19.56 | | | | | | | | | | | | | (8855) ~ (all_56_31 = e0)
% 134.53/19.56 | | | | | | | | | | | | | (8856) op(e0, e0) = all_56_31
% 134.53/19.56 | | | | | | | | | | | | | (8857) op(e3, e0) = e3
% 134.53/19.56 | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 134.53/19.56 | | | | | | | | | | | | | all_56_31, e0, e0, simplifying with (36), (8856)
% 134.53/19.56 | | | | | | | | | | | | | gives:
% 134.53/19.56 | | | | | | | | | | | | | (8858) all_56_31 = all_4_2
% 134.53/19.56 | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 134.53/19.56 | | | | | | | | | | | | | e3, e0, e3, simplifying with (168), (8857) gives:
% 134.53/19.56 | | | | | | | | | | | | | (8859) all_52_12 = e3
% 134.53/19.56 | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | REDUCE: (8855), (8858) imply:
% 134.53/19.56 | | | | | | | | | | | | | (8860) ~ (all_4_2 = e0)
% 134.53/19.56 | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | REDUCE: (368), (8859) imply:
% 134.53/19.56 | | | | | | | | | | | | | (8861) ~ (all_4_2 = e3)
% 134.53/19.56 | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | SIMP: (8861) implies:
% 134.53/19.56 | | | | | | | | | | | | | (8862) ~ (all_4_2 = e3)
% 134.53/19.56 | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | BETA: splitting (189) gives:
% 134.53/19.56 | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | Case 1:
% 134.53/19.56 | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | (8863) all_54_15 = e3
% 134.53/19.56 | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | COMBINE_EQS: (245), (8863) imply:
% 134.53/19.56 | | | | | | | | | | | | | | (8864) all_4_2 = e3
% 134.53/19.56 | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | REDUCE: (8862), (8864) imply:
% 134.53/19.56 | | | | | | | | | | | | | | (8865) $false
% 134.53/19.56 | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | CLOSE: (8865) is inconsistent.
% 134.53/19.56 | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | Case 2:
% 134.53/19.56 | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | (8866) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 134.53/19.56 | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | | REF_CLOSE: (245), (371), (8850), (8860), (8866) are
% 134.53/19.56 | | | | | | | | | | | | | | inconsistent by sub-proof #746.
% 134.53/19.56 | | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | End of split
% 134.53/19.56 | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | Case 2:
% 134.53/19.56 | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | (8867) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.53/19.56 | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 134.53/19.56 | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.56 | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.56 | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2,
% 134.53/19.56 | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.56 | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 134.53/19.56 | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | ALPHA: (8867) implies:
% 134.53/19.56 | | | | | | | | | | | | | (8868) op(e2, e2) = e3
% 134.53/19.56 | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | | REF_CLOSE: (8), (8545), (8868), (function-axioms) are
% 134.53/19.56 | | | | | | | | | | | | | inconsistent by sub-proof #325.
% 134.53/19.56 | | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | | End of split
% 134.53/19.56 | | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | | End of split
% 134.53/19.56 | | | | | | | | | | |
% 134.53/19.56 | | | | | | | | | | Case 2:
% 134.53/19.56 | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | (8869) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.53/19.57 | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.57 | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.57 | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.57 | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.53/19.57 | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.57 | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.53/19.57 | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.53/19.57 | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.53/19.57 | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.53/19.57 | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.53/19.57 | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.53/19.57 | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.57 | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 134.53/19.57 | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 134.53/19.57 | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.57 | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 134.53/19.57 | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.57 | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 134.53/19.57 | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.57 | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 134.53/19.57 | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 134.53/19.57 | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.53/19.57 | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.57 | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 134.53/19.57 | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 134.53/19.57 | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.57 | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 134.53/19.57 | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 134.53/19.57 | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 134.53/19.57 | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 134.53/19.57 | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.57 | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 134.53/19.57 | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 134.53/19.57 | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.57 | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 134.53/19.57 | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 134.53/19.57 | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 134.53/19.57 | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.57 | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.57 | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 134.53/19.57 | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.57 | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 134.53/19.57 | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 134.53/19.57 | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 134.53/19.57 | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 134.53/19.57 | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 134.53/19.57 | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 134.53/19.57 | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.57 | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.57 | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.57 | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.57 | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.57 | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.57 | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.57 | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.57 | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.57 | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | BETA: splitting (8869) gives:
% 134.53/19.57 | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | Case 1:
% 134.53/19.57 | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | (8870) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.53/19.57 | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.57 | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.57 | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.57 | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.53/19.57 | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.57 | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.53/19.57 | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.53/19.57 | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.53/19.57 | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.53/19.57 | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.53/19.57 | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.53/19.57 | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.57 | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.53/19.57 | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | REF_CLOSE: (9), (165), (7000), (7007), (8870),
% 134.53/19.57 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.57 | | | | | | | | | | | | #108.
% 134.53/19.57 | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | Case 2:
% 134.53/19.57 | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | (8871) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.53/19.57 | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.57 | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 134.53/19.57 | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.57 | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.57 | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.57 | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.57 | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.57 | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.57 | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.53/19.57 | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.57 | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.53/19.57 | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.53/19.57 | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.57 | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.57 | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.53/19.57 | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.53/19.57 | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.57 | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.53/19.57 | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.53/19.57 | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.53/19.57 | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.53/19.57 | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.53/19.57 | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.53/19.57 | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.53/19.57 | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.53/19.57 | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.57 | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.53/19.57 | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.53/19.57 | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.53/19.57 | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.57 | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.57 | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.57 | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.57 | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.57 | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.53/19.57 | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.57 | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.57 | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.57 | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.57 | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.57 | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.57 | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.57 | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.57 | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | BETA: splitting (8871) gives:
% 134.53/19.57 | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | Case 1:
% 134.53/19.57 | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | (8872) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.53/19.57 | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 134.53/19.57 | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 134.53/19.57 | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.57 | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 134.53/19.57 | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.57 | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 134.53/19.57 | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | ALPHA: (8872) implies:
% 134.53/19.57 | | | | | | | | | | | | | (8873) op(e2, e2) = e0
% 134.53/19.57 | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | REF_CLOSE: (4), (8545), (8873), (function-axioms) are
% 134.53/19.57 | | | | | | | | | | | | | inconsistent by sub-proof #675.
% 134.53/19.57 | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | Case 2:
% 134.53/19.57 | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | (8874) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.57 | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.57 | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.53/19.57 | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.57 | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.53/19.57 | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.53/19.57 | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.57 | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.57 | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.53/19.57 | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.53/19.57 | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.57 | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.53/19.57 | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.53/19.57 | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.53/19.57 | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.53/19.57 | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.53/19.57 | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.53/19.57 | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.53/19.57 | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.53/19.57 | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.57 | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.53/19.57 | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.53/19.57 | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.53/19.57 | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.57 | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.57 | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.57 | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.57 | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.57 | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.53/19.57 | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.57 | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.57 | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.57 | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.57 | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.57 | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.57 | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.57 | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.57 | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | BETA: splitting (8874) gives:
% 134.53/19.57 | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | Case 1:
% 134.53/19.57 | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | (8875) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.57 | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 134.53/19.57 | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.57 | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.57 | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 134.53/19.57 | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.57 | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 134.53/19.57 | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | ALPHA: (8875) implies:
% 134.53/19.57 | | | | | | | | | | | | | | (8876) op(e1, e2) = e1
% 134.53/19.57 | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | REF_CLOSE: (162), (8537), (8876), (function-axioms) are
% 134.53/19.57 | | | | | | | | | | | | | | inconsistent by sub-proof #65.
% 134.53/19.57 | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | Case 2:
% 134.53/19.57 | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | (8877) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.57 | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.53/19.57 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 134.53/19.57 | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.57 | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 134.53/19.57 | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 134.53/19.57 | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.57 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 134.53/19.57 | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 134.53/19.57 | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.53/19.57 | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.57 | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.57 | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 134.53/19.57 | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.57 | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 134.53/19.57 | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.57 | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.57 | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.57 | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.57 | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.57 | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 134.53/19.57 | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 134.53/19.57 | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 134.53/19.57 | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 134.53/19.57 | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 134.53/19.57 | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 134.53/19.57 | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 134.53/19.57 | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 134.53/19.57 | | | | | | | | | | | | | | $i(all_56_29)))
% 134.53/19.57 | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | ALPHA: (8877) implies:
% 134.53/19.57 | | | | | | | | | | | | | | (8878) op(e0, e0) = all_56_31
% 134.53/19.57 | | | | | | | | | | | | | | (8879) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.53/19.57 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.57 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.57 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.57 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 134.53/19.57 | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 134.53/19.57 | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 134.53/19.57 | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 134.53/19.57 | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 134.53/19.57 | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 134.53/19.57 | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 134.53/19.57 | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 134.53/19.57 | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 134.53/19.57 | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.57 | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.57 | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 134.53/19.57 | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.57 | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.57 | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 134.53/19.57 | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 134.53/19.57 | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.57 | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 134.53/19.57 | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 134.53/19.57 | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 134.53/19.57 | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.57 | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.53/19.57 | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 134.53/19.57 | | | | | | | | | | | | | | all_56_31, e0, e0, simplifying with (36), (8878)
% 134.53/19.57 | | | | | | | | | | | | | | gives:
% 134.53/19.57 | | | | | | | | | | | | | | (8880) all_56_31 = all_4_2
% 134.53/19.57 | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | BETA: splitting (8879) gives:
% 134.53/19.57 | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | Case 1:
% 134.53/19.57 | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | (8881) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.53/19.57 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.57 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.57 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.57 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 134.53/19.57 | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 134.53/19.57 | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 134.53/19.57 | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 134.53/19.57 | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 134.53/19.57 | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 134.53/19.57 | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 134.53/19.57 | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 134.53/19.57 | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27))
% 134.53/19.57 | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | BETA: splitting (8881) gives:
% 134.53/19.57 | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | Case 1:
% 134.53/19.57 | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | (8882) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.53/19.57 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 134.53/19.57 | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.57 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.57 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 134.53/19.57 | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 134.53/19.57 | | | | | | | | | | | | | | | | $i(all_56_25)
% 134.53/19.57 | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | ALPHA: (8882) implies:
% 134.53/19.57 | | | | | | | | | | | | | | | | (8883) op(e0, e3) = e0
% 134.53/19.57 | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | REF_CLOSE: (159), (8846), (8883), (function-axioms) are
% 134.53/19.57 | | | | | | | | | | | | | | | | inconsistent by sub-proof #219.
% 134.53/19.57 | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | Case 2:
% 134.53/19.57 | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | (8884) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 134.53/19.57 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 134.53/19.57 | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.57 | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.57 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.53/19.57 | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 134.53/19.57 | | | | | | | | | | | | | | | | $i(all_56_27)
% 134.53/19.57 | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | REF_CLOSE: (8850), (8880), (8884) are inconsistent by
% 134.53/19.57 | | | | | | | | | | | | | | | | sub-proof #765.
% 134.53/19.57 | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | End of split
% 134.53/19.57 | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | Case 2:
% 134.53/19.57 | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | (8885) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 134.53/19.57 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.57 | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 134.53/19.57 | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.57 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.57 | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 134.53/19.57 | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 134.53/19.57 | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.57 | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 134.53/19.57 | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 134.53/19.57 | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 134.53/19.57 | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.57 | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.53/19.57 | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | REF_CLOSE: (5), (371), (7007), (8880), (8885),
% 134.53/19.57 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.57 | | | | | | | | | | | | | | | #86.
% 134.53/19.57 | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | End of split
% 134.53/19.57 | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | End of split
% 134.53/19.57 | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | End of split
% 134.53/19.57 | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | End of split
% 134.53/19.57 | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | End of split
% 134.53/19.57 | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | Case 2:
% 134.53/19.57 | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | (8886) all_20_2 = e2
% 134.53/19.57 | | | | | | | | | | (8887) ( ~ (all_20_0 = e3) & op(e2, e0) = all_20_0 &
% 134.53/19.57 | | | | | | | | | | $i(all_20_0)) | ( ~ (all_20_1 = e1) & op(e2, e2)
% 134.53/19.57 | | | | | | | | | | = all_20_1 & $i(all_20_1))
% 134.53/19.57 | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | COMBINE_EQS: (318), (8886) imply:
% 134.53/19.57 | | | | | | | | | | (8888) all_4_2 = e2
% 134.53/19.57 | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | SIMP: (8888) implies:
% 134.53/19.57 | | | | | | | | | | (8889) all_4_2 = e2
% 134.53/19.57 | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | REDUCE: (349), (8889) imply:
% 134.53/19.57 | | | | | | | | | | (8890) ~ (all_52_3 = e2)
% 134.53/19.57 | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | REDUCE: (368), (8889) imply:
% 134.53/19.57 | | | | | | | | | | (8891) ~ (all_52_12 = e2)
% 134.53/19.57 | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | REDUCE: (369), (8889) imply:
% 134.53/19.57 | | | | | | | | | | (8892) ~ (all_52_13 = e2)
% 134.53/19.57 | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | REDUCE: (36), (8889) imply:
% 134.53/19.57 | | | | | | | | | | (8893) op(e0, e0) = e2
% 134.53/19.57 | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | BETA: splitting (67) gives:
% 134.53/19.57 | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | Case 1:
% 134.53/19.57 | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | (8894) ~ (all_24_2 = e0)
% 134.53/19.57 | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | REDUCE: (8845), (8894) imply:
% 134.53/19.57 | | | | | | | | | | | (8895) $false
% 134.53/19.57 | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | CLOSE: (8895) is inconsistent.
% 134.53/19.57 | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | Case 2:
% 134.53/19.57 | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | (8896) ( ~ (all_24_0 = e1) & op(e0, e3) = all_24_0 &
% 134.53/19.57 | | | | | | | | | | | $i(all_24_0)) | ( ~ (all_24_1 = e2) & op(e0, e0)
% 134.53/19.57 | | | | | | | | | | | = all_24_1 & $i(all_24_1))
% 134.53/19.57 | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | BETA: splitting (8896) gives:
% 134.53/19.57 | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | Case 1:
% 134.53/19.57 | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | (8897) ~ (all_24_0 = e1) & op(e0, e3) = all_24_0 &
% 134.53/19.57 | | | | | | | | | | | | $i(all_24_0)
% 134.53/19.57 | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | ALPHA: (8897) implies:
% 134.53/19.57 | | | | | | | | | | | | (8898) ~ (all_24_0 = e1)
% 134.53/19.57 | | | | | | | | | | | | (8899) op(e0, e3) = all_24_0
% 134.53/19.57 | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | BETA: splitting (236) gives:
% 134.53/19.57 | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | Case 1:
% 134.53/19.57 | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | (8900) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 134.53/19.57 | | | | | | | | | | | | | & op(e3, e2) = e2)
% 134.53/19.57 | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | BETA: splitting (8900) gives:
% 134.53/19.57 | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | Case 1:
% 134.53/19.57 | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | (8901) all_57_0 = e2 & op(e3, e3) = e2
% 134.53/19.57 | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | ALPHA: (8901) implies:
% 134.53/19.57 | | | | | | | | | | | | | | (8902) op(e3, e3) = e2
% 134.53/19.57 | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | REF_CLOSE: (5), (8848), (8902), (function-axioms) are
% 134.53/19.57 | | | | | | | | | | | | | | inconsistent by sub-proof #495.
% 134.53/19.57 | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | Case 2:
% 134.53/19.57 | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | (8903) all_57_1 = e2 & op(e3, e2) = e2
% 134.53/19.57 | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | ALPHA: (8903) implies:
% 134.53/19.57 | | | | | | | | | | | | | | (8904) op(e3, e2) = e2
% 134.53/19.57 | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 134.53/19.57 | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | Case 1:
% 134.53/19.57 | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | (8905) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 134.53/19.57 | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 134.53/19.57 | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | BETA: splitting (8905) gives:
% 134.53/19.57 | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | Case 1:
% 134.53/19.57 | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | (8906) all_57_2 = e2 & op(e2, e3) = e2
% 134.53/19.57 | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | ALPHA: (8906) implies:
% 134.53/19.57 | | | | | | | | | | | | | | | | (8907) all_57_2 = e2
% 134.53/19.57 | | | | | | | | | | | | | | | | (8908) op(e2, e3) = e2
% 134.53/19.57 | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | BETA: splitting (8887) gives:
% 134.53/19.57 | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.57 | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | (8909) ~ (all_20_0 = e3) & op(e2, e0) = all_20_0 &
% 134.53/19.57 | | | | | | | | | | | | | | | | | $i(all_20_0)
% 134.53/19.57 | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | ALPHA: (8909) implies:
% 134.53/19.57 | | | | | | | | | | | | | | | | | (8910) ~ (all_20_0 = e3)
% 134.53/19.57 | | | | | | | | | | | | | | | | | (8911) op(e2, e0) = all_20_0
% 134.53/19.57 | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 134.53/19.57 | | | | | | | | | | | | | | | | | all_24_0, e3, e0, simplifying with (159), (8899)
% 134.53/19.57 | | | | | | | | | | | | | | | | | gives:
% 134.53/19.57 | | | | | | | | | | | | | | | | | (8912) all_52_3 = all_24_0
% 134.53/19.57 | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 134.53/19.57 | | | | | | | | | | | | | | | | | all_20_0, e0, e2, simplifying with (164), (8911)
% 134.53/19.57 | | | | | | | | | | | | | | | | | gives:
% 134.53/19.57 | | | | | | | | | | | | | | | | | (8913) all_52_13 = all_20_0
% 134.53/19.57 | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 134.53/19.57 | | | | | | | | | | | | | | | | | e3, e2, simplifying with (167), (8908) gives:
% 134.53/19.57 | | | | | | | | | | | | | | | | | (8914) all_52_1 = e2
% 134.53/19.57 | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e2,
% 134.53/19.57 | | | | | | | | | | | | | | | | | e2, e3, simplifying with (170), (8904) gives:
% 134.53/19.57 | | | | | | | | | | | | | | | | | (8915) all_52_4 = e2
% 134.53/19.57 | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (8912) imply:
% 134.53/19.57 | | | | | | | | | | | | | | | | | (8916) all_54_12 = all_24_0
% 134.53/19.57 | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (8913) imply:
% 134.53/19.57 | | | | | | | | | | | | | | | | | (8917) all_54_7 = all_20_0
% 134.53/19.57 | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | REDUCE: (146), (8914) imply:
% 134.53/19.57 | | | | | | | | | | | | | | | | | (8918) ~ (all_52_9 = e2)
% 134.53/19.57 | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | REDUCE: (140), (8912) imply:
% 134.53/19.57 | | | | | | | | | | | | | | | | | (8919) ~ (all_52_7 = all_24_0)
% 134.53/19.57 | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | SIMP: (8919) implies:
% 134.53/19.57 | | | | | | | | | | | | | | | | | (8920) ~ (all_52_7 = all_24_0)
% 134.53/19.57 | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | REDUCE: (139), (8912) imply:
% 134.53/19.57 | | | | | | | | | | | | | | | | | (8921) ~ (all_52_11 = all_24_0)
% 134.53/19.57 | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | SIMP: (8921) implies:
% 134.53/19.57 | | | | | | | | | | | | | | | | | (8922) ~ (all_52_11 = all_24_0)
% 134.53/19.57 | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | REDUCE: (8890), (8912) imply:
% 134.53/19.57 | | | | | | | | | | | | | | | | | (8923) ~ (all_24_0 = e2)
% 134.53/19.57 | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | REDUCE: (8846), (8912) imply:
% 134.53/19.57 | | | | | | | | | | | | | | | | | (8924) ~ (all_24_0 = e0)
% 134.53/19.57 | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | REDUCE: (8892), (8913) imply:
% 134.53/19.57 | | | | | | | | | | | | | | | | | (8925) ~ (all_20_0 = e2)
% 134.53/19.57 | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | REDUCE: (8540), (8913) imply:
% 134.53/19.57 | | | | | | | | | | | | | | | | | (8926) ~ (all_20_0 = e1)
% 134.53/19.57 | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 134.53/19.57 | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.57 | | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | | (8927) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 134.53/19.57 | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 134.53/19.57 | | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (167), (8535), (8848), (8927),
% 134.53/19.57 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.57 | | | | | | | | | | | | | | | | | | #118.
% 134.53/19.57 | | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.57 | | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | | (8928) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 134.53/19.57 | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 134.53/19.57 | | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | | BETA: splitting (8928) gives:
% 134.53/19.57 | | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.57 | | | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | (8929) all_57_6 = e1 & op(e1, e3) = e1
% 134.53/19.57 | | | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | ALPHA: (8929) implies:
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | (8930) all_57_6 = e1
% 134.53/19.57 | | | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 134.53/19.57 | | | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | (8931) all_54_7 = e3
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8910), (8917), (8931) are inconsistent by
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | sub-proof #119.
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | (8932) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | (8933) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (8848), (8907), (8933),
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | #70.
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | (8934) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8934) gives:
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | (8935) all_57_6 = e3 & op(e1, e3) = e3
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8930), (8935) are inconsistent by sub-proof
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | #61.
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | (8936) all_57_12 = e3 & op(e0, e3) = e3
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8936) implies:
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | (8937) all_57_12 = e3
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | (8938) op(e0, e3) = e3
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8932) gives:
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | | (8939) all_54_7 = e2
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8917), (8925), (8939) are inconsistent by
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #63.
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | | (8940) all_54_7 = e1 | all_54_7 = e0
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | (8941) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8941) gives:
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | (8942) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8942) gives:
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (8943) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8943) implies:
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (8944) op(e3, e3) = e2
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (231), (233), (8907),
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (8937), (8944), (function-axioms) are inconsistent
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #489.
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (8945) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8945) implies:
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (8946) op(e3, e3) = e1
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8848), (8946), (function-axioms) are
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #717.
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | (8947) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8545), (8938), (8947), (function-axioms) are
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #115.
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | (8948) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8948) gives:
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | (8949) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (7000), (7007), (8949),
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | #108.
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | (8950) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8950) gives:
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (8951) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8951) implies:
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (8952) op(e2, e2) = e0
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8545), (8952), (function-axioms) are
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675.
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (8953) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8953) gives:
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8954) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8954) implies:
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8955) op(e1, e2) = e1
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (8537), (8955), (function-axioms) are
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #65.
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8956) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8956) implies:
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8957) op(e0, e0) = all_56_31
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8958) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8940) gives:
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8959) all_54_7 = e1
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8917), (8926), (8959) are inconsistent by
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #62.
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8960) all_54_7 = e0
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8917), (8960) imply:
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8961) all_20_0 = e0
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8961) implies:
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8962) all_20_0 = e0
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8911), (8962) imply:
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8963) op(e2, e0) = e0
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (39), (91), (157), (190), (246), (332),
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (364), (7001), (8893), (8957), (8958), (8963),
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #273.
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.58 | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.58 | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | (8964) all_57_12 = e1 & op(e0, e3) = e1
% 134.53/19.58 | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | ALPHA: (8964) implies:
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | (8965) all_57_12 = e1
% 134.53/19.58 | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (158), (192), (211), (8893), (8898),
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | (8916), (8920), (8922), (8923), (8924), (8965),
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.58 | | | | | | | | | | | | | | | | | | | #120.
% 134.53/19.58 | | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.58 | | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | End of split
% 134.53/19.58 | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.58 | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | (8966) ~ (all_20_1 = e1) & op(e2, e2) = all_20_1 &
% 134.53/19.58 | | | | | | | | | | | | | | | | | $i(all_20_1)
% 134.53/19.58 | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | | REF_CLOSE: (8545), (8966), (function-axioms) are inconsistent
% 134.53/19.58 | | | | | | | | | | | | | | | | | by sub-proof #113.
% 134.53/19.58 | | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | End of split
% 134.53/19.58 | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | Case 2:
% 134.53/19.58 | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | (8967) all_57_3 = e2 & op(e2, e2) = e2
% 134.53/19.58 | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | ALPHA: (8967) implies:
% 134.53/19.58 | | | | | | | | | | | | | | | | (8968) all_57_3 = e2
% 134.53/19.58 | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8544), (8968) are inconsistent by sub-proof
% 134.53/19.58 | | | | | | | | | | | | | | | | #728.
% 134.53/19.58 | | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | End of split
% 134.53/19.58 | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | Case 2:
% 134.53/19.58 | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | (8969) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 134.53/19.58 | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 134.53/19.58 | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | | REF_CLOSE: (164), (165), (7000), (8892), (8969),
% 134.53/19.58 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.58 | | | | | | | | | | | | | | | #625.
% 134.53/19.58 | | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | End of split
% 134.53/19.58 | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | End of split
% 134.53/19.58 | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | Case 2:
% 134.53/19.58 | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | (8970) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 134.53/19.58 | | | | | | | | | | | | | & op(e3, e0) = e2)
% 134.53/19.58 | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | BETA: splitting (8970) gives:
% 134.53/19.58 | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | Case 1:
% 134.53/19.58 | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | (8971) all_57_4 = e2 & op(e3, e1) = e2
% 134.53/19.58 | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | REF_CLOSE: (169), (6999), (8971), (function-axioms) are
% 134.53/19.58 | | | | | | | | | | | | | | inconsistent by sub-proof #442.
% 134.53/19.58 | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | Case 2:
% 134.53/19.58 | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | (8972) all_57_9 = e2 & op(e3, e0) = e2
% 134.53/19.58 | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | | REF_CLOSE: (168), (8891), (8972), (function-axioms) are
% 134.53/19.58 | | | | | | | | | | | | | | inconsistent by sub-proof #460.
% 134.53/19.58 | | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | | End of split
% 134.53/19.58 | | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | End of split
% 134.53/19.58 | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | Case 2:
% 134.53/19.58 | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | (8973) ~ (all_24_1 = e2) & op(e0, e0) = all_24_1 &
% 134.53/19.58 | | | | | | | | | | | | $i(all_24_1)
% 134.53/19.58 | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | | REF_CLOSE: (8893), (8973), (function-axioms) are inconsistent
% 134.53/19.58 | | | | | | | | | | | | by sub-proof #204.
% 134.53/19.58 | | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | | End of split
% 134.53/19.58 | | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | | End of split
% 134.53/19.58 | | | | | | | | | |
% 134.53/19.58 | | | | | | | | | End of split
% 134.53/19.58 | | | | | | | | |
% 134.53/19.58 | | | | | | | | End of split
% 134.53/19.58 | | | | | | | |
% 134.53/19.58 | | | | | | | End of split
% 134.53/19.58 | | | | | | |
% 134.53/19.58 | | | | | | Case 2:
% 134.53/19.58 | | | | | | |
% 134.53/19.58 | | | | | | | (8974) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 &
% 134.53/19.58 | | | | | | | op(e2, e0) = e1)
% 134.53/19.58 | | | | | | |
% 134.53/19.58 | | | | | | | REF_CLOSE: (164), (165), (8539), (8540), (8974), (function-axioms)
% 134.53/19.58 | | | | | | | are inconsistent by sub-proof #112.
% 134.53/19.58 | | | | | | |
% 134.53/19.58 | | | | | | End of split
% 134.53/19.58 | | | | | |
% 134.53/19.58 | | | | | End of split
% 134.53/19.58 | | | | |
% 134.53/19.58 | | | | Case 2:
% 134.53/19.58 | | | | |
% 134.53/19.58 | | | | | (8975) all_57_14 = e2 & op(e0, e1) = e2
% 134.53/19.58 | | | | |
% 134.53/19.58 | | | | | REF_CLOSE: (157), (7001), (8975), (function-axioms) are inconsistent
% 134.53/19.58 | | | | | by sub-proof #512.
% 134.53/19.58 | | | | |
% 134.53/19.58 | | | | End of split
% 134.53/19.58 | | | |
% 134.53/19.58 | | | End of split
% 134.53/19.58 | | |
% 134.53/19.58 | | End of split
% 134.53/19.58 | |
% 134.53/19.58 | Case 2:
% 134.53/19.58 | |
% 134.53/19.58 | | (8976) all_4_2 = e1
% 134.53/19.58 | | (8977) ( ~ (all_4_0 = e3) & op(e1, e0) = all_4_0 & $i(all_4_0)) | ( ~
% 134.53/19.58 | | (all_4_1 = e2) & op(e1, e1) = all_4_1 & $i(all_4_1))
% 134.53/19.58 | |
% 134.53/19.58 | | COMBINE_EQS: (330), (8976) imply:
% 134.53/19.58 | | (8978) all_12_2 = e1
% 134.53/19.58 | |
% 134.53/19.58 | | REDUCE: (349), (8976) imply:
% 134.53/19.58 | | (8979) ~ (all_52_3 = e1)
% 134.53/19.58 | |
% 134.53/19.58 | | REDUCE: (360), (8976) imply:
% 134.53/19.58 | | (8980) ~ (all_52_7 = e1)
% 134.53/19.58 | |
% 134.53/19.58 | | REDUCE: (367), (8976) imply:
% 134.53/19.58 | | (8981) ~ (all_52_11 = e1)
% 134.53/19.58 | |
% 134.53/19.58 | | REDUCE: (368), (8976) imply:
% 134.53/19.58 | | (8982) ~ (all_52_12 = e1)
% 134.53/19.58 | |
% 134.53/19.58 | | REDUCE: (369), (8976) imply:
% 134.53/19.58 | | (8983) ~ (all_52_13 = e1)
% 134.53/19.58 | |
% 134.53/19.58 | | REDUCE: (370), (8976) imply:
% 134.53/19.58 | | (8984) ~ (all_52_14 = e1)
% 134.53/19.58 | |
% 134.53/19.58 | | BETA: splitting (212) gives:
% 134.53/19.58 | |
% 134.53/19.58 | | Case 1:
% 134.53/19.58 | | |
% 134.53/19.58 | | | (8985) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0)
% 134.53/19.58 | | | = e1)
% 134.53/19.58 | | |
% 134.53/19.58 | | | REF_CLOSE: (164), (168), (8982), (8983), (8985), (function-axioms) are
% 134.53/19.58 | | | inconsistent by sub-proof #179.
% 134.53/19.58 | | |
% 134.53/19.58 | | Case 2:
% 134.53/19.58 | | |
% 134.53/19.58 | | | (8986) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0,
% 134.53/19.58 | | | e0) = e1)
% 134.53/19.58 | | |
% 134.53/19.58 | | | BETA: splitting (8986) gives:
% 134.53/19.58 | | |
% 134.53/19.58 | | | Case 1:
% 134.53/19.58 | | | |
% 134.53/19.58 | | | | (8987) all_57_11 = e1 & op(e1, e0) = e1
% 134.53/19.58 | | | |
% 134.53/19.58 | | | | ALPHA: (8987) implies:
% 134.53/19.58 | | | | (8988) op(e1, e0) = e1
% 134.53/19.58 | | | |
% 134.53/19.58 | | | | REF_CLOSE: (160), (8984), (8988), (function-axioms) are inconsistent by
% 134.53/19.58 | | | | sub-proof #327.
% 134.53/19.58 | | | |
% 134.53/19.58 | | | Case 2:
% 134.53/19.58 | | | |
% 134.53/19.58 | | | | (8989) all_57_15 = e1 & op(e0, e0) = e1
% 134.53/19.58 | | | |
% 134.53/19.58 | | | | ALPHA: (8989) implies:
% 134.53/19.59 | | | | (8990) all_57_15 = e1
% 134.53/19.59 | | | | (8991) op(e0, e0) = e1
% 134.53/19.59 | | | |
% 134.53/19.59 | | | | BETA: splitting (40) gives:
% 134.53/19.59 | | | |
% 134.53/19.59 | | | | Case 1:
% 134.53/19.59 | | | | |
% 134.53/19.59 | | | | | (8992) ~ (all_6_2 = e2)
% 134.53/19.59 | | | | |
% 134.53/19.59 | | | | | BETA: splitting (43) gives:
% 134.53/19.59 | | | | |
% 134.53/19.59 | | | | | Case 1:
% 134.53/19.59 | | | | | |
% 134.53/19.59 | | | | | | (8993) ~ (all_8_2 = e1)
% 134.53/19.59 | | | | | |
% 134.53/19.59 | | | | | | BETA: splitting (46) gives:
% 134.53/19.59 | | | | | |
% 134.53/19.59 | | | | | | Case 1:
% 134.53/19.59 | | | | | | |
% 134.53/19.59 | | | | | | | (8994) ~ (all_10_2 = e0)
% 134.53/19.59 | | | | | | |
% 134.53/19.59 | | | | | | | BETA: splitting (49) gives:
% 134.53/19.59 | | | | | | |
% 134.53/19.59 | | | | | | | Case 1:
% 134.53/19.59 | | | | | | | |
% 134.53/19.59 | | | | | | | | (8995) ~ (all_12_2 = e1)
% 134.53/19.59 | | | | | | | |
% 134.53/19.59 | | | | | | | | REDUCE: (8978), (8995) imply:
% 134.53/19.59 | | | | | | | | (8996) $false
% 134.53/19.59 | | | | | | | |
% 134.53/19.59 | | | | | | | | CLOSE: (8996) is inconsistent.
% 134.53/19.59 | | | | | | | |
% 134.53/19.59 | | | | | | | Case 2:
% 134.53/19.59 | | | | | | | |
% 134.53/19.59 | | | | | | | | (8997) ( ~ (all_12_0 = e2) & op(e1, e0) = all_12_0 &
% 134.53/19.59 | | | | | | | | $i(all_12_0)) | ( ~ (all_12_1 = e3) & op(e1, e1) =
% 134.53/19.59 | | | | | | | | all_12_1 & $i(all_12_1))
% 134.53/19.59 | | | | | | | |
% 134.53/19.59 | | | | | | | | BETA: splitting (52) gives:
% 134.53/19.59 | | | | | | | |
% 134.53/19.59 | | | | | | | | Case 1:
% 134.53/19.59 | | | | | | | | |
% 134.53/19.59 | | | | | | | | | (8998) ~ (all_14_2 = e3)
% 134.53/19.59 | | | | | | | | |
% 134.53/19.59 | | | | | | | | | REDUCE: (329), (8998) imply:
% 134.53/19.59 | | | | | | | | | (8999) ~ (all_8_2 = e3)
% 134.53/19.59 | | | | | | | | |
% 134.53/19.59 | | | | | | | | | BETA: splitting (55) gives:
% 134.53/19.59 | | | | | | | | |
% 134.53/19.59 | | | | | | | | | Case 1:
% 134.53/19.59 | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | (9000) ~ (all_16_2 = e2)
% 134.53/19.59 | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | REDUCE: (327), (9000) imply:
% 134.53/19.59 | | | | | | | | | | (9001) ~ (all_10_2 = e2)
% 134.53/19.59 | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | BETA: splitting (73) gives:
% 134.53/19.59 | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | Case 1:
% 134.53/19.59 | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | (9002) ~ (all_28_2 = e3)
% 134.53/19.59 | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | REDUCE: (316), (9002) imply:
% 134.53/19.59 | | | | | | | | | | | (9003) ~ (all_6_2 = e3)
% 134.53/19.59 | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | BETA: splitting (76) gives:
% 134.53/19.59 | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | Case 1:
% 134.53/19.59 | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | (9004) ~ (all_30_2 = e0)
% 134.53/19.59 | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | REDUCE: (309), (9004) imply:
% 134.53/19.59 | | | | | | | | | | | | (9005) ~ (all_8_2 = e0)
% 134.53/19.59 | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | BETA: splitting (199) gives:
% 134.53/19.59 | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | Case 1:
% 134.53/19.59 | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | (9006) all_54_5 = e3
% 134.53/19.59 | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | REF_CLOSE: (267), (8999), (9006) are inconsistent by
% 134.53/19.59 | | | | | | | | | | | | | sub-proof #554.
% 134.53/19.59 | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | Case 2:
% 134.53/19.59 | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | (9007) ~ (all_54_5 = e3)
% 134.53/19.59 | | | | | | | | | | | | | (9008) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 134.53/19.59 | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | BETA: splitting (9008) gives:
% 134.53/19.59 | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | Case 1:
% 134.53/19.59 | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | (9009) all_54_5 = e2
% 134.53/19.59 | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | COMBINE_EQS: (267), (9009) imply:
% 134.53/19.59 | | | | | | | | | | | | | | (9010) all_8_2 = e2
% 134.53/19.59 | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | SIMP: (9010) implies:
% 134.53/19.59 | | | | | | | | | | | | | | (9011) all_8_2 = e2
% 134.53/19.59 | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | REDUCE: (347), (9011) imply:
% 134.53/19.59 | | | | | | | | | | | | | | (9012) ~ (all_52_1 = e2)
% 134.53/19.59 | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | REDUCE: (350), (9011) imply:
% 134.53/19.59 | | | | | | | | | | | | | | (9013) ~ (all_52_4 = e2)
% 134.53/19.59 | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | REDUCE: (356), (9011) imply:
% 134.53/19.59 | | | | | | | | | | | | | | (9014) ~ (all_52_9 = e2)
% 134.53/19.59 | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | REDUCE: (8999), (9011) imply:
% 134.53/19.59 | | | | | | | | | | | | | | (9015) ~ (e3 = e2)
% 134.53/19.59 | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 134.53/19.59 | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | Case 1:
% 134.53/19.59 | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | (9016) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 134.53/19.59 | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 134.53/19.59 | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | BETA: splitting (9016) gives:
% 134.53/19.59 | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | Case 1:
% 134.53/19.59 | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | (9017) all_57_2 = e2 & op(e2, e3) = e2
% 134.53/19.59 | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | ALPHA: (9017) implies:
% 134.53/19.59 | | | | | | | | | | | | | | | | (9018) op(e2, e3) = e2
% 134.53/19.59 | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | REF_CLOSE: (167), (9012), (9018), (function-axioms) are
% 134.53/19.59 | | | | | | | | | | | | | | | | inconsistent by sub-proof #779.
% 134.53/19.59 | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | Case 2:
% 134.53/19.59 | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | (9019) all_57_3 = e2 & op(e2, e2) = e2
% 134.53/19.59 | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | ALPHA: (9019) implies:
% 134.53/19.59 | | | | | | | | | | | | | | | | (9020) all_57_3 = e2
% 134.53/19.59 | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 134.53/19.59 | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.59 | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | (9021) ~ (all_32_2 = e1)
% 134.53/19.59 | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | REDUCE: (312), (9021) imply:
% 134.53/19.59 | | | | | | | | | | | | | | | | | (9022) ~ (all_10_2 = e1)
% 134.53/19.59 | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 134.53/19.59 | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.59 | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | (9023) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 134.53/19.59 | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 134.53/19.59 | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.59 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.59 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 134.53/19.59 | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | BETA: splitting (9023) gives:
% 134.53/19.59 | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.59 | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | (9024) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 134.53/19.59 | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (204), (278), (8994), (9001), (9022),
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | (9024), (function-axioms) are inconsistent by
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | sub-proof #66.
% 134.53/19.59 | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.59 | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | (9025) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 134.53/19.59 | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | BETA: splitting (9025) gives:
% 134.53/19.59 | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | (9026) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3,
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | ALPHA: (9026) implies:
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | (9027) op(e3, e3) = e0
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (204), (278), (8994), (9001), (9022),
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | (9027), (function-axioms) are inconsistent by
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | sub-proof #772.
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | (9028) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2,
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | ALPHA: (9028) implies:
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | (9029) op(e2, e2) = e3
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (8999), (9029), (function-axioms) are
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #228.
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.59 | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.59 | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.59 | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | (9030) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.59 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.53/19.59 | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.53/19.59 | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.53/19.59 | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.53/19.59 | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.53/19.59 | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 134.53/19.59 | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 134.53/19.59 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.59 | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 134.53/19.59 | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 134.53/19.59 | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 134.53/19.59 | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 134.53/19.59 | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.53/19.59 | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 134.53/19.59 | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 134.53/19.59 | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 134.53/19.59 | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 134.53/19.59 | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 134.53/19.59 | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 134.53/19.59 | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 134.53/19.59 | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.59 | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.59 | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.59 | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.59 | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.59 | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | BETA: splitting (9030) gives:
% 134.53/19.59 | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.59 | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | (9031) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.53/19.59 | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (165), (9003), (9014), (9031),
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | #769.
% 134.53/19.59 | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.59 | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | (9032) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.59 | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | BETA: splitting (9032) gives:
% 134.53/19.59 | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | (9033) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | ALPHA: (9033) implies:
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | (9034) op(e2, e0) = e2
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (267), (358), (8993), (9005), (9008),
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | (9034), (function-axioms) are inconsistent by
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | sub-proof #60.
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | (9035) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | BETA: splitting (9035) gives:
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | (9036) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9036) implies:
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | (9037) op(e1, e1) = e2
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (8992), (9037), (function-axioms) are
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | (9038) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9038) implies:
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | (9039) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | (9040) all_54_0 = e3
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (9040) imply:
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | (9041) all_10_2 = e3
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | SIMP: (9041) implies:
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | (9042) all_10_2 = e3
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (9042) imply:
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | (9043) op(e3, e3) = e3
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (42), (157), (158), (160), (194), (199),
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | (267), (334), (354), (364), (8984), (8992),
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | (8993), (8999), (9003), (9039), (9043),
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | #58.
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | (9044) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (8994), (9001), (9022), (9044) are
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #777.
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.59 | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.59 | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | End of split
% 134.53/19.59 | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.59 | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | (9045) all_32_2 = e1
% 134.53/19.59 | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | COMBINE_EQS: (312), (9045) imply:
% 134.53/19.59 | | | | | | | | | | | | | | | | | (9046) all_10_2 = e1
% 134.53/19.59 | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | SIMP: (9046) implies:
% 134.53/19.59 | | | | | | | | | | | | | | | | | (9047) all_10_2 = e1
% 134.53/19.59 | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (9047) imply:
% 134.53/19.59 | | | | | | | | | | | | | | | | | (9048) all_50_2 = e1
% 134.53/19.59 | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | REDUCE: (336), (9047) imply:
% 134.53/19.59 | | | | | | | | | | | | | | | | | (9049) ~ (all_52_1 = e1)
% 134.53/19.59 | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | REDUCE: (342), (9047) imply:
% 134.53/19.59 | | | | | | | | | | | | | | | | | (9050) ~ (all_52_4 = e1)
% 134.53/19.59 | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | REDUCE: (45), (9047) imply:
% 134.53/19.59 | | | | | | | | | | | | | | | | | (9051) op(e3, e3) = e1
% 134.53/19.59 | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 134.53/19.59 | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.59 | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | (9052) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 134.53/19.59 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 134.53/19.59 | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | BETA: splitting (9052) gives:
% 134.53/19.59 | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.59 | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | (9053) all_57_2 = e1 & op(e2, e3) = e1
% 134.53/19.59 | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (9049), (9053), (function-axioms) are
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #676.
% 134.53/19.59 | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.59 | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | (9054) all_57_3 = e1 & op(e2, e2) = e1
% 134.53/19.59 | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | ALPHA: (9054) implies:
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | (9055) op(e2, e2) = e1
% 134.53/19.59 | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (8993), (9055), (function-axioms) are
% 134.53/19.59 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #57.
% 134.53/19.59 | | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.59 | | | | | | | | | | | | | | | | | |
% 134.53/19.59 | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.59 | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | (9056) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 134.53/19.60 | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | BETA: splitting (9056) gives:
% 134.53/19.60 | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | (9057) all_57_5 = e1 & op(e2, e1) = e1
% 134.53/19.60 | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | ALPHA: (9057) implies:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | (9058) op(e2, e1) = e1
% 134.53/19.60 | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | (9059) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | BETA: splitting (9059) gives:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | (9060) all_57_1 = e1 & op(e3, e2) = e1
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (9050), (9060), (function-axioms) are
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #684.
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | (9061) all_57_3 = e1 & op(e2, e2) = e1
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9061) implies:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | (9062) op(e2, e2) = e1
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (8993), (9062), (function-axioms) are
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #57.
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | (9063) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | BETA: splitting (9063) gives:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | (9064) all_57_7 = e1 & op(e1, e2) = e1
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9064) implies:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | (9065) op(e1, e2) = e1
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e1,
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | e2, e1, simplifying with (162), (9065) gives:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | (9066) all_52_6 = e1
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e1,
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (165), (9058) gives:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | (9067) all_52_9 = e1
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (9066) imply:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | (9068) ~ (all_52_2 = e1)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (9066) imply:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | (9069) ~ (all_52_14 = e1)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (9067) imply:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | (9070) ~ (all_52_8 = e1)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (9067) imply:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | (9071) ~ (all_6_2 = e1)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | SIMP: (9071) implies:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | (9072) ~ (all_6_2 = e1)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | REDUCE: (9014), (9067) imply:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | (9073) ~ (e2 = e1)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | (9074) all_54_10 = e3
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (9003), (9074) are inconsistent by
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | sub-proof #742.
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | (9075) ~ (all_54_10 = e3)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | (9076) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9076) gives:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | (9077) all_54_10 = e2
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (8992), (9077) are inconsistent by
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #741.
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | (9078) ~ (all_54_10 = e2)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | (9079) all_54_10 = e1 | all_54_10 = e0
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9079) gives:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | (9080) all_54_10 = e1
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (9072), (9080) are inconsistent by
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #736.
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | (9081) all_54_10 = e0
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (9081) imply:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | (9082) all_6_2 = e0
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9082) implies:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | (9083) all_6_2 = e0
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (364), (9083) imply:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | (9084) ~ (all_52_11 = e0)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9003), (9083) imply:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | (9085) ~ (e3 = e0)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9072), (9083) imply:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | (9086) ~ (e1 = e0)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (9083) imply:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | (9087) op(e1, e1) = e0
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | (9088) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9088) gives:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (9089) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9089) gives:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9090) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9090) implies:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9091) op(e3, e3) = e2
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9051), (9091), (function-axioms) are
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743.
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9092) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9092) implies:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9093) ~ (all_56_13 = e2)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9094) ~ (all_56_5 = e3)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9095) op(e1, e2) = all_56_13
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9096) op(e1, e3) = all_56_5
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9097) op(e3, e1) = e3
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13, e2, e1, simplifying with (9065), (9095)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9098) all_56_13 = e1
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2,
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5, e3, e1, simplifying with (163), (9096)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9099) all_56_5 = all_52_2
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e3,
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (169), (9097) gives:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9100) all_52_8 = e3
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (9100) imply:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9101) ~ (all_52_4 = e3)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (9100) imply:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9102) ~ (all_52_12 = e3)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9102) implies:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9103) ~ (all_52_12 = e3)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (39), (106), (163), (168), (170),
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (194), (203), (216), (217), (218), (228), (230),
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (271), (334), (8992), (9003), (9013),
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9020), (9048), (9050), (9051), (9068), (9072),
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9094), (9096), (9101), (9103), (function-axioms)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #718.
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (9104) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9104) gives:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9105) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3,
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9105) implies:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9106) op(e3, e3) = e0
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9051), (9106), (function-axioms) are
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #717.
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9107) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2,
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9107) implies:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9108) op(e2, e2) = e3
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (8999), (9108), (function-axioms) are
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #228.
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | (9109) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9109) gives:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (9110) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (165), (9014), (9087), (9110),
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | #143.
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (9111) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9111) gives:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9112) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9112) implies:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9113) op(e2, e0) = e2
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (267), (358), (8993), (9005), (9008),
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9113), (function-axioms) are inconsistent by
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #60.
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9114) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9114) gives:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9115) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9115) implies:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9116) ~ (all_56_19 = e1)
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9117) op(e2, e1) = all_56_19
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9058), (9116), (9117), (function-axioms) are
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #106.
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9118) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9118) implies:
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9119) op(e0, e0) = all_56_31
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9120) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (157), (160), (8984), (8991), (9058), (9084),
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9119), (9120), (function-axioms) are inconsistent
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #55.
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | (9121) all_57_13 = e1 & op(e0, e2) = e1
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (8980), (9121), (function-axioms) are
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #178.
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.61 | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.61 | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | (9122) all_57_10 = e1 & op(e2, e0) = e1
% 134.53/19.61 | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | ALPHA: (9122) implies:
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | (9123) op(e2, e0) = e1
% 134.53/19.61 | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8983), (9123), (function-axioms) are
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #180.
% 134.53/19.61 | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.61 | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | End of split
% 134.53/19.61 | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | End of split
% 134.53/19.61 | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | End of split
% 134.53/19.61 | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | Case 2:
% 134.53/19.61 | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | (9124) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 134.53/19.61 | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 134.53/19.61 | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | BETA: splitting (9124) gives:
% 134.53/19.61 | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | Case 1:
% 134.53/19.61 | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | (9125) all_57_5 = e2 & op(e2, e1) = e2
% 134.53/19.61 | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | ALPHA: (9125) implies:
% 134.53/19.61 | | | | | | | | | | | | | | | | (9126) op(e2, e1) = e2
% 134.53/19.61 | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | REF_CLOSE: (165), (9014), (9126), (function-axioms) are
% 134.53/19.61 | | | | | | | | | | | | | | | | inconsistent by sub-proof #770.
% 134.53/19.61 | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | Case 2:
% 134.53/19.61 | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | (9127) all_57_10 = e2 & op(e2, e0) = e2
% 134.53/19.61 | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | ALPHA: (9127) implies:
% 134.53/19.61 | | | | | | | | | | | | | | | | (9128) op(e2, e0) = e2
% 134.53/19.61 | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | REF_CLOSE: (164), (267), (358), (8993), (9005), (9008),
% 134.53/19.61 | | | | | | | | | | | | | | | | (9128), (function-axioms) are inconsistent by
% 134.53/19.61 | | | | | | | | | | | | | | | | sub-proof #60.
% 134.53/19.61 | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | End of split
% 134.53/19.61 | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | End of split
% 134.53/19.61 | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | Case 2:
% 134.53/19.61 | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | (9129) all_54_5 = e1 | all_54_5 = e0
% 134.53/19.61 | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | REF_CLOSE: (267), (8993), (9005), (9129) are inconsistent by
% 134.53/19.61 | | | | | | | | | | | | | | sub-proof #624.
% 134.53/19.61 | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | End of split
% 134.53/19.61 | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | End of split
% 134.53/19.61 | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | Case 2:
% 134.53/19.61 | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | (9130) all_30_2 = e0
% 134.53/19.61 | | | | | | | | | | | | (9131) ( ~ (all_30_0 = e3) & op(e0, e2) = all_30_0 &
% 134.53/19.61 | | | | | | | | | | | | $i(all_30_0)) | ( ~ (all_30_1 = e1) & op(e0, e0)
% 134.53/19.61 | | | | | | | | | | | | = all_30_1 & $i(all_30_1))
% 134.53/19.61 | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | COMBINE_EQS: (309), (9130) imply:
% 134.53/19.61 | | | | | | | | | | | | (9132) all_8_2 = e0
% 134.53/19.61 | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | SIMP: (9132) implies:
% 134.53/19.61 | | | | | | | | | | | | (9133) all_8_2 = e0
% 134.53/19.61 | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | REDUCE: (350), (9133) imply:
% 134.53/19.61 | | | | | | | | | | | | (9134) ~ (all_52_4 = e0)
% 134.53/19.61 | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | REDUCE: (352), (9133) imply:
% 134.53/19.61 | | | | | | | | | | | | (9135) ~ (all_52_6 = e0)
% 134.53/19.61 | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | REDUCE: (354), (9133) imply:
% 134.53/19.61 | | | | | | | | | | | | (9136) ~ (all_52_7 = e0)
% 134.53/19.61 | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | REDUCE: (8993), (9133) imply:
% 134.53/19.61 | | | | | | | | | | | | (9137) ~ (e1 = e0)
% 134.53/19.61 | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | REDUCE: (42), (9133) imply:
% 134.53/19.61 | | | | | | | | | | | | (9138) op(e2, e2) = e0
% 134.53/19.61 | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | BETA: splitting (9131) gives:
% 134.53/19.61 | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | Case 1:
% 134.53/19.61 | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | (9139) ~ (all_30_0 = e3) & op(e0, e2) = all_30_0 &
% 134.53/19.61 | | | | | | | | | | | | | $i(all_30_0)
% 134.53/19.61 | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | ALPHA: (9139) implies:
% 134.53/19.61 | | | | | | | | | | | | | (9140) ~ (all_30_0 = e3)
% 134.53/19.61 | | | | | | | | | | | | | (9141) op(e0, e2) = all_30_0
% 134.53/19.61 | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7,
% 134.53/19.61 | | | | | | | | | | | | | all_30_0, e2, e0, simplifying with (158), (9141)
% 134.53/19.61 | | | | | | | | | | | | | gives:
% 134.53/19.61 | | | | | | | | | | | | | (9142) all_52_7 = all_30_0
% 134.53/19.61 | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | COMBINE_EQS: (247), (9142) imply:
% 134.53/19.61 | | | | | | | | | | | | | (9143) all_54_13 = all_30_0
% 134.53/19.61 | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | REDUCE: (135), (9142) imply:
% 134.53/19.61 | | | | | | | | | | | | | (9144) ~ (all_52_4 = all_30_0)
% 134.53/19.61 | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | REDUCE: (128), (9142) imply:
% 134.53/19.61 | | | | | | | | | | | | | (9145) ~ (all_52_6 = all_30_0)
% 134.53/19.61 | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | BETA: splitting (191) gives:
% 134.53/19.61 | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | Case 1:
% 134.53/19.61 | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | (9146) all_54_13 = e3
% 134.53/19.61 | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | REF_CLOSE: (9140), (9143), (9146) are inconsistent by
% 134.53/19.61 | | | | | | | | | | | | | | sub-proof #54.
% 134.53/19.61 | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | Case 2:
% 134.53/19.61 | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | (9147) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 134.53/19.61 | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | BETA: splitting (9147) gives:
% 134.53/19.61 | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | Case 1:
% 134.53/19.61 | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | (9148) all_54_13 = e2
% 134.53/19.61 | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | COMBINE_EQS: (9143), (9148) imply:
% 134.53/19.61 | | | | | | | | | | | | | | | (9149) all_30_0 = e2
% 134.53/19.61 | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | SIMP: (9149) implies:
% 134.53/19.61 | | | | | | | | | | | | | | | (9150) all_30_0 = e2
% 134.53/19.61 | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | REDUCE: (9144), (9150) imply:
% 134.53/19.61 | | | | | | | | | | | | | | | (9151) ~ (all_52_4 = e2)
% 134.53/19.61 | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | REDUCE: (9145), (9150) imply:
% 134.53/19.61 | | | | | | | | | | | | | | | (9152) ~ (all_52_6 = e2)
% 134.53/19.61 | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | REDUCE: (9141), (9150) imply:
% 134.53/19.61 | | | | | | | | | | | | | | | (9153) op(e0, e2) = e2
% 134.53/19.61 | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 134.53/19.61 | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | Case 1:
% 134.53/19.61 | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | (9154) ~ (all_32_2 = e1)
% 134.53/19.61 | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | REDUCE: (312), (9154) imply:
% 134.53/19.61 | | | | | | | | | | | | | | | | (9155) ~ (all_10_2 = e1)
% 134.53/19.61 | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 134.53/19.61 | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.61 | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | (9156) all_54_0 = e3
% 134.53/19.61 | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (9156) imply:
% 134.53/19.61 | | | | | | | | | | | | | | | | | (9157) all_10_2 = e3
% 134.53/19.61 | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | REDUCE: (346), (9157) imply:
% 134.53/19.61 | | | | | | | | | | | | | | | | | (9158) ~ (all_52_12 = e3)
% 134.53/19.61 | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | REDUCE: (45), (9157) imply:
% 134.53/19.61 | | | | | | | | | | | | | | | | | (9159) op(e3, e3) = e3
% 134.53/19.61 | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 134.53/19.61 | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.61 | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | (9160) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 134.53/19.61 | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 134.53/19.61 | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.61 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.61 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 134.53/19.61 | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | BETA: splitting (9160) gives:
% 134.53/19.61 | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.61 | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | (9161) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 134.53/19.61 | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (9159), (9161), (function-axioms) are
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #623.
% 134.53/19.61 | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.61 | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | (9162) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 134.53/19.61 | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (9138), (9158), (9162),
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | #622.
% 134.53/19.61 | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.61 | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.61 | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | (9163) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.61 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.53/19.61 | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.53/19.61 | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.53/19.61 | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.53/19.61 | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.53/19.61 | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 134.53/19.61 | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 134.53/19.61 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.61 | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 134.53/19.61 | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 134.53/19.61 | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 134.53/19.61 | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 134.53/19.61 | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.53/19.61 | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 134.53/19.61 | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 134.53/19.61 | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 134.53/19.61 | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 134.53/19.61 | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 134.53/19.61 | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 134.53/19.61 | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 134.53/19.61 | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.61 | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.61 | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.61 | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.61 | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.61 | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | BETA: splitting (9163) gives:
% 134.53/19.61 | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.61 | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | (9164) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.53/19.61 | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (9003), (9138), (9164),
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | #621.
% 134.53/19.61 | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.61 | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | (9165) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.61 | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | BETA: splitting (9165) gives:
% 134.53/19.61 | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | (9166) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | ALPHA: (9166) implies:
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | (9167) ~ (all_56_15 = e2)
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | (9168) op(e0, e2) = all_56_15
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9153), (9167), (9168), (function-axioms) are
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #609.
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | (9169) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | BETA: splitting (9169) gives:
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | (9170) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9170) implies:
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | (9171) op(e1, e1) = e2
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (8992), (9171), (function-axioms) are
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | (9172) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9172) implies:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (9173) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (42), (157), (158), (160), (194), (199),
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (267), (334), (354), (364), (8984), (8992),
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (8993), (8999), (9003), (9159), (9173),
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | #58.
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.62 | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.62 | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | End of split
% 134.53/19.62 | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.62 | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | (9174) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 134.53/19.62 | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (8994), (9001), (9155), (9174) are
% 134.53/19.62 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #777.
% 134.53/19.62 | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | End of split
% 134.53/19.62 | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | Case 2:
% 134.53/19.62 | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | (9175) all_32_2 = e1
% 134.53/19.62 | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | COMBINE_EQS: (312), (9175) imply:
% 134.53/19.62 | | | | | | | | | | | | | | | | (9176) all_10_2 = e1
% 134.53/19.62 | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | SIMP: (9176) implies:
% 134.53/19.62 | | | | | | | | | | | | | | | | (9177) all_10_2 = e1
% 134.53/19.62 | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | REDUCE: (336), (9177) imply:
% 134.53/19.62 | | | | | | | | | | | | | | | | (9178) ~ (all_52_1 = e1)
% 134.53/19.62 | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | REDUCE: (342), (9177) imply:
% 134.53/19.62 | | | | | | | | | | | | | | | | (9179) ~ (all_52_4 = e1)
% 134.53/19.62 | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | REDUCE: (9001), (9177) imply:
% 134.53/19.62 | | | | | | | | | | | | | | | | (9180) ~ (e2 = e1)
% 134.53/19.62 | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | REDUCE: (45), (9177) imply:
% 134.53/19.62 | | | | | | | | | | | | | | | | (9181) op(e3, e3) = e1
% 134.53/19.62 | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 134.53/19.62 | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.62 | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | (9182) all_54_1 = e3
% 134.53/19.62 | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (9182) imply:
% 134.53/19.62 | | | | | | | | | | | | | | | | | (9183) all_52_4 = e3
% 134.53/19.62 | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | REDUCE: (136), (9183) imply:
% 134.53/19.62 | | | | | | | | | | | | | | | | | (9184) ~ (all_52_6 = e3)
% 134.53/19.62 | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | SIMP: (9184) implies:
% 134.53/19.62 | | | | | | | | | | | | | | | | | (9185) ~ (all_52_6 = e3)
% 134.53/19.62 | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 134.53/19.62 | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.62 | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | (9186) all_54_9 = e3
% 134.53/19.62 | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (9185), (9186) are inconsistent by
% 134.53/19.62 | | | | | | | | | | | | | | | | | | sub-proof #64.
% 134.53/19.62 | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.62 | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | (9187) ~ (all_54_9 = e3)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | (9188) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 134.53/19.62 | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 134.53/19.62 | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | (9189) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 134.53/19.62 | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | BETA: splitting (9189) gives:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | (9190) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | BETA: splitting (9190) gives:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (9191) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9191) implies:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (9192) op(e3, e3) = e2
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9181), (9192), (function-axioms) are
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743.
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (9193) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9193) implies:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (9194) op(e3, e1) = e3
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (134), (169), (203), (271), (9134), (9151),
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (9179), (9194), (function-axioms) are inconsistent
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | by sub-proof #700.
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | (9195) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (133), (168), (203), (271), (9134), (9138),
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | (9151), (9179), (9195), (function-axioms) are
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #215.
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.62 | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | (9196) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.62 | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | BETA: splitting (9196) gives:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | (9197) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (9003), (9138), (9197),
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | #621.
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | (9198) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | BETA: splitting (9198) gives:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (9199) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9199) implies:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (9200) ~ (all_56_15 = e2)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (9201) op(e0, e2) = all_56_15
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9153), (9200), (9201), (function-axioms) are
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #609.
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (9202) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9202) gives:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | (9203) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9203) implies:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | (9204) op(e1, e1) = e2
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (8992), (9204), (function-axioms) are
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | (9205) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9205) implies:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | (9206) op(e0, e0) = all_56_31
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | (9207) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | (9208) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (167), (9138), (9178), (9208),
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | #674.
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | (9209) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9209) gives:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | (9210) all_57_5 = e1 & op(e2, e1) = e1
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9210) implies:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | (9211) op(e2, e1) = e1
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9188) gives:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | (9212) all_54_9 = e2
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (9152), (9212) are inconsistent by
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #582.
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | (9213) all_54_9 = e1 | all_54_9 = e0
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9213) gives:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (9214) all_54_9 = e1
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (9214) imply:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (9215) all_52_6 = e1
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9215) implies:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (9216) all_52_6 = e1
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (9216) imply:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (9217) ~ (all_52_14 = e1)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (359), (9216) imply:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (9218) ~ (all_6_2 = e1)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9218) implies:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (9219) ~ (all_6_2 = e1)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9185), (9216) imply:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (9220) ~ (e3 = e1)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9221) all_54_10 = e3
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (9003), (9221) are inconsistent by
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #742.
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9222) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9222) gives:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9223) all_54_10 = e2
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (8992), (9223) are inconsistent by
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #741.
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9224) all_54_10 = e1 | all_54_10 = e0
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9224) gives:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9225) all_54_10 = e1
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (9219), (9225) are inconsistent by
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #736.
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9226) all_54_10 = e0
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (9226) imply:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9227) all_6_2 = e0
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9227) implies:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9228) all_6_2 = e0
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (364), (9228) imply:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9229) ~ (all_52_11 = e0)
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (157), (160), (8984), (8991), (9206), (9207),
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9211), (9229), (function-axioms) are inconsistent
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #55.
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (9230) all_54_9 = e0
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (9135), (9230) are inconsistent by
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #568.
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | (9231) all_57_10 = e1 & op(e2, e0) = e1
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9231) implies:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | (9232) op(e2, e0) = e1
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8983), (9232), (function-axioms) are
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #180.
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.63 | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.63 | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | End of split
% 134.53/19.63 | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.63 | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | (9233) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 134.53/19.63 | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | REF_CLOSE: (271), (9134), (9151), (9179), (9233) are
% 134.53/19.63 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #701.
% 134.53/19.63 | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | End of split
% 134.53/19.63 | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | End of split
% 134.53/19.63 | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | Case 2:
% 134.53/19.63 | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | (9234) all_54_13 = e1 | all_54_13 = e0
% 134.53/19.63 | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | REF_CLOSE: (247), (8980), (9136), (9234) are inconsistent by
% 134.53/19.63 | | | | | | | | | | | | | | | sub-proof #470.
% 134.53/19.63 | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | End of split
% 134.53/19.63 | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | End of split
% 134.53/19.63 | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | Case 2:
% 134.53/19.63 | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | (9235) ~ (all_30_1 = e1) & op(e0, e0) = all_30_1 &
% 134.53/19.63 | | | | | | | | | | | | | $i(all_30_1)
% 134.53/19.63 | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | REF_CLOSE: (8991), (9235), (function-axioms) are inconsistent
% 134.53/19.63 | | | | | | | | | | | | | by sub-proof #53.
% 134.53/19.63 | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | End of split
% 134.53/19.63 | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | End of split
% 134.53/19.63 | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | Case 2:
% 134.53/19.63 | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | (9236) all_28_2 = e3
% 134.53/19.63 | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | COMBINE_EQS: (316), (9236) imply:
% 134.53/19.63 | | | | | | | | | | | (9237) all_6_2 = e3
% 134.53/19.63 | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | SIMP: (9237) implies:
% 134.53/19.63 | | | | | | | | | | | (9238) all_6_2 = e3
% 134.53/19.63 | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | REDUCE: (348), (9238) imply:
% 134.53/19.63 | | | | | | | | | | | (9239) ~ (all_52_2 = e3)
% 134.53/19.63 | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | REDUCE: (359), (9238) imply:
% 134.53/19.63 | | | | | | | | | | | (9240) ~ (all_52_6 = e3)
% 134.53/19.63 | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | REDUCE: (362), (9238) imply:
% 134.53/19.63 | | | | | | | | | | | (9241) ~ (all_52_9 = e3)
% 134.53/19.63 | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | REDUCE: (364), (9238) imply:
% 134.53/19.63 | | | | | | | | | | | (9242) ~ (all_52_11 = e3)
% 134.53/19.63 | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | REDUCE: (366), (9238) imply:
% 134.53/19.63 | | | | | | | | | | | (9243) ~ (all_52_14 = e3)
% 134.53/19.63 | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | BETA: splitting (218) gives:
% 134.53/19.63 | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | Case 1:
% 134.53/19.63 | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | (9244) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 134.53/19.63 | | | | | | | | | | | | & op(e1, e2) = e3)
% 134.53/19.63 | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | REF_CLOSE: (162), (163), (9239), (9240), (9244),
% 134.53/19.63 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.63 | | | | | | | | | | | | #323.
% 134.53/19.63 | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | Case 2:
% 134.53/19.63 | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | (9245) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 134.53/19.63 | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 134.53/19.63 | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | BETA: splitting (9245) gives:
% 134.53/19.63 | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | Case 1:
% 134.53/19.63 | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | (9246) all_57_8 = e3 & op(e1, e1) = e3
% 134.53/19.63 | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | ALPHA: (9246) implies:
% 134.53/19.63 | | | | | | | | | | | | | (9247) all_57_8 = e3
% 134.53/19.63 | | | | | | | | | | | | | (9248) op(e1, e1) = e3
% 134.53/19.63 | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | BETA: splitting (8997) gives:
% 134.53/19.63 | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | Case 1:
% 134.53/19.63 | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | (9249) ~ (all_12_0 = e2) & op(e1, e0) = all_12_0 &
% 134.53/19.63 | | | | | | | | | | | | | | $i(all_12_0)
% 134.53/19.63 | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | ALPHA: (9249) implies:
% 134.53/19.63 | | | | | | | | | | | | | | (9250) ~ (all_12_0 = e2)
% 134.53/19.63 | | | | | | | | | | | | | | (9251) op(e1, e0) = all_12_0
% 134.53/19.63 | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 134.53/19.63 | | | | | | | | | | | | | | all_12_0, e0, e1, simplifying with (160), (9251)
% 134.53/19.63 | | | | | | | | | | | | | | gives:
% 134.53/19.63 | | | | | | | | | | | | | | (9252) all_52_14 = all_12_0
% 134.53/19.63 | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | COMBINE_EQS: (249), (9252) imply:
% 134.53/19.63 | | | | | | | | | | | | | | (9253) all_54_11 = all_12_0
% 134.53/19.63 | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | REDUCE: (141), (9252) imply:
% 134.53/19.63 | | | | | | | | | | | | | | (9254) ~ (all_52_2 = all_12_0)
% 134.53/19.63 | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | REDUCE: (126), (9252) imply:
% 134.53/19.63 | | | | | | | | | | | | | | (9255) ~ (all_52_6 = all_12_0)
% 134.53/19.63 | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | REDUCE: (112), (9252) imply:
% 134.53/19.63 | | | | | | | | | | | | | | (9256) ~ (all_52_12 = all_12_0)
% 134.53/19.63 | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | REDUCE: (9243), (9252) imply:
% 134.53/19.63 | | | | | | | | | | | | | | (9257) ~ (all_12_0 = e3)
% 134.53/19.63 | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | REDUCE: (8984), (9252) imply:
% 134.53/19.63 | | | | | | | | | | | | | | (9258) ~ (all_12_0 = e1)
% 134.53/19.63 | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 134.53/19.63 | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | Case 1:
% 134.53/19.63 | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | (9259) all_54_11 = e3
% 134.53/19.63 | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | REF_CLOSE: (9253), (9257), (9259) are inconsistent by
% 134.53/19.63 | | | | | | | | | | | | | | | sub-proof #52.
% 134.53/19.63 | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | Case 2:
% 134.53/19.63 | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | (9260) ~ (all_54_11 = e3)
% 134.53/19.63 | | | | | | | | | | | | | | | (9261) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 134.53/19.63 | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | BETA: splitting (9261) gives:
% 134.53/19.63 | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | Case 1:
% 134.53/19.63 | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | (9262) all_54_11 = e2
% 134.53/19.63 | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | REF_CLOSE: (9250), (9253), (9262) are inconsistent by
% 134.53/19.63 | | | | | | | | | | | | | | | | sub-proof #51.
% 134.53/19.63 | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | Case 2:
% 134.53/19.63 | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | (9263) ~ (all_54_11 = e2)
% 134.53/19.63 | | | | | | | | | | | | | | | | (9264) all_54_11 = e1 | all_54_11 = e0
% 134.53/19.63 | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | BETA: splitting (9264) gives:
% 134.53/19.63 | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.63 | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | (9265) all_54_11 = e1
% 134.53/19.63 | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | REF_CLOSE: (9253), (9258), (9265) are inconsistent by
% 134.53/19.63 | | | | | | | | | | | | | | | | | sub-proof #50.
% 134.53/19.63 | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.63 | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | (9266) all_54_11 = e0
% 134.53/19.63 | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | COMBINE_EQS: (9253), (9266) imply:
% 134.53/19.63 | | | | | | | | | | | | | | | | | (9267) all_12_0 = e0
% 134.53/19.63 | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | SIMP: (9267) implies:
% 134.53/19.63 | | | | | | | | | | | | | | | | | (9268) all_12_0 = e0
% 134.53/19.63 | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | REDUCE: (9254), (9268) imply:
% 134.53/19.63 | | | | | | | | | | | | | | | | | (9269) ~ (all_52_2 = e0)
% 134.53/19.63 | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | REDUCE: (9255), (9268) imply:
% 134.53/19.63 | | | | | | | | | | | | | | | | | (9270) ~ (all_52_6 = e0)
% 134.53/19.63 | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | REDUCE: (9256), (9268) imply:
% 134.53/19.63 | | | | | | | | | | | | | | | | | (9271) ~ (all_52_12 = e0)
% 134.53/19.63 | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | REDUCE: (9257), (9268) imply:
% 134.53/19.63 | | | | | | | | | | | | | | | | | (9272) ~ (e3 = e0)
% 134.53/19.63 | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | REDUCE: (9250), (9268) imply:
% 134.53/19.63 | | | | | | | | | | | | | | | | | (9273) ~ (e2 = e0)
% 134.53/19.63 | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | REDUCE: (9258), (9268) imply:
% 134.53/19.63 | | | | | | | | | | | | | | | | | (9274) ~ (e1 = e0)
% 134.53/19.63 | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 134.53/19.63 | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.63 | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | (9275) all_57_15 = e0 & op(e0, e0) = e0
% 134.53/19.63 | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | ALPHA: (9275) implies:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | (9276) op(e0, e0) = e0
% 134.53/19.63 | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8991), (9276), (function-axioms) are
% 134.53/19.63 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #220.
% 134.53/19.63 | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.63 | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | (9277) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 134.53/19.63 | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 134.53/19.63 | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 134.53/19.63 | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 134.53/19.63 | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 134.53/19.63 | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | ALPHA: (9277) implies:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | (9278) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 134.53/19.63 | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 134.53/19.63 | | | | | | | | | | | | | | | | | | e0) = e0)
% 134.53/19.63 | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | BETA: splitting (9278) gives:
% 134.53/19.63 | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | (9279) all_57_9 = e0 & op(e3, e0) = e0
% 134.53/19.63 | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (9271), (9279), (function-axioms) are
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #618.
% 134.53/19.63 | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | (9280) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 134.53/19.63 | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | BETA: splitting (9280) gives:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | (9281) all_57_10 = e0 & op(e2, e0) = e0
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | ALPHA: (9281) implies:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | (9282) all_57_10 = e0
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | (9283) op(e2, e0) = e0
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | (9284) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9284) gives:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | (9285) all_57_2 = e3 & op(e2, e3) = e3
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9285) implies:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | (9286) all_57_2 = e3
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | (9287) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9287) gives:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | (9288) all_57_9 = e3 & op(e3, e0) = e3
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9288) implies:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | (9289) op(e3, e0) = e3
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | (9290) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9290) gives:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | (9291) all_57_0 = e0 & op(e3, e3) = e0
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9291) implies:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | (9292) op(e3, e3) = e0
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (8994), (9292), (function-axioms) are
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #534.
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | (9293) all_57_2 = e0 & op(e2, e3) = e0
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9286), (9293) are inconsistent by sub-proof
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | #521.
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | (9294) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9294) gives:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | (9295) all_57_6 = e0 & op(e1, e3) = e0
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (9269), (9295), (function-axioms) are
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #73.
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | (9296) all_57_12 = e0 & op(e0, e3) = e0
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9296) implies:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | (9297) all_57_12 = e0
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9298) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9298) gives:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9299) all_57_9 = e2 & op(e3, e0) = e2
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9299) implies:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9300) op(e3, e0) = e2
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (9289), (9300), (function-axioms) are
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #111.
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9301) all_57_10 = e2 & op(e2, e0) = e2
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9301) implies:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9302) op(e2, e0) = e2
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9283), (9302), (function-axioms) are
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #451.
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9303) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9303) gives:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9304) all_57_11 = e2 & op(e1, e0) = e2
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9304) implies:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9305) all_57_11 = e2
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9306) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9306) gives:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9307) all_57_0 = e2 & op(e3, e3) = e2
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9307) implies:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9308) op(e3, e3) = e2
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (9001), (9308), (function-axioms) are
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #536.
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9309) all_57_2 = e2 & op(e2, e3) = e2
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9309) implies:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9310) all_57_2 = e2
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9286), (9310) imply:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9311) e3 = e2
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9247), (9311) imply:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9312) all_57_8 = e2
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (215), (216),
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218), (9240), (9305), (9312), (function-axioms)
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #571.
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9313) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9313) gives:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9314) all_57_6 = e2 & op(e1, e3) = e2
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9314) implies:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9315) all_57_6 = e2
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9316) op(e1, e3) = e2
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9317) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9317) gives:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9318) all_57_0 = e1 & op(e3, e3) = e1
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9318) implies:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9319) op(e3, e3) = e1
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9320) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9320) gives:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9321) all_57_6 = e0 & op(e1, e3) = e0
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9321) implies:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9322) all_57_6 = e0
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (235), (9286), (9297), (9319),
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9322), (function-axioms) are inconsistent by
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #49.
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9323) all_57_7 = e0 & op(e1, e2) = e0
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (9270), (9323), (function-axioms) are
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #505.
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9324) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9324) gives:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9325) all_57_8 = e0 & op(e1, e1) = e0
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9325) implies:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9326) op(e1, e1) = e0
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9248), (9326), (function-axioms) are
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753.
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9327) all_57_11 = e0 & op(e1, e0) = e0
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9327) implies:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9328) all_57_11 = e0
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9305), (9328) imply:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9329) e2 = e0
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9315), (9329) imply:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9330) all_57_6 = e0
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (235), (9286), (9297), (9319),
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9330), (function-axioms) are inconsistent by
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #49.
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9331) all_57_2 = e1 & op(e2, e3) = e1
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9286), (9331) are inconsistent by sub-proof
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #453.
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9332) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (159), (163), (8979), (9316), (9332),
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #47.
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9333) all_57_12 = e2 & op(e0, e3) = e2
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9333) implies:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9334) all_57_12 = e2
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9297), (9334) imply:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9335) e2 = e0
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (9335) imply:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9336) $false
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9336) is inconsistent.
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9337) all_57_15 = e2 & op(e0, e0) = e2
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9337) implies:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9338) op(e0, e0) = e2
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8991), (9338), (function-axioms) are
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #636.
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | (9339) all_57_10 = e3 & op(e2, e0) = e3
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9339) implies:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | (9340) all_57_10 = e3
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9282), (9340) are inconsistent by sub-proof
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | #448.
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | (9341) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (160), (8991), (9243), (9341),
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | #46.
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | (9342) all_57_3 = e3 & op(e2, e2) = e3
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9342) implies:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | (9343) op(e2, e2) = e3
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (8999), (9343), (function-axioms) are
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #228.
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | (9344) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9344) gives:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | (9345) all_57_5 = e3 & op(e2, e1) = e3
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (9241), (9345), (function-axioms) are
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547.
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | (9346) all_57_10 = e3 & op(e2, e0) = e3
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9346) implies:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | (9347) all_57_10 = e3
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9282), (9347) are inconsistent by sub-proof
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | #448.
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | (9348) all_57_11 = e0 & op(e1, e0) = e0
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | ALPHA: (9348) implies:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | (9349) all_57_11 = e0
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | (9350) op(e1, e0) = e0
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | (9351) ~ (all_30_2 = e0)
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | REDUCE: (309), (9351) imply:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | (9352) ~ (all_8_2 = e0)
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | (9353) all_54_5 = e3
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (9353) imply:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | (9354) all_8_2 = e3
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8999), (9354) imply:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | (9355) $false
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9355) is inconsistent.
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | (9356) ~ (all_54_5 = e3)
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | (9357) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | (9358) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (45), (8994), (8999), (9001), (9350),
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | (9358), (function-axioms) are inconsistent by
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #43.
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | (9359) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9359) gives:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | (9360) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9360) gives:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (9361) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9361) implies:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (9362) op(e1, e3) = e1
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9357) gives:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (9363) all_54_5 = e2
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (9363) imply:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (9364) all_8_2 = e2
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (352), (9364) imply:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (9365) ~ (all_52_6 = e2)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8999), (9364) imply:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (9366) ~ (e3 = e2)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9367) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9367) gives:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9368) all_57_6 = e2 & op(e1, e3) = e2
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9368) implies:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9369) op(e1, e3) = e2
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (9362), (9369), (function-axioms) are
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #517.
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9370) all_57_7 = e2 & op(e1, e2) = e2
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (9365), (9370), (function-axioms) are
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #515.
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9371) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9371) gives:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9372) all_57_8 = e2 & op(e1, e1) = e2
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9372) implies:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9373) op(e1, e1) = e2
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (42), (45), (158), (160), (164), (199),
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206), (267), (354), (358), (8984), (8991),
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8993), (8994), (8999), (9001), (9350), (9352),
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9357), (9373), (function-axioms) are inconsistent
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #38.
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9374) all_57_11 = e2 & op(e1, e0) = e2
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9374) implies:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9375) all_57_11 = e2
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9349), (9375) are inconsistent by sub-proof
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #638.
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (9376) all_54_5 = e1 | all_54_5 = e0
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (8993), (9352), (9376) are inconsistent by
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #624.
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (9377) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2,
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9377) implies:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (9378) ~ (all_56_29 = e0)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (9379) op(e1, e0) = all_56_29
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9350), (9378), (9379), (function-axioms) are
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #45.
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | (9380) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9380) gives:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (9381) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9381) implies:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (9382) op(e2, e0) = e2
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (267), (358), (8993), (9352), (9357),
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (9382), (function-axioms) are inconsistent by
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #60.
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (9383) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9383) gives:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (9384) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9384) implies:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (9385) op(e1, e1) = e2
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (42), (45), (158), (160), (164), (199),
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (206), (267), (354), (358), (8984), (8991),
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (8993), (8994), (8999), (9001), (9350), (9352),
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (9357), (9385), (function-axioms) are inconsistent
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #38.
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (9386) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (42), (158), (160), (199), (267), (354),
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (8984), (8991), (8993), (8999), (9350), (9386),
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | #39.
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | (9387) all_30_2 = e0
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | (9388) ( ~ (all_30_0 = e3) & op(e0, e2) = all_30_0 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | $i(all_30_0)) | ( ~ (all_30_1 = e1) & op(e0, e0)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | = all_30_1 & $i(all_30_1))
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (309), (9387) imply:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | (9389) all_8_2 = e0
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | SIMP: (9389) implies:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | (9390) all_8_2 = e0
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | REDUCE: (347), (9390) imply:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | (9391) ~ (all_52_1 = e0)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | (9392) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (167), (8994), (9391), (9392),
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | #142.
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | (9393) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9393) gives:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | (9394) all_57_6 = e0 & op(e1, e3) = e0
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (9269), (9394), (function-axioms) are
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #73.
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | (9395) all_57_12 = e0 & op(e0, e3) = e0
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9395) implies:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | (9396) all_57_12 = e0
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | (9397) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9397) gives:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (9398) all_57_12 = e3 & op(e0, e3) = e3
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9398) implies:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (9399) all_57_12 = e3
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9396), (9399) are inconsistent by sub-proof
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | #492.
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (9400) all_57_13 = e3 & op(e0, e2) = e3
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9400) implies:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (9401) op(e0, e2) = e3
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9388) gives:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (9402) ~ (all_30_0 = e3) & op(e0, e2) = all_30_0 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_30_0)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9402) implies:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (9403) ~ (all_30_0 = e3)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (9404) op(e0, e2) = all_30_0
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_30_0,
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (9401), (9404) gives:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (9405) all_30_0 = e3
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9403), (9405) imply:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (9406) $false
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9406) is inconsistent.
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (9407) ~ (all_30_1 = e1) & op(e0, e0) = all_30_1 &
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_30_1)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8991), (9407), (function-axioms) are inconsistent
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #53.
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | (9408) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (157), (8991), (9242), (9408),
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | #37.
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.64 | | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.64 | | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | | End of split
% 134.53/19.64 | | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | | End of split
% 134.53/19.64 | | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | | End of split
% 134.53/19.64 | | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | End of split
% 134.53/19.64 | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | Case 2:
% 134.53/19.64 | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | (9409) ~ (all_12_1 = e3) & op(e1, e1) = all_12_1 &
% 134.53/19.64 | | | | | | | | | | | | | | $i(all_12_1)
% 134.53/19.64 | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | ALPHA: (9409) implies:
% 134.53/19.64 | | | | | | | | | | | | | | (9410) ~ (all_12_1 = e3)
% 134.53/19.64 | | | | | | | | | | | | | | (9411) op(e1, e1) = all_12_1
% 134.53/19.64 | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | | REF_CLOSE: (9248), (9410), (9411), (function-axioms) are
% 134.53/19.64 | | | | | | | | | | | | | | inconsistent by sub-proof #36.
% 134.53/19.64 | | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | End of split
% 134.53/19.64 | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | Case 2:
% 134.53/19.64 | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | (9412) all_57_11 = e3 & op(e1, e0) = e3
% 134.53/19.64 | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | REF_CLOSE: (160), (9243), (9412), (function-axioms) are
% 134.53/19.64 | | | | | | | | | | | | | inconsistent by sub-proof #750.
% 134.53/19.64 | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | End of split
% 134.53/19.64 | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | End of split
% 134.53/19.64 | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | End of split
% 134.53/19.64 | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | Case 2:
% 134.53/19.64 | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | (9413) all_16_2 = e2
% 134.53/19.64 | | | | | | | | | | (9414) ( ~ (all_16_0 = e1) & op(e2, e3) = all_16_0 &
% 134.53/19.64 | | | | | | | | | | $i(all_16_0)) | ( ~ (all_16_1 = e0) & op(e2, e2)
% 134.53/19.64 | | | | | | | | | | = all_16_1 & $i(all_16_1))
% 134.53/19.64 | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | COMBINE_EQS: (327), (9413) imply:
% 134.53/19.64 | | | | | | | | | | (9415) all_10_2 = e2
% 134.53/19.64 | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | SIMP: (9415) implies:
% 134.53/19.64 | | | | | | | | | | (9416) all_10_2 = e2
% 134.53/19.64 | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | REDUCE: (344), (9416) imply:
% 134.53/19.64 | | | | | | | | | | (9417) ~ (all_52_8 = e2)
% 134.53/19.64 | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | REDUCE: (346), (9416) imply:
% 134.53/19.64 | | | | | | | | | | (9418) ~ (all_52_12 = e2)
% 134.53/19.64 | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | REDUCE: (45), (9416) imply:
% 134.53/19.64 | | | | | | | | | | (9419) op(e3, e3) = e2
% 134.53/19.64 | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | BETA: splitting (76) gives:
% 134.53/19.64 | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | Case 1:
% 134.53/19.64 | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | (9420) ~ (all_30_2 = e0)
% 134.53/19.64 | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | REDUCE: (309), (9420) imply:
% 134.53/19.64 | | | | | | | | | | | (9421) ~ (all_8_2 = e0)
% 134.53/19.64 | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | BETA: splitting (199) gives:
% 134.53/19.64 | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | Case 1:
% 134.53/19.64 | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | (9422) all_54_5 = e3
% 134.53/19.64 | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | REF_CLOSE: (267), (8999), (9422) are inconsistent by
% 134.53/19.64 | | | | | | | | | | | | sub-proof #554.
% 134.53/19.64 | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | Case 2:
% 134.53/19.64 | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | (9423) ~ (all_54_5 = e3)
% 134.53/19.64 | | | | | | | | | | | | (9424) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 134.53/19.64 | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | BETA: splitting (9424) gives:
% 134.53/19.64 | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | Case 1:
% 134.53/19.64 | | | | | | | | | | | | |
% 134.53/19.64 | | | | | | | | | | | | | (9425) all_54_5 = e2
% 134.53/19.65 | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | COMBINE_EQS: (267), (9425) imply:
% 134.53/19.65 | | | | | | | | | | | | | (9426) all_8_2 = e2
% 134.53/19.65 | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | SIMP: (9426) implies:
% 134.53/19.65 | | | | | | | | | | | | | (9427) all_8_2 = e2
% 134.53/19.65 | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | REDUCE: (354), (9427) imply:
% 134.53/19.65 | | | | | | | | | | | | | (9428) ~ (all_52_7 = e2)
% 134.53/19.65 | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | REDUCE: (358), (9427) imply:
% 134.53/19.65 | | | | | | | | | | | | | (9429) ~ (all_52_13 = e2)
% 134.53/19.65 | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | REDUCE: (8999), (9427) imply:
% 134.53/19.65 | | | | | | | | | | | | | (9430) ~ (e3 = e2)
% 134.53/19.65 | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | REDUCE: (42), (9427) imply:
% 134.53/19.65 | | | | | | | | | | | | | (9431) op(e2, e2) = e2
% 134.53/19.65 | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | BETA: splitting (213) gives:
% 134.53/19.65 | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | Case 1:
% 134.53/19.65 | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | (9432) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 134.53/19.65 | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 134.53/19.65 | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (9418), (9429), (9432),
% 134.53/19.65 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.65 | | | | | | | | | | | | | | #440.
% 134.53/19.65 | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | Case 2:
% 134.53/19.65 | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | (9433) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 134.53/19.65 | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 134.53/19.65 | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | BETA: splitting (9433) gives:
% 134.53/19.65 | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | Case 1:
% 134.53/19.65 | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | (9434) all_57_11 = e2 & op(e1, e0) = e2
% 134.53/19.65 | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | ALPHA: (9434) implies:
% 134.53/19.65 | | | | | | | | | | | | | | | (9435) op(e1, e0) = e2
% 134.53/19.65 | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 134.53/19.65 | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | Case 1:
% 134.53/19.65 | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | (9436) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 134.53/19.65 | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 134.53/19.65 | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | BETA: splitting (9436) gives:
% 134.53/19.65 | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.65 | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | (9437) all_57_12 = e2 & op(e0, e3) = e2
% 134.53/19.65 | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | ALPHA: (9437) implies:
% 134.53/19.65 | | | | | | | | | | | | | | | | | (9438) all_57_12 = e2
% 134.53/19.65 | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 134.53/19.65 | | | | | | | | | | | | | | | | | (9419), (9438), (function-axioms) are inconsistent
% 134.53/19.65 | | | | | | | | | | | | | | | | | by sub-proof #290.
% 134.53/19.65 | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.65 | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | (9439) all_57_13 = e2 & op(e0, e2) = e2
% 134.53/19.65 | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (9428), (9439), (function-axioms) are
% 134.53/19.65 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #100.
% 134.53/19.65 | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | End of split
% 134.53/19.65 | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | Case 2:
% 134.53/19.65 | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | (9440) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 134.53/19.65 | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 134.53/19.65 | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | BETA: splitting (9440) gives:
% 134.53/19.65 | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.65 | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | (9441) all_57_14 = e2 & op(e0, e1) = e2
% 134.53/19.65 | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | ALPHA: (9441) implies:
% 134.53/19.65 | | | | | | | | | | | | | | | | | (9442) op(e0, e1) = e2
% 134.53/19.65 | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 134.53/19.65 | | | | | | | | | | | | | | | | | e2, e1, e0, simplifying with (157), (9442) gives:
% 134.53/19.65 | | | | | | | | | | | | | | | | | (9443) all_52_11 = e2
% 134.53/19.65 | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 134.53/19.65 | | | | | | | | | | | | | | | | | e2, e0, e1, simplifying with (160), (9435) gives:
% 134.53/19.65 | | | | | | | | | | | | | | | | | (9444) all_52_14 = e2
% 134.53/19.65 | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | REDUCE: (118), (9443) imply:
% 134.53/19.65 | | | | | | | | | | | | | | | | | (9445) ~ (all_52_9 = e2)
% 134.53/19.65 | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | REDUCE: (366), (9444) imply:
% 134.53/19.65 | | | | | | | | | | | | | | | | | (9446) ~ (all_6_2 = e2)
% 134.53/19.65 | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | BETA: splitting (8997) gives:
% 134.53/19.65 | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.65 | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | (9447) ~ (all_12_0 = e2) & op(e1, e0) = all_12_0 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | $i(all_12_0)
% 134.53/19.65 | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | ALPHA: (9447) implies:
% 134.53/19.65 | | | | | | | | | | | | | | | | | | (9448) ~ (all_12_0 = e2)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | (9449) op(e1, e0) = all_12_0
% 134.53/19.65 | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | REF_CLOSE: (9435), (9448), (9449), (function-axioms) are
% 134.53/19.65 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #35.
% 134.53/19.65 | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.65 | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | (9450) ~ (all_12_1 = e3) & op(e1, e1) = all_12_1 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | $i(all_12_1)
% 134.53/19.65 | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | ALPHA: (9450) implies:
% 134.53/19.65 | | | | | | | | | | | | | | | | | | (9451) ~ (all_12_1 = e3)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | (9452) op(e1, e1) = all_12_1
% 134.53/19.65 | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 134.53/19.65 | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.65 | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | (9453) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 134.53/19.65 | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (42), (8999), (9419), (9431), (9453),
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | #80.
% 134.53/19.65 | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.65 | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | (9454) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.65 | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | BETA: splitting (9454) gives:
% 134.53/19.65 | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | (9455) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | BETA: splitting (9455) gives:
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | (9456) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9456) implies:
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | (9457) op(e1, e1) = e3
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9451), (9452), (9457), (function-axioms) are
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #36.
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | (9458) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2,
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9458) implies:
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | (9459) op(e2, e1) = e2
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (9445), (9459), (function-axioms) are
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #770.
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | (9460) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | BETA: splitting (9460) gives:
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | (9461) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9461) implies:
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | (9462) op(e2, e0) = e2
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (9429), (9462), (function-axioms) are
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | (9463) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9463) gives:
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | (9464) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9464) implies:
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | (9465) op(e1, e1) = e2
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (8992), (9465), (function-axioms) are
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | (9466) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9466) implies:
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | (9467) op(e0, e0) = all_56_31
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | (9468) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9468) gives:
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | (9469) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27))
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (42), (158), (199), (267), (354), (8991),
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | (8993), (8999), (9467), (9469), (function-axioms)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #41.
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | (9470) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9435), (9442), (9470),
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | #428.
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.65 | | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.65 | | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | End of split
% 134.53/19.65 | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.65 | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | (9471) all_57_15 = e2 & op(e0, e0) = e2
% 134.53/19.65 | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | ALPHA: (9471) implies:
% 134.53/19.65 | | | | | | | | | | | | | | | | | (9472) op(e0, e0) = e2
% 134.53/19.65 | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8991), (9472), (function-axioms) are
% 134.53/19.65 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #636.
% 134.53/19.65 | | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | | End of split
% 134.53/19.65 | | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | End of split
% 134.53/19.65 | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | Case 2:
% 134.53/19.65 | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | (9473) all_57_15 = e2 & op(e0, e0) = e2
% 134.53/19.65 | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | ALPHA: (9473) implies:
% 134.53/19.65 | | | | | | | | | | | | | | | (9474) op(e0, e0) = e2
% 134.53/19.65 | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | | REF_CLOSE: (6), (8991), (9474), (function-axioms) are
% 134.53/19.65 | | | | | | | | | | | | | | | inconsistent by sub-proof #636.
% 134.53/19.65 | | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | | End of split
% 134.53/19.65 | | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | End of split
% 134.53/19.65 | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | Case 2:
% 134.53/19.65 | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | (9475) all_54_5 = e1 | all_54_5 = e0
% 134.53/19.65 | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | | REF_CLOSE: (267), (8993), (9421), (9475) are inconsistent by
% 134.53/19.65 | | | | | | | | | | | | | sub-proof #624.
% 134.53/19.65 | | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | | End of split
% 134.53/19.65 | | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | End of split
% 134.53/19.65 | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | Case 2:
% 134.53/19.65 | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | (9476) all_30_2 = e0
% 134.53/19.65 | | | | | | | | | | | (9477) ( ~ (all_30_0 = e3) & op(e0, e2) = all_30_0 &
% 134.53/19.65 | | | | | | | | | | | $i(all_30_0)) | ( ~ (all_30_1 = e1) & op(e0, e0)
% 134.53/19.65 | | | | | | | | | | | = all_30_1 & $i(all_30_1))
% 134.53/19.65 | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | COMBINE_EQS: (309), (9476) imply:
% 134.53/19.65 | | | | | | | | | | | (9478) all_8_2 = e0
% 134.53/19.65 | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | SIMP: (9478) implies:
% 134.53/19.65 | | | | | | | | | | | (9479) all_8_2 = e0
% 134.53/19.65 | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | REDUCE: (354), (9479) imply:
% 134.53/19.65 | | | | | | | | | | | (9480) ~ (all_52_7 = e0)
% 134.53/19.65 | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | REDUCE: (8999), (9479) imply:
% 134.53/19.65 | | | | | | | | | | | (9481) ~ (e3 = e0)
% 134.53/19.65 | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | REDUCE: (8993), (9479) imply:
% 134.53/19.65 | | | | | | | | | | | (9482) ~ (e1 = e0)
% 134.53/19.65 | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | REDUCE: (42), (9479) imply:
% 134.53/19.65 | | | | | | | | | | | (9483) op(e2, e2) = e0
% 134.53/19.65 | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | BETA: splitting (9477) gives:
% 134.53/19.65 | | | | | | | | | | |
% 134.53/19.65 | | | | | | | | | | | Case 1:
% 134.53/19.65 | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | (9484) ~ (all_30_0 = e3) & op(e0, e2) = all_30_0 &
% 134.53/19.66 | | | | | | | | | | | | $i(all_30_0)
% 134.53/19.66 | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | ALPHA: (9484) implies:
% 134.53/19.66 | | | | | | | | | | | | (9485) ~ (all_30_0 = e3)
% 134.53/19.66 | | | | | | | | | | | | (9486) op(e0, e2) = all_30_0
% 134.53/19.66 | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | BETA: splitting (9414) gives:
% 134.53/19.66 | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | Case 1:
% 134.53/19.66 | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | (9487) ~ (all_16_0 = e1) & op(e2, e3) = all_16_0 &
% 134.53/19.66 | | | | | | | | | | | | | $i(all_16_0)
% 134.53/19.66 | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | ALPHA: (9487) implies:
% 134.53/19.66 | | | | | | | | | | | | | (9488) ~ (all_16_0 = e1)
% 134.53/19.66 | | | | | | | | | | | | | (9489) op(e2, e3) = all_16_0
% 134.53/19.66 | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7,
% 134.53/19.66 | | | | | | | | | | | | | all_30_0, e2, e0, simplifying with (158), (9486)
% 134.53/19.66 | | | | | | | | | | | | | gives:
% 134.53/19.66 | | | | | | | | | | | | | (9490) all_52_7 = all_30_0
% 134.53/19.66 | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 134.53/19.66 | | | | | | | | | | | | | all_16_0, e3, e2, simplifying with (167), (9489)
% 134.53/19.66 | | | | | | | | | | | | | gives:
% 134.53/19.66 | | | | | | | | | | | | | (9491) all_52_1 = all_16_0
% 134.53/19.66 | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | COMBINE_EQS: (247), (9490) imply:
% 134.53/19.66 | | | | | | | | | | | | | (9492) all_54_13 = all_30_0
% 134.53/19.66 | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | REDUCE: (125), (9490) imply:
% 134.53/19.66 | | | | | | | | | | | | | (9493) ~ (all_52_11 = all_30_0)
% 134.53/19.66 | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | SIMP: (9493) implies:
% 134.53/19.66 | | | | | | | | | | | | | (9494) ~ (all_52_11 = all_30_0)
% 134.53/19.66 | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | REDUCE: (8980), (9490) imply:
% 134.53/19.66 | | | | | | | | | | | | | (9495) ~ (all_30_0 = e1)
% 134.53/19.66 | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | REDUCE: (9480), (9490) imply:
% 134.53/19.66 | | | | | | | | | | | | | (9496) ~ (all_30_0 = e0)
% 134.53/19.66 | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | BETA: splitting (191) gives:
% 134.53/19.66 | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | Case 1:
% 134.53/19.66 | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | (9497) all_54_13 = e3
% 134.53/19.66 | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | REF_CLOSE: (9485), (9492), (9497) are inconsistent by
% 134.53/19.66 | | | | | | | | | | | | | | sub-proof #54.
% 134.53/19.66 | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | Case 2:
% 134.53/19.66 | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | (9498) ~ (all_54_13 = e3)
% 134.53/19.66 | | | | | | | | | | | | | | (9499) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 134.53/19.66 | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | BETA: splitting (9499) gives:
% 134.53/19.66 | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | Case 1:
% 134.53/19.66 | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | (9500) all_54_13 = e2
% 134.53/19.66 | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | COMBINE_EQS: (9492), (9500) imply:
% 134.53/19.66 | | | | | | | | | | | | | | | (9501) all_30_0 = e2
% 134.53/19.66 | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | SIMP: (9501) implies:
% 134.53/19.66 | | | | | | | | | | | | | | | (9502) all_30_0 = e2
% 134.53/19.66 | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | REDUCE: (9494), (9502) imply:
% 134.53/19.66 | | | | | | | | | | | | | | | (9503) ~ (all_52_11 = e2)
% 134.53/19.66 | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | REDUCE: (9485), (9502) imply:
% 134.53/19.66 | | | | | | | | | | | | | | | (9504) ~ (e3 = e2)
% 134.53/19.66 | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 134.53/19.66 | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | Case 1:
% 134.53/19.66 | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | (9505) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 134.53/19.66 | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 134.53/19.66 | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9483), (9488), (9489), (9505),
% 134.53/19.66 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.66 | | | | | | | | | | | | | | | | #415.
% 134.53/19.66 | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | Case 2:
% 134.53/19.66 | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | (9506) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 134.53/19.66 | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 134.53/19.66 | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | BETA: splitting (9506) gives:
% 134.53/19.66 | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.66 | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | (9507) all_57_5 = e1 & op(e2, e1) = e1
% 134.53/19.66 | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | ALPHA: (9507) implies:
% 134.53/19.66 | | | | | | | | | | | | | | | | | (9508) all_57_5 = e1
% 134.53/19.66 | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 134.53/19.66 | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.66 | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | (9509) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 134.53/19.66 | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 134.53/19.66 | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | BETA: splitting (9509) gives:
% 134.53/19.66 | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.66 | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | (9510) all_57_12 = e2 & op(e0, e3) = e2
% 134.53/19.66 | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | ALPHA: (9510) implies:
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | (9511) all_57_12 = e2
% 134.53/19.66 | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | (9419), (9511), (function-axioms) are inconsistent
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | by sub-proof #290.
% 134.53/19.66 | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.66 | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | (9512) all_57_13 = e2 & op(e0, e2) = e2
% 134.53/19.66 | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | ALPHA: (9512) implies:
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | (9513) all_57_13 = e2
% 134.53/19.66 | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 134.53/19.66 | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | (9514) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | BETA: splitting (9514) gives:
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | (9515) all_57_4 = e2 & op(e3, e1) = e2
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (9417), (9515), (function-axioms) are
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #442.
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | (9516) all_57_5 = e2 & op(e2, e1) = e2
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9516) implies:
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | (9517) all_57_5 = e2
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9508), (9517) are inconsistent by sub-proof
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | #418.
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | (9518) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | BETA: splitting (9518) gives:
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | (9519) all_57_8 = e2 & op(e1, e1) = e2
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9519) implies:
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | (9520) op(e1, e1) = e2
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (8992), (9520), (function-axioms) are
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | (9521) all_57_14 = e2 & op(e0, e1) = e2
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9521) implies:
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | (9522) all_57_14 = e2
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (208), (209), (211),
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | (9513), (9522) are inconsistent by sub-proof #401.
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.66 | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.66 | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.66 | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | (9523) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 134.53/19.66 | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 134.53/19.66 | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (157), (8991), (9503), (9523),
% 134.53/19.66 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.66 | | | | | | | | | | | | | | | | | | #34.
% 134.53/19.66 | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | End of split
% 134.53/19.66 | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.66 | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | (9524) all_57_10 = e1 & op(e2, e0) = e1
% 134.53/19.66 | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | ALPHA: (9524) implies:
% 134.53/19.66 | | | | | | | | | | | | | | | | | (9525) op(e2, e0) = e1
% 134.53/19.66 | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8983), (9525), (function-axioms) are
% 134.53/19.66 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #180.
% 134.53/19.66 | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | End of split
% 134.53/19.66 | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | End of split
% 134.53/19.66 | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | Case 2:
% 134.53/19.66 | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | (9526) all_54_13 = e1 | all_54_13 = e0
% 134.53/19.66 | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | REF_CLOSE: (247), (8980), (9480), (9526) are inconsistent by
% 134.53/19.66 | | | | | | | | | | | | | | | sub-proof #470.
% 134.53/19.66 | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | End of split
% 134.53/19.66 | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | End of split
% 134.53/19.66 | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | Case 2:
% 134.53/19.66 | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | (9527) ~ (all_16_1 = e0) & op(e2, e2) = all_16_1 &
% 134.53/19.66 | | | | | | | | | | | | | $i(all_16_1)
% 134.53/19.66 | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | REF_CLOSE: (9483), (9527), (function-axioms) are inconsistent
% 134.53/19.66 | | | | | | | | | | | | | by sub-proof #380.
% 134.53/19.66 | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | End of split
% 134.53/19.66 | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | Case 2:
% 134.53/19.66 | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | (9528) ~ (all_30_1 = e1) & op(e0, e0) = all_30_1 &
% 134.53/19.66 | | | | | | | | | | | | $i(all_30_1)
% 134.53/19.66 | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | REF_CLOSE: (8991), (9528), (function-axioms) are inconsistent
% 134.53/19.66 | | | | | | | | | | | | by sub-proof #53.
% 134.53/19.66 | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | End of split
% 134.53/19.66 | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | End of split
% 134.53/19.66 | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | End of split
% 134.53/19.66 | | | | | | | | |
% 134.53/19.66 | | | | | | | | Case 2:
% 134.53/19.66 | | | | | | | | |
% 134.53/19.66 | | | | | | | | | (9529) all_14_2 = e3
% 134.53/19.66 | | | | | | | | |
% 134.53/19.66 | | | | | | | | | COMBINE_EQS: (329), (9529) imply:
% 134.53/19.66 | | | | | | | | | (9530) all_8_2 = e3
% 134.53/19.66 | | | | | | | | |
% 134.53/19.66 | | | | | | | | | SIMP: (9530) implies:
% 134.53/19.66 | | | | | | | | | (9531) all_8_2 = e3
% 134.53/19.66 | | | | | | | | |
% 134.53/19.66 | | | | | | | | | COMBINE_EQS: (322), (9531) imply:
% 134.53/19.66 | | | | | | | | | (9532) all_22_2 = e3
% 134.53/19.66 | | | | | | | | |
% 134.53/19.66 | | | | | | | | | REDUCE: (347), (9531) imply:
% 134.53/19.66 | | | | | | | | | (9533) ~ (all_52_1 = e3)
% 134.53/19.66 | | | | | | | | |
% 134.53/19.66 | | | | | | | | | REDUCE: (350), (9531) imply:
% 134.53/19.66 | | | | | | | | | (9534) ~ (all_52_4 = e3)
% 134.53/19.66 | | | | | | | | |
% 134.53/19.66 | | | | | | | | | REDUCE: (354), (9531) imply:
% 134.53/19.66 | | | | | | | | | (9535) ~ (all_52_7 = e3)
% 134.53/19.66 | | | | | | | | |
% 134.53/19.66 | | | | | | | | | REDUCE: (356), (9531) imply:
% 134.53/19.66 | | | | | | | | | (9536) ~ (all_52_9 = e3)
% 134.53/19.66 | | | | | | | | |
% 134.53/19.66 | | | | | | | | | REDUCE: (358), (9531) imply:
% 134.53/19.66 | | | | | | | | | (9537) ~ (all_52_13 = e3)
% 134.53/19.66 | | | | | | | | |
% 134.53/19.66 | | | | | | | | | BETA: splitting (226) gives:
% 134.53/19.66 | | | | | | | | |
% 134.53/19.66 | | | | | | | | | Case 1:
% 134.53/19.66 | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | (9538) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 134.53/19.66 | | | | | | | | | | & op(e2, e2) = e3)
% 134.53/19.66 | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | BETA: splitting (9538) gives:
% 134.53/19.66 | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | Case 1:
% 134.53/19.66 | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | (9539) all_57_2 = e3 & op(e2, e3) = e3
% 134.53/19.66 | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | ALPHA: (9539) implies:
% 134.53/19.66 | | | | | | | | | | | (9540) op(e2, e3) = e3
% 134.53/19.66 | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | REF_CLOSE: (167), (9533), (9540), (function-axioms) are
% 134.53/19.66 | | | | | | | | | | | inconsistent by sub-proof #763.
% 134.53/19.66 | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | Case 2:
% 134.53/19.66 | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | (9541) all_57_3 = e3 & op(e2, e2) = e3
% 134.53/19.66 | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | ALPHA: (9541) implies:
% 134.53/19.66 | | | | | | | | | | | (9542) all_57_3 = e3
% 134.53/19.66 | | | | | | | | | | | (9543) op(e2, e2) = e3
% 134.53/19.66 | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | BETA: splitting (55) gives:
% 134.53/19.66 | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | Case 1:
% 134.53/19.66 | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | (9544) ~ (all_16_2 = e2)
% 134.53/19.66 | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | REDUCE: (327), (9544) imply:
% 134.53/19.66 | | | | | | | | | | | | (9545) ~ (all_10_2 = e2)
% 134.53/19.66 | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | BETA: splitting (64) gives:
% 134.53/19.66 | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | Case 1:
% 134.53/19.66 | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | (9546) ~ (all_22_2 = e3)
% 134.53/19.66 | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | REDUCE: (9532), (9546) imply:
% 134.53/19.66 | | | | | | | | | | | | | (9547) $false
% 134.53/19.66 | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | CLOSE: (9547) is inconsistent.
% 134.53/19.66 | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | Case 2:
% 134.53/19.66 | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | (9548) ( ~ (all_22_0 = e0) & op(e3, e2) = all_22_0 &
% 134.53/19.66 | | | | | | | | | | | | | $i(all_22_0)) | ( ~ (all_22_1 = e1) & op(e3, e3)
% 134.53/19.66 | | | | | | | | | | | | | = all_22_1 & $i(all_22_1))
% 134.53/19.66 | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | BETA: splitting (73) gives:
% 134.53/19.66 | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | Case 1:
% 134.53/19.66 | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | (9549) ~ (all_28_2 = e3)
% 134.53/19.66 | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | REDUCE: (316), (9549) imply:
% 134.53/19.66 | | | | | | | | | | | | | | (9550) ~ (all_6_2 = e3)
% 134.53/19.66 | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 134.53/19.66 | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | Case 1:
% 134.53/19.66 | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | (9551) ~ (all_32_2 = e1)
% 134.53/19.66 | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | REDUCE: (312), (9551) imply:
% 134.53/19.66 | | | | | | | | | | | | | | | (9552) ~ (all_10_2 = e1)
% 134.53/19.66 | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 134.53/19.66 | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | Case 1:
% 134.53/19.66 | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | (9553) all_54_0 = e3
% 134.53/19.66 | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (9553) imply:
% 134.53/19.66 | | | | | | | | | | | | | | | | (9554) all_10_2 = e3
% 134.53/19.66 | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | SIMP: (9554) implies:
% 134.53/19.66 | | | | | | | | | | | | | | | | (9555) all_10_2 = e3
% 134.53/19.66 | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | REDUCE: (346), (9555) imply:
% 134.53/19.66 | | | | | | | | | | | | | | | | (9556) ~ (all_52_12 = e3)
% 134.53/19.66 | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | REDUCE: (45), (9555) imply:
% 134.53/19.66 | | | | | | | | | | | | | | | | (9557) op(e3, e3) = e3
% 134.53/19.66 | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 134.53/19.66 | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.66 | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | (9558) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 134.53/19.66 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.66 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 134.53/19.66 | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 134.53/19.66 | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.66 | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.53/19.66 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.66 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 134.53/19.66 | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 134.53/19.66 | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 134.53/19.66 | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.53/19.66 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.66 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.66 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.66 | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.66 | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.53/19.66 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.66 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.66 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 134.53/19.66 | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | BETA: splitting (9558) gives:
% 134.53/19.66 | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.66 | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | (9559) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 134.53/19.66 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.66 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 134.53/19.66 | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 134.53/19.66 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 134.53/19.66 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 134.53/19.66 | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 134.53/19.66 | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (9557), (9559), (function-axioms) are
% 134.53/19.66 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #623.
% 134.53/19.66 | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.66 | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | (9560) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 134.53/19.66 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.66 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.66 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 134.53/19.66 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.66 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 134.53/19.66 | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (9556), (9557), (9560), (function-axioms)
% 134.53/19.66 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #553.
% 134.53/19.66 | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | End of split
% 134.53/19.66 | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.66 | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | (9561) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.53/19.66 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.66 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.66 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.53/19.66 | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.53/19.66 | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.53/19.66 | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.53/19.66 | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.53/19.66 | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.53/19.66 | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.66 | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 134.53/19.66 | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 134.53/19.66 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.66 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 134.53/19.66 | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.66 | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 134.53/19.66 | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.66 | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 134.53/19.66 | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 134.53/19.66 | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 134.53/19.66 | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 134.53/19.66 | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.66 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 134.53/19.66 | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 134.53/19.66 | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 134.53/19.66 | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 134.53/19.66 | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 134.53/19.66 | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.66 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 134.53/19.66 | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 134.53/19.66 | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 134.53/19.66 | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.66 | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 134.53/19.66 | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 134.53/19.66 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 134.53/19.66 | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 134.53/19.66 | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 134.53/19.66 | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 134.53/19.66 | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.66 | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.66 | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.66 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.66 | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.66 | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.66 | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.66 | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | BETA: splitting (9561) gives:
% 134.53/19.66 | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.66 | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | (9562) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 134.53/19.66 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 134.53/19.66 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 134.53/19.66 | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 134.53/19.66 | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 134.53/19.66 | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 134.53/19.66 | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 134.53/19.66 | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 134.53/19.66 | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 134.53/19.66 | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (9543), (9550), (9562),
% 134.53/19.66 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.66 | | | | | | | | | | | | | | | | | | #324.
% 134.53/19.66 | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.66 | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | (9563) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.53/19.66 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 134.53/19.66 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.66 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.66 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.66 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.53/19.66 | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.66 | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.53/19.66 | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.53/19.66 | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.53/19.66 | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.66 | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.53/19.66 | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.53/19.66 | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.53/19.66 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.53/19.66 | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.53/19.66 | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.53/19.66 | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.66 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.66 | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.66 | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.66 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.66 | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.66 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.66 | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.66 | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.66 | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.66 | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | BETA: splitting (9563) gives:
% 134.53/19.66 | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.66 | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | (9564) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 134.53/19.66 | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | ALPHA: (9564) implies:
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | (9565) op(e2, e2) = e0
% 134.53/19.66 | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9543), (9565), (function-axioms) are
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641.
% 134.53/19.66 | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.66 | | | | | | | | | | | | | | | | | | |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | (9566) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 134.53/19.66 | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 134.53/19.66 | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (39), (157), (160), (194), (334), (364),
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | (8984), (8991), (8992), (9550), (9566),
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | #30.
% 134.53/19.67 | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | End of split
% 134.53/19.67 | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | End of split
% 134.53/19.67 | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | End of split
% 134.53/19.67 | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | Case 2:
% 134.53/19.67 | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | (9567) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 134.53/19.67 | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | REF_CLOSE: (278), (8994), (9545), (9552), (9567) are
% 134.53/19.67 | | | | | | | | | | | | | | | | inconsistent by sub-proof #777.
% 134.53/19.67 | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | End of split
% 134.53/19.67 | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | Case 2:
% 134.53/19.67 | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | (9568) all_32_2 = e1
% 134.53/19.67 | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | COMBINE_EQS: (312), (9568) imply:
% 134.53/19.67 | | | | | | | | | | | | | | | (9569) all_10_2 = e1
% 134.53/19.67 | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | SIMP: (9569) implies:
% 134.53/19.67 | | | | | | | | | | | | | | | (9570) all_10_2 = e1
% 134.53/19.67 | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | COMBINE_EQS: (280), (9570) imply:
% 134.53/19.67 | | | | | | | | | | | | | | | (9571) all_50_2 = e1
% 134.53/19.67 | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | REDUCE: (336), (9570) imply:
% 134.53/19.67 | | | | | | | | | | | | | | | (9572) ~ (all_52_1 = e1)
% 134.53/19.67 | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | REDUCE: (342), (9570) imply:
% 134.53/19.67 | | | | | | | | | | | | | | | (9573) ~ (all_52_4 = e1)
% 134.53/19.67 | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | REDUCE: (45), (9570) imply:
% 134.53/19.67 | | | | | | | | | | | | | | | (9574) op(e3, e3) = e1
% 134.53/19.67 | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 134.53/19.67 | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | Case 1:
% 134.53/19.67 | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | (9575) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 134.53/19.67 | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 134.53/19.67 | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (167), (9543), (9572), (9575),
% 134.53/19.67 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 134.53/19.67 | | | | | | | | | | | | | | | | #77.
% 134.53/19.67 | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | Case 2:
% 134.53/19.67 | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | (9576) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 134.53/19.67 | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 134.53/19.67 | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | BETA: splitting (9576) gives:
% 134.53/19.67 | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.67 | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | (9577) all_57_5 = e1 & op(e2, e1) = e1
% 134.53/19.67 | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | ALPHA: (9577) implies:
% 134.53/19.67 | | | | | | | | | | | | | | | | | (9578) op(e2, e1) = e1
% 134.53/19.67 | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | BETA: splitting (9548) gives:
% 134.53/19.67 | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.67 | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | (9579) ~ (all_22_0 = e0) & op(e3, e2) = all_22_0 &
% 134.53/19.67 | | | | | | | | | | | | | | | | | | $i(all_22_0)
% 134.53/19.67 | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | ALPHA: (9579) implies:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | (9580) ~ (all_22_0 = e0)
% 134.53/19.67 | | | | | | | | | | | | | | | | | | (9581) op(e3, e2) = all_22_0
% 134.53/19.67 | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e1,
% 134.53/19.67 | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (165), (9578) gives:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | (9582) all_52_9 = e1
% 134.53/19.67 | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4,
% 134.53/19.67 | | | | | | | | | | | | | | | | | | all_22_0, e2, e3, simplifying with (170), (9581)
% 134.53/19.67 | | | | | | | | | | | | | | | | | | gives:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | (9583) all_52_4 = all_22_0
% 134.53/19.67 | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (9583) imply:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | (9584) all_54_1 = all_22_0
% 134.53/19.67 | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | REDUCE: (134), (9583) imply:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | (9585) ~ (all_52_8 = all_22_0)
% 134.53/19.67 | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | SIMP: (9585) implies:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | (9586) ~ (all_52_8 = all_22_0)
% 134.53/19.67 | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | REDUCE: (133), (9583) imply:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | (9587) ~ (all_52_12 = all_22_0)
% 134.53/19.67 | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | SIMP: (9587) implies:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | (9588) ~ (all_52_12 = all_22_0)
% 134.53/19.67 | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | REDUCE: (9534), (9583) imply:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | (9589) ~ (all_22_0 = e3)
% 134.53/19.67 | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | REDUCE: (9573), (9583) imply:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | (9590) ~ (all_22_0 = e1)
% 134.53/19.67 | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | REDUCE: (123), (9582) imply:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | (9591) ~ (all_52_8 = e1)
% 134.53/19.67 | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | REDUCE: (117), (9582) imply:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | (9592) ~ (all_52_13 = e1)
% 134.53/19.67 | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | REDUCE: (362), (9582) imply:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | (9593) ~ (all_6_2 = e1)
% 134.53/19.67 | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | SIMP: (9593) implies:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | (9594) ~ (all_6_2 = e1)
% 134.53/19.67 | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 134.53/19.67 | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | (9595) all_54_10 = e3
% 134.53/19.67 | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (9550), (9595) are inconsistent by
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | sub-proof #742.
% 134.53/19.67 | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | (9596) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 134.53/19.67 | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | (9597) all_54_1 = e3
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9584), (9597) imply:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | (9598) all_22_0 = e3
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | REDUCE: (9589), (9598) imply:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | (9599) $false
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | CLOSE: (9599) is inconsistent.
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | (9600) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | BETA: splitting (9600) gives:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | (9601) all_54_1 = e2
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9584), (9601) imply:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | (9602) all_22_0 = e2
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | REDUCE: (9586), (9602) imply:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | (9603) ~ (all_52_8 = e2)
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | REDUCE: (9588), (9602) imply:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | (9604) ~ (all_52_12 = e2)
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9596) gives:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | (9605) all_54_10 = e2
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (8992), (9605) are inconsistent by
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | sub-proof #741.
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | (9606) all_54_10 = e1 | all_54_10 = e0
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9606) gives:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | (9607) all_54_10 = e1
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (9594), (9607) are inconsistent by
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #736.
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | (9608) all_54_10 = e0
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (9608) imply:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | (9609) all_6_2 = e0
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9609) implies:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | (9610) all_6_2 = e0
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (9610) imply:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | (9611) ~ (all_52_8 = e0)
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (9610) imply:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | (9612) op(e1, e1) = e0
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (9613) ~ (all_50_2 = e1)
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9571), (9613) imply:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (9614) $false
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9614) is inconsistent.
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (9615) ( ~ (all_50_0 = e2) & op(e1, e3) = all_50_0 &
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_50_0)) | ( ~ (all_50_1 = e0) & op(e1, e1)
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | = all_50_1 & $i(all_50_1))
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | (9616) all_54_2 = e3
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (9616) imply:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | (9617) all_52_8 = e3
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9617) implies:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | (9618) all_52_8 = e3
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (9618) imply:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | (9619) ~ (all_52_11 = e3)
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9619) implies:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | (9620) ~ (all_52_11 = e3)
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (9618) imply:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | (9621) ~ (all_52_12 = e3)
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9621) implies:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | (9622) ~ (all_52_12 = e3)
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | (9623) all_54_3 = e3
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (9622), (9623) are inconsistent by
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #216.
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | (9624) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9624) gives:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9625) all_54_3 = e2
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (9625) imply:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9626) all_52_12 = e2
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9626) implies:
% 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9627) all_52_12 = e2
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9604), (9627) imply:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9628) $false
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9628) is inconsistent.
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9629) all_54_3 = e1 | all_54_3 = e0
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9629) gives:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9630) all_54_3 = e1
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (9630) imply:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9631) all_52_12 = e1
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9631) implies:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9632) all_52_12 = e1
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8982), (9632) imply:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9633) $false
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9633) is inconsistent.
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9634) all_54_3 = e0
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (9634) imply:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9635) all_52_12 = e0
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9635) implies:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9636) all_52_12 = e0
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (9636) imply:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9637) ~ (all_52_13 = e0)
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9637) implies:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9638) ~ (all_52_13 = e0)
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9639) all_54_7 = e3
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (9639) imply:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9640) all_52_13 = e3
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9537), (9640) imply:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9641) $false
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9641) is inconsistent.
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9642) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9643) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9643) gives:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9644) all_57_0 = e2 & op(e3, e3) = e2
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9644) implies:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9645) op(e3, e3) = e2
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9574), (9645), (function-axioms) are
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743.
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9646) all_57_2 = e2 & op(e2, e3) = e2
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9646) implies:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9647) op(e2, e3) = e2
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (145), (167), (259), (8983), (9638), (9642),
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9647), (function-axioms) are inconsistent by
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #312.
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9648) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9648) gives:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9649) all_57_6 = e2 & op(e1, e3) = e2
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9649) implies:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9650) op(e1, e3) = e2
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9615) gives:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9651) ~ (all_50_0 = e2) & op(e1, e3) = all_50_0 &
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_50_0)
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9651) implies:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9652) ~ (all_50_0 = e2)
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9653) op(e1, e3) = all_50_0
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9650), (9652), (9653), (function-axioms) are
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #735.
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9654) ~ (all_50_1 = e0) & op(e1, e1) = all_50_1 &
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_50_1)
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9612), (9654), (function-axioms) are inconsistent
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #719.
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9655) all_57_12 = e2 & op(e0, e3) = e2
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9655) implies:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9656) all_57_12 = e2
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (157), (158), (211), (8991), (9535),
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9620), (9656), (function-axioms) are inconsistent
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #29.
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | (9657) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (9591), (9603), (9611), (9657) are
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #71.
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | End of split
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | (9658) all_54_1 = e1 | all_54_1 = e0
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9580), (9584), (9590), (9658) are inconsistent by
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | sub-proof #306.
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | End of split
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | End of split
% 135.13/19.67 | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | End of split
% 135.13/19.67 | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | Case 2:
% 135.13/19.67 | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | (9659) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 &
% 135.13/19.67 | | | | | | | | | | | | | | | | | | $i(all_22_1)
% 135.13/19.67 | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | REF_CLOSE: (9574), (9659), (function-axioms) are inconsistent
% 135.13/19.67 | | | | | | | | | | | | | | | | | | by sub-proof #305.
% 135.13/19.67 | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | End of split
% 135.13/19.67 | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | Case 2:
% 135.13/19.67 | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | (9660) all_57_10 = e1 & op(e2, e0) = e1
% 135.13/19.67 | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | ALPHA: (9660) implies:
% 135.13/19.67 | | | | | | | | | | | | | | | | | (9661) op(e2, e0) = e1
% 135.13/19.67 | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8983), (9661), (function-axioms) are
% 135.13/19.67 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #180.
% 135.13/19.67 | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | End of split
% 135.13/19.67 | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | End of split
% 135.13/19.67 | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | End of split
% 135.13/19.67 | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | Case 2:
% 135.13/19.67 | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | (9662) all_28_2 = e3
% 135.13/19.67 | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | COMBINE_EQS: (316), (9662) imply:
% 135.13/19.67 | | | | | | | | | | | | | | (9663) all_6_2 = e3
% 135.13/19.67 | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | SIMP: (9663) implies:
% 135.13/19.67 | | | | | | | | | | | | | | (9664) all_6_2 = e3
% 135.13/19.67 | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | REDUCE: (364), (9664) imply:
% 135.13/19.67 | | | | | | | | | | | | | | (9665) ~ (all_52_11 = e3)
% 135.13/19.67 | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | REDUCE: (366), (9664) imply:
% 135.13/19.67 | | | | | | | | | | | | | | (9666) ~ (all_52_14 = e3)
% 135.13/19.67 | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | REDUCE: (39), (9664) imply:
% 135.13/19.67 | | | | | | | | | | | | | | (9667) op(e1, e1) = e3
% 135.13/19.67 | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 135.13/19.67 | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | Case 1:
% 135.13/19.67 | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | (9668) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 135.13/19.67 | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 135.13/19.67 | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | BETA: splitting (9668) gives:
% 135.13/19.67 | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | Case 1:
% 135.13/19.67 | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | (9669) all_57_12 = e3 & op(e0, e3) = e3
% 135.13/19.67 | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | ALPHA: (9669) implies:
% 135.13/19.67 | | | | | | | | | | | | | | | | (9670) all_57_12 = e3
% 135.13/19.67 | | | | | | | | | | | | | | | | (9671) op(e0, e3) = e3
% 135.13/19.67 | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 135.13/19.67 | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | Case 1:
% 135.13/19.67 | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | (9672) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 135.13/19.67 | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 135.13/19.67 | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | BETA: splitting (9672) gives:
% 135.13/19.67 | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | Case 1:
% 135.13/19.67 | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | (9673) all_57_9 = e3 & op(e3, e0) = e3
% 135.13/19.67 | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | ALPHA: (9673) implies:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | (9674) op(e3, e0) = e3
% 135.13/19.67 | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | BETA: splitting (8997) gives:
% 135.13/19.67 | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | Case 1:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | (9675) ~ (all_12_0 = e2) & op(e1, e0) = all_12_0 &
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | $i(all_12_0)
% 135.13/19.67 | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | ALPHA: (9675) implies:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | (9676) ~ (all_12_0 = e2)
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | (9677) op(e1, e0) = all_12_0
% 135.13/19.67 | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e3,
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (159), (9671) gives:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | (9678) all_52_3 = e3
% 135.13/19.67 | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | all_12_0, e0, e1, simplifying with (160), (9677)
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | gives:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | (9679) all_52_14 = all_12_0
% 135.13/19.67 | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | e3, e0, e3, simplifying with (168), (9674) gives:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | (9680) all_52_12 = e3
% 135.13/19.67 | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (9679) imply:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | (9681) all_54_11 = all_12_0
% 135.13/19.67 | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | REDUCE: (141), (9679) imply:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | (9682) ~ (all_52_2 = all_12_0)
% 135.13/19.67 | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | REDUCE: (140), (9678) imply:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | (9683) ~ (all_52_7 = e3)
% 135.13/19.67 | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | REDUCE: (139), (9678) imply:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | (9684) ~ (all_52_11 = e3)
% 135.13/19.67 | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | REDUCE: (113), (9680) imply:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | (9685) ~ (all_52_13 = e3)
% 135.13/19.67 | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | REDUCE: (346), (9680) imply:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | (9686) ~ (all_10_2 = e3)
% 135.13/19.67 | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | SIMP: (9686) implies:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | (9687) ~ (all_10_2 = e3)
% 135.13/19.67 | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | REDUCE: (110), (9679) imply:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | (9688) ~ (all_52_13 = all_12_0)
% 135.13/19.67 | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | REDUCE: (9666), (9679) imply:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | (9689) ~ (all_12_0 = e3)
% 135.13/19.67 | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | REDUCE: (8984), (9679) imply:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | (9690) ~ (all_12_0 = e1)
% 135.13/19.67 | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | Case 1:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | (9691) all_54_0 = e3
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (9691) imply:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | (9692) all_10_2 = e3
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | REDUCE: (9687), (9692) imply:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | (9693) $false
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | CLOSE: (9693) is inconsistent.
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | Case 2:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | (9694) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | (9695) all_54_11 = e3
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9681), (9689), (9695) are inconsistent by
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | sub-proof #52.
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | (9696) ~ (all_54_11 = e3)
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | (9697) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9697) gives:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | (9698) all_54_11 = e2
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9676), (9681), (9698) are inconsistent by
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | sub-proof #51.
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | (9699) ~ (all_54_11 = e2)
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | (9700) all_54_11 = e1 | all_54_11 = e0
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9694) gives:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | (9701) all_54_0 = e2
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (9701) imply:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | (9702) all_10_2 = e2
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9545), (9702) imply:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | (9703) $false
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9703) is inconsistent.
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | (9704) ~ (all_54_0 = e2)
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | (9705) all_54_0 = e1 | all_54_0 = e0
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9700) gives:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (9706) all_54_11 = e1
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9681), (9690), (9706) are inconsistent by
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #50.
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (9707) all_54_11 = e0
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9681), (9707) imply:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (9708) all_12_0 = e0
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9708) implies:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (9709) all_12_0 = e0
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9682), (9709) imply:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (9710) ~ (all_52_2 = e0)
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9688), (9709) imply:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (9711) ~ (all_52_13 = e0)
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9689), (9709) imply:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (9712) ~ (e3 = e0)
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9676), (9709) imply:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (9713) ~ (e2 = e0)
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9690), (9709) imply:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (9714) ~ (e1 = e0)
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9677), (9709) imply:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (9715) op(e1, e0) = e0
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | (9716) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9716) gives:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | (9717) all_57_0 = e0 & op(e3, e3) = e0
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9717) implies:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | (9718) op(e3, e3) = e0
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (278), (8994), (9705), (9718),
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | #263.
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | (9719) all_57_2 = e0 & op(e2, e3) = e0
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9719) implies:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | (9720) all_57_2 = e0
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9721) all_54_7 = e3
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (9537), (9721) are inconsistent by
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #338.
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9722) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9723) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9723) gives:
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9724) all_57_2 = e1 & op(e2, e3) = e1
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9724) implies:
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9725) all_57_2 = e1
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9720), (9725) are inconsistent by sub-proof
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #646.
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9726) all_57_3 = e1 & op(e2, e2) = e1
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9726) implies:
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9727) op(e2, e2) = e1
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9543), (9727), (function-axioms) are
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #325.
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9728) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9728) gives:
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9729) all_57_5 = e1 & op(e2, e1) = e1
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9729) implies:
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9730) op(e2, e1) = e1
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9731) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9731) gives:
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9732) all_57_0 = e2 & op(e3, e3) = e2
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9732) implies:
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9733) op(e3, e3) = e2
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (9545), (9733), (function-axioms) are
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #536.
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9734) all_57_2 = e2 & op(e2, e3) = e2
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9734) implies:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9735) op(e2, e3) = e2
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (145), (167), (259), (8983), (9711), (9722),
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9735), (function-axioms) are inconsistent by
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #312.
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9736) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9736) gives:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9737) all_57_6 = e2 & op(e1, e3) = e2
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9737) implies:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9738) all_57_6 = e2
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9739) op(e1, e3) = e2
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9740) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9740) gives:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9741) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9741) gives:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9742) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9742) implies:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9743) op(e3, e3) = e2
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (233), (237), (9542), (9738), (9743),
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #360.
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9744) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9744) implies:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9745) ~ (all_56_29 = e0)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9746) op(e1, e0) = all_56_29
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9715), (9745), (9746), (function-axioms) are
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #45.
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9747) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9747) gives:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9748) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3,
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9748) implies:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9749) op(e3, e3) = e0
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (278), (8994), (9705), (9749),
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #263.
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9750) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2,
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9750) implies:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9751) op(e2, e3) = e2
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (145), (167), (259), (8983), (9711), (9722),
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9751), (function-axioms) are inconsistent by
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #312.
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9752) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9752) gives:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9753) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (9715), (9739), (9753),
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #28.
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9754) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9754) gives:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9755) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9755) implies:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9756) op(e2, e2) = e0
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9543), (9756), (function-axioms) are
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641.
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9757) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9757) gives:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9758) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9758) implies:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9759) ~ (all_56_19 = e1)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9760) op(e2, e1) = all_56_19
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9730), (9759), (9760), (function-axioms) are
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #106.
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9761) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9761) implies:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9762) op(e0, e0) = all_56_31
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9763) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9763) gives:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9764) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27))
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8991), (9730), (9762), (9764),
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #56.
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9765) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (8984), (9715), (9765), (function-axioms)
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #40.
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9766) all_57_12 = e2 & op(e0, e3) = e2
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9766) implies:
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9767) all_57_12 = e2
% 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (157), (158), (211), (8991), (9535),
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9665), (9767), (function-axioms) are inconsistent
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #29.
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9768) all_57_10 = e1 & op(e2, e0) = e1
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9768) implies:
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9769) op(e2, e0) = e1
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8983), (9769), (function-axioms) are
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #180.
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | (9770) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (163), (9670), (9710), (9770),
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | #27.
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | End of split
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | | End of split
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | End of split
% 135.15/19.69 | | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | | Case 2:
% 135.15/19.69 | | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | (9771) ~ (all_12_1 = e3) & op(e1, e1) = all_12_1 &
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | $i(all_12_1)
% 135.15/19.69 | | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | ALPHA: (9771) implies:
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | (9772) ~ (all_12_1 = e3)
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | (9773) op(e1, e1) = all_12_1
% 135.15/19.69 | | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9667), (9772), (9773), (function-axioms) are
% 135.15/19.69 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #36.
% 135.15/19.69 | | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | | End of split
% 135.15/19.69 | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | Case 2:
% 135.15/19.69 | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | | (9774) all_57_10 = e3 & op(e2, e0) = e3
% 135.15/19.69 | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (9537), (9774), (function-axioms) are
% 135.15/19.69 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749.
% 135.15/19.69 | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | End of split
% 135.15/19.69 | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | Case 2:
% 135.15/19.69 | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | (9775) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 135.15/19.69 | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 135.15/19.69 | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (160), (8991), (9666), (9775),
% 135.15/19.69 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.15/19.69 | | | | | | | | | | | | | | | | | #46.
% 135.15/19.69 | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | End of split
% 135.15/19.69 | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | Case 2:
% 135.15/19.69 | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | (9776) all_57_13 = e3 & op(e0, e2) = e3
% 135.15/19.69 | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | REF_CLOSE: (158), (9535), (9776), (function-axioms) are
% 135.15/19.69 | | | | | | | | | | | | | | | | inconsistent by sub-proof #556.
% 135.15/19.69 | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | End of split
% 135.15/19.69 | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | Case 2:
% 135.15/19.69 | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | (9777) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 135.15/19.69 | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 135.15/19.69 | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | REF_CLOSE: (8), (157), (8991), (9665), (9777),
% 135.15/19.69 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.15/19.69 | | | | | | | | | | | | | | | #37.
% 135.15/19.69 | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | End of split
% 135.15/19.69 | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | End of split
% 135.15/19.69 | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | End of split
% 135.15/19.69 | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | Case 2:
% 135.15/19.69 | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | (9778) all_16_2 = e2
% 135.15/19.69 | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | COMBINE_EQS: (327), (9778) imply:
% 135.15/19.69 | | | | | | | | | | | | (9779) all_10_2 = e2
% 135.15/19.69 | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | REDUCE: (336), (9779) imply:
% 135.15/19.69 | | | | | | | | | | | | (9780) ~ (all_52_1 = e2)
% 135.15/19.69 | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | REDUCE: (342), (9779) imply:
% 135.15/19.69 | | | | | | | | | | | | (9781) ~ (all_52_4 = e2)
% 135.15/19.69 | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | REDUCE: (344), (9779) imply:
% 135.15/19.69 | | | | | | | | | | | | (9782) ~ (all_52_8 = e2)
% 135.15/19.69 | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | REDUCE: (346), (9779) imply:
% 135.15/19.69 | | | | | | | | | | | | (9783) ~ (all_52_12 = e2)
% 135.15/19.69 | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | REDUCE: (45), (9779) imply:
% 135.15/19.69 | | | | | | | | | | | | (9784) op(e3, e3) = e2
% 135.15/19.69 | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | BETA: splitting (73) gives:
% 135.15/19.69 | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | Case 1:
% 135.15/19.69 | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | (9785) ~ (all_28_2 = e3)
% 135.15/19.69 | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | REDUCE: (316), (9785) imply:
% 135.15/19.69 | | | | | | | | | | | | | (9786) ~ (all_6_2 = e3)
% 135.15/19.69 | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | BETA: splitting (206) gives:
% 135.15/19.69 | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | Case 1:
% 135.15/19.69 | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | (9787) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 135.15/19.69 | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.15/19.69 | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.15/19.69 | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 135.15/19.69 | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.15/19.69 | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.15/19.69 | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.15/19.69 | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.15/19.69 | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.15/19.69 | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 135.15/19.69 | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 135.15/19.69 | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 135.15/19.69 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.15/19.69 | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 135.15/19.69 | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 135.15/19.69 | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.15/19.69 | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.15/19.69 | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 135.15/19.69 | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.15/19.69 | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.15/19.69 | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.15/19.69 | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 135.15/19.69 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.15/19.69 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.15/19.69 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.15/19.69 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 135.15/19.69 | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.15/19.69 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 135.15/19.69 | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | BETA: splitting (9787) gives:
% 135.15/19.69 | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | Case 1:
% 135.15/19.69 | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | (9788) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 135.15/19.69 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.15/19.69 | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.15/19.69 | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 135.15/19.69 | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.15/19.69 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.15/19.69 | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.15/19.69 | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.15/19.69 | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.15/19.69 | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 135.15/19.69 | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 135.15/19.69 | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 135.15/19.69 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.15/19.69 | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 135.15/19.69 | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | REF_CLOSE: (6), (170), (9534), (9784), (9788),
% 135.15/19.69 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.15/19.69 | | | | | | | | | | | | | | | #254.
% 135.15/19.69 | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | Case 2:
% 135.15/19.69 | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | (9789) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 135.15/19.69 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.15/19.69 | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.15/19.69 | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 135.15/19.69 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.15/19.69 | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.15/19.69 | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.15/19.69 | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 135.15/19.69 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.15/19.69 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.15/19.69 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.15/19.69 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 135.15/19.69 | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.15/19.69 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 135.15/19.69 | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | REF_CLOSE: (5), (167), (9780), (9784), (9789),
% 135.15/19.69 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.15/19.69 | | | | | | | | | | | | | | | #443.
% 135.15/19.69 | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | End of split
% 135.15/19.69 | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | Case 2:
% 135.15/19.69 | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | (9790) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 135.15/19.69 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.15/19.69 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.15/19.69 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.15/19.69 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 135.15/19.69 | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.15/19.69 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 135.15/19.69 | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 135.15/19.69 | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.15/19.69 | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 135.15/19.69 | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.15/19.69 | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.15/19.69 | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.15/19.69 | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 135.15/19.69 | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 135.15/19.69 | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.15/19.69 | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 135.15/19.69 | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.15/19.69 | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 135.15/19.69 | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 135.15/19.69 | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 135.15/19.69 | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 135.15/19.69 | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.15/19.69 | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.15/19.69 | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 135.15/19.69 | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 135.15/19.69 | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 135.15/19.69 | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 135.15/19.69 | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 135.15/19.69 | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 135.15/19.69 | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 135.15/19.69 | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.15/19.69 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 135.15/19.69 | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 135.15/19.69 | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.15/19.69 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 135.15/19.69 | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 135.15/19.69 | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 135.15/19.69 | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.15/19.69 | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.15/19.69 | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 135.15/19.69 | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.15/19.69 | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 135.15/19.69 | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 135.15/19.69 | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 135.15/19.69 | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 135.15/19.69 | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 135.15/19.69 | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 135.15/19.69 | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 135.15/19.69 | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.15/19.69 | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.15/19.69 | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.15/19.69 | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.15/19.69 | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.15/19.69 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.15/19.69 | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.15/19.69 | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.15/19.69 | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | BETA: splitting (9790) gives:
% 135.15/19.69 | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | Case 1:
% 135.15/19.69 | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | (9791) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 135.15/19.69 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.15/19.69 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.15/19.69 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.15/19.69 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 135.15/19.69 | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.15/19.69 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 135.15/19.69 | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 135.15/19.69 | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.15/19.69 | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 135.15/19.69 | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.15/19.69 | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.15/19.69 | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.15/19.69 | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 135.15/19.69 | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (9543), (9786), (9791),
% 135.15/19.69 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.15/19.69 | | | | | | | | | | | | | | | #324.
% 135.15/19.69 | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | Case 2:
% 135.15/19.69 | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | (9792) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 135.15/19.69 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.15/19.69 | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 135.15/19.69 | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 135.15/19.69 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.15/19.69 | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.15/19.69 | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.15/19.69 | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.15/19.69 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.15/19.69 | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.15/19.69 | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.15/19.69 | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 135.15/19.69 | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 135.15/19.69 | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.15/19.69 | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.15/19.69 | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 135.15/19.69 | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 135.15/19.69 | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.15/19.69 | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 135.15/19.69 | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.15/19.69 | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 135.15/19.69 | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 135.15/19.69 | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 135.15/19.69 | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.15/19.69 | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.15/19.69 | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 135.15/19.69 | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 135.15/19.69 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.15/19.69 | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 135.15/19.69 | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 135.15/19.69 | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.15/19.69 | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.15/19.69 | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.15/19.69 | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.15/19.69 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.15/19.69 | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 135.15/19.69 | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.15/19.69 | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.15/19.69 | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.15/19.69 | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.15/19.69 | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.15/19.69 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.15/19.69 | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.15/19.69 | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.15/19.69 | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | BETA: splitting (9792) gives:
% 135.15/19.69 | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | Case 1:
% 135.15/19.69 | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | (9793) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 135.15/19.69 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 135.15/19.69 | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 135.15/19.69 | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.15/19.69 | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 135.15/19.69 | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 135.15/19.69 | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 135.15/19.69 | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | ALPHA: (9793) implies:
% 135.15/19.69 | | | | | | | | | | | | | | | | (9794) op(e2, e2) = e0
% 135.15/19.69 | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9543), (9794), (function-axioms) are
% 135.15/19.69 | | | | | | | | | | | | | | | | inconsistent by sub-proof #641.
% 135.15/19.69 | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | Case 2:
% 135.15/19.69 | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | (9795) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.15/19.69 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.15/19.69 | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.15/19.69 | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.15/19.69 | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 135.15/19.69 | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 135.15/19.69 | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.15/19.69 | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.15/19.69 | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 135.15/19.69 | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 135.15/19.69 | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.15/19.69 | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 135.15/19.69 | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.15/19.69 | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 135.15/19.69 | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 135.15/19.69 | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 135.15/19.69 | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.15/19.69 | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.15/19.69 | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 135.15/19.69 | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 135.15/19.69 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.15/19.69 | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 135.15/19.69 | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 135.15/19.69 | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.15/19.69 | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.15/19.69 | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.15/19.69 | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.15/19.69 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.15/19.69 | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 135.15/19.69 | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.15/19.69 | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.15/19.69 | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.15/19.69 | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.15/19.69 | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.15/19.69 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.15/19.69 | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.15/19.69 | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.15/19.69 | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | BETA: splitting (9795) gives:
% 135.15/19.69 | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | Case 1:
% 135.15/19.69 | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | (9796) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.15/19.69 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 135.15/19.69 | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.15/19.69 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.15/19.69 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 135.15/19.69 | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 135.15/19.69 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 135.15/19.69 | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | ALPHA: (9796) implies:
% 135.15/19.69 | | | | | | | | | | | | | | | | | (9797) op(e1, e1) = e2
% 135.15/19.69 | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (8992), (9797), (function-axioms) are
% 135.15/19.69 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 135.15/19.69 | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | Case 2:
% 135.15/19.69 | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | (9798) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.15/19.69 | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 135.15/19.69 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 135.15/19.69 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.15/19.69 | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 135.15/19.69 | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 135.15/19.69 | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.15/19.69 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 135.15/19.69 | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 135.15/19.69 | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.15/19.69 | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.15/19.69 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.15/19.69 | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 135.15/19.69 | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.15/19.69 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 135.15/19.69 | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.15/19.69 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.15/19.69 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.15/19.69 | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.15/19.69 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.15/19.69 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 135.15/19.69 | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 135.15/19.69 | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.15/19.69 | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 135.15/19.69 | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 135.15/19.69 | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 135.15/19.69 | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 135.15/19.69 | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 135.15/19.69 | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 135.15/19.69 | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | ALPHA: (9798) implies:
% 135.15/19.69 | | | | | | | | | | | | | | | | | (9799) op(e0, e0) = all_56_31
% 135.15/19.69 | | | | | | | | | | | | | | | | | (9800) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 135.15/19.69 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.15/19.69 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.15/19.69 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.15/19.69 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 135.15/19.69 | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.15/19.69 | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 135.15/19.69 | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 135.15/19.69 | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.15/19.69 | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.15/19.69 | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 135.15/19.69 | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 135.15/19.69 | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 135.15/19.69 | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.15/19.69 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.15/19.69 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 135.15/19.69 | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.15/19.69 | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 135.15/19.69 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 135.15/19.69 | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 135.15/19.69 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.15/19.69 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 135.15/19.69 | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.15/19.69 | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 135.15/19.69 | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.15/19.69 | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 135.15/19.69 | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (39), (157), (160), (194), (334), (364),
% 135.15/19.69 | | | | | | | | | | | | | | | | | (8984), (8991), (8992), (9786), (9799), (9800),
% 135.15/19.69 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.15/19.69 | | | | | | | | | | | | | | | | | #31.
% 135.15/19.69 | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | End of split
% 135.15/19.69 | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | End of split
% 135.15/19.69 | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | End of split
% 135.15/19.69 | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | End of split
% 135.15/19.69 | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | Case 2:
% 135.15/19.69 | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | (9801) all_28_2 = e3
% 135.15/19.69 | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | COMBINE_EQS: (316), (9801) imply:
% 135.15/19.69 | | | | | | | | | | | | | (9802) all_6_2 = e3
% 135.15/19.69 | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | SIMP: (9802) implies:
% 135.15/19.69 | | | | | | | | | | | | | (9803) all_6_2 = e3
% 135.15/19.69 | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | COMBINE_EQS: (302), (9803) imply:
% 135.15/19.69 | | | | | | | | | | | | | (9804) all_36_2 = e3
% 135.15/19.69 | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | REDUCE: (361), (9803) imply:
% 135.15/19.69 | | | | | | | | | | | | | (9805) ~ (all_52_8 = e3)
% 135.15/19.69 | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | REDUCE: (366), (9803) imply:
% 135.15/19.69 | | | | | | | | | | | | | (9806) ~ (all_52_14 = e3)
% 135.15/19.69 | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | REDUCE: (39), (9803) imply:
% 135.15/19.69 | | | | | | | | | | | | | (9807) op(e1, e1) = e3
% 135.15/19.69 | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | BETA: splitting (85) gives:
% 135.15/19.69 | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | Case 1:
% 135.15/19.69 | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | (9808) ~ (all_36_2 = e3)
% 135.15/19.69 | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | REDUCE: (9804), (9808) imply:
% 135.15/19.69 | | | | | | | | | | | | | | (9809) $false
% 135.15/19.69 | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | CLOSE: (9809) is inconsistent.
% 135.15/19.69 | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | Case 2:
% 135.15/19.69 | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | (9810) ( ~ (all_36_0 = e0) & op(e3, e1) = all_36_0 &
% 135.15/19.69 | | | | | | | | | | | | | | $i(all_36_0)) | ( ~ (all_36_1 = e2) & op(e3, e3)
% 135.15/19.69 | | | | | | | | | | | | | | = all_36_1 & $i(all_36_1))
% 135.15/19.69 | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | BETA: splitting (9810) gives:
% 135.15/19.69 | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | Case 1:
% 135.15/19.69 | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | (9811) ~ (all_36_0 = e0) & op(e3, e1) = all_36_0 &
% 135.15/19.69 | | | | | | | | | | | | | | | $i(all_36_0)
% 135.15/19.69 | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | ALPHA: (9811) implies:
% 135.15/19.69 | | | | | | | | | | | | | | | (9812) ~ (all_36_0 = e0)
% 135.15/19.69 | | | | | | | | | | | | | | | (9813) op(e3, e1) = all_36_0
% 135.15/19.69 | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 135.15/19.69 | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | Case 1:
% 135.15/19.69 | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | (9814) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 135.15/19.69 | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 135.15/19.69 | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | BETA: splitting (9814) gives:
% 135.15/19.69 | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | Case 1:
% 135.15/19.69 | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | (9815) all_57_9 = e3 & op(e3, e0) = e3
% 135.15/19.69 | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | ALPHA: (9815) implies:
% 135.15/19.69 | | | | | | | | | | | | | | | | | (9816) all_57_9 = e3
% 135.15/19.69 | | | | | | | | | | | | | | | | | (9817) op(e3, e0) = e3
% 135.15/19.69 | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | BETA: splitting (8997) gives:
% 135.15/19.69 | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | Case 1:
% 135.15/19.69 | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | | (9818) ~ (all_12_0 = e2) & op(e1, e0) = all_12_0 &
% 135.15/19.69 | | | | | | | | | | | | | | | | | | $i(all_12_0)
% 135.15/19.69 | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | | ALPHA: (9818) implies:
% 135.15/19.69 | | | | | | | | | | | | | | | | | | (9819) ~ (all_12_0 = e2)
% 135.15/19.69 | | | | | | | | | | | | | | | | | | (9820) op(e1, e0) = all_12_0
% 135.15/19.69 | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 135.15/19.69 | | | | | | | | | | | | | | | | | | all_12_0, e0, e1, simplifying with (160), (9820)
% 135.15/19.69 | | | | | | | | | | | | | | | | | | gives:
% 135.15/19.69 | | | | | | | | | | | | | | | | | | (9821) all_52_14 = all_12_0
% 135.15/19.69 | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 135.15/19.69 | | | | | | | | | | | | | | | | | | e3, e0, e3, simplifying with (168), (9817) gives:
% 135.15/19.69 | | | | | | | | | | | | | | | | | | (9822) all_52_12 = e3
% 135.15/19.69 | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8,
% 135.15/19.69 | | | | | | | | | | | | | | | | | | all_36_0, e1, e3, simplifying with (169), (9813)
% 135.15/19.69 | | | | | | | | | | | | | | | | | | gives:
% 135.15/19.69 | | | | | | | | | | | | | | | | | | (9823) all_52_8 = all_36_0
% 135.15/19.69 | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (9823) imply:
% 135.15/19.69 | | | | | | | | | | | | | | | | | | (9824) all_54_2 = all_36_0
% 135.15/19.69 | | | | | | | | | | | | | | | | | |
% 135.15/19.69 | | | | | | | | | | | | | | | | | | REDUCE: (134), (9823) imply:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | (9825) ~ (all_52_4 = all_36_0)
% 135.15/19.70 | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | REDUCE: (9805), (9823) imply:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | (9826) ~ (all_36_0 = e3)
% 135.15/19.70 | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | REDUCE: (9782), (9823) imply:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | (9827) ~ (all_36_0 = e2)
% 135.15/19.70 | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 135.15/19.70 | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | Case 1:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | (9828) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 135.15/19.70 | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | BETA: splitting (9828) gives:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | Case 1:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | (9829) all_57_9 = e2 & op(e3, e0) = e2
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | ALPHA: (9829) implies:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | (9830) all_57_9 = e2
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (234),
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | (238), (9534), (9784), (9830), (function-axioms)
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #250.
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | Case 2:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | (9831) all_57_10 = e2 & op(e2, e0) = e2
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | ALPHA: (9831) implies:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | (9832) all_57_10 = e2
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | (9833) all_54_2 = e3
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9824), (9833) imply:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | (9834) all_36_0 = e3
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | REDUCE: (9826), (9834) imply:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | (9835) $false
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | CLOSE: (9835) is inconsistent.
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | (9836) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | (9837) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9837) gives:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | (9838) all_57_6 = e2 & op(e1, e3) = e2
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9838) implies:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | (9839) all_57_6 = e2
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (231),
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | (233), (237), (9542), (9784), (9832), (9839),
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | #361.
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | (9840) all_57_7 = e2 & op(e1, e2) = e2
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9840) implies:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | (9841) all_57_7 = e2
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | (9842) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9842) gives:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | (9843) all_57_1 = e1 & op(e3, e2) = e1
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9843) implies:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | (9844) op(e3, e2) = e1
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (203), (271), (9534), (9781), (9812),
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | (9824), (9825), (9827), (9836), (9844),
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | #235.
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | (9845) all_57_3 = e1 & op(e2, e2) = e1
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9845) implies:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | (9846) op(e2, e2) = e1
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9543), (9846), (function-axioms) are
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #325.
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | (9847) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9847) gives:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | (9848) all_57_7 = e1 & op(e1, e2) = e1
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9848) implies:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | (9849) all_57_7 = e1
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9841), (9849) are inconsistent by sub-proof
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | #288.
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | (9850) all_57_13 = e1 & op(e0, e2) = e1
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (8980), (9850), (function-axioms) are
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #178.
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | (9851) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (208), (8990), (9807), (9816),
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | (9832), (9851), (function-axioms) are inconsistent
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #26.
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | End of split
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | End of split
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | End of split
% 135.15/19.70 | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | Case 2:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | (9852) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 135.15/19.70 | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | BETA: splitting (9852) gives:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | Case 1:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | (9853) all_57_11 = e2 & op(e1, e0) = e2
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | ALPHA: (9853) implies:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | (9854) op(e1, e0) = e2
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9819), (9820), (9854), (function-axioms) are
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #35.
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | Case 2:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | (9855) all_57_15 = e2 & op(e0, e0) = e2
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | ALPHA: (9855) implies:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | (9856) op(e0, e0) = e2
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8991), (9856), (function-axioms) are
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #636.
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | | End of split
% 135.15/19.70 | | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | End of split
% 135.15/19.70 | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | Case 2:
% 135.15/19.70 | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | (9857) ~ (all_12_1 = e3) & op(e1, e1) = all_12_1 &
% 135.15/19.70 | | | | | | | | | | | | | | | | | | $i(all_12_1)
% 135.15/19.70 | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | ALPHA: (9857) implies:
% 135.15/19.70 | | | | | | | | | | | | | | | | | | (9858) ~ (all_12_1 = e3)
% 135.15/19.70 | | | | | | | | | | | | | | | | | | (9859) op(e1, e1) = all_12_1
% 135.15/19.70 | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | | REF_CLOSE: (9807), (9858), (9859), (function-axioms) are
% 135.15/19.70 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #36.
% 135.15/19.70 | | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | End of split
% 135.15/19.70 | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | Case 2:
% 135.15/19.70 | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | (9860) all_57_10 = e3 & op(e2, e0) = e3
% 135.15/19.70 | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (9537), (9860), (function-axioms) are
% 135.15/19.70 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749.
% 135.15/19.70 | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | End of split
% 135.15/19.70 | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | Case 2:
% 135.15/19.70 | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | (9861) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 135.15/19.70 | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 135.15/19.70 | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (160), (8991), (9806), (9861),
% 135.15/19.70 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.15/19.70 | | | | | | | | | | | | | | | | #46.
% 135.15/19.70 | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | End of split
% 135.15/19.70 | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | Case 2:
% 135.15/19.70 | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | (9862) ~ (all_36_1 = e2) & op(e3, e3) = all_36_1 &
% 135.15/19.70 | | | | | | | | | | | | | | | $i(all_36_1)
% 135.15/19.70 | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | REF_CLOSE: (9784), (9862), (function-axioms) are inconsistent
% 135.15/19.70 | | | | | | | | | | | | | | | by sub-proof #342.
% 135.15/19.70 | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | End of split
% 135.15/19.70 | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | End of split
% 135.15/19.70 | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | End of split
% 135.15/19.70 | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | End of split
% 135.15/19.70 | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | End of split
% 135.15/19.70 | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | Case 2:
% 135.15/19.70 | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | (9863) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 135.15/19.70 | | | | | | | | | | e3 & op(e2, e0) = e3)
% 135.15/19.70 | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | BETA: splitting (9863) gives:
% 135.15/19.70 | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | Case 1:
% 135.15/19.70 | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | (9864) all_57_5 = e3 & op(e2, e1) = e3
% 135.15/19.70 | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | REF_CLOSE: (165), (9536), (9864), (function-axioms) are
% 135.15/19.70 | | | | | | | | | | | inconsistent by sub-proof #547.
% 135.15/19.70 | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | Case 2:
% 135.15/19.70 | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | (9865) all_57_10 = e3 & op(e2, e0) = e3
% 135.15/19.70 | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | REF_CLOSE: (164), (9537), (9865), (function-axioms) are
% 135.15/19.70 | | | | | | | | | | | inconsistent by sub-proof #749.
% 135.15/19.70 | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | End of split
% 135.15/19.70 | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | End of split
% 135.15/19.70 | | | | | | | | |
% 135.15/19.70 | | | | | | | | End of split
% 135.15/19.70 | | | | | | | |
% 135.15/19.70 | | | | | | | End of split
% 135.15/19.70 | | | | | | |
% 135.15/19.70 | | | | | | Case 2:
% 135.15/19.70 | | | | | | |
% 135.15/19.70 | | | | | | | (9866) all_10_2 = e0
% 135.15/19.70 | | | | | | | (9867) ( ~ (all_10_0 = e2) & op(e0, e3) = all_10_0 &
% 135.15/19.70 | | | | | | | $i(all_10_0)) | ( ~ (all_10_1 = e1) & op(e0, e0) =
% 135.15/19.70 | | | | | | | all_10_1 & $i(all_10_1))
% 135.15/19.70 | | | | | | |
% 135.15/19.70 | | | | | | | REDUCE: (336), (9866) imply:
% 135.15/19.70 | | | | | | | (9868) ~ (all_52_1 = e0)
% 135.15/19.70 | | | | | | |
% 135.15/19.70 | | | | | | | REDUCE: (338), (9866) imply:
% 135.15/19.70 | | | | | | | (9869) ~ (all_52_2 = e0)
% 135.15/19.70 | | | | | | |
% 135.15/19.70 | | | | | | | REDUCE: (340), (9866) imply:
% 135.15/19.70 | | | | | | | (9870) ~ (all_52_3 = e0)
% 135.15/19.70 | | | | | | |
% 135.15/19.70 | | | | | | | REDUCE: (342), (9866) imply:
% 135.15/19.70 | | | | | | | (9871) ~ (all_52_4 = e0)
% 135.15/19.70 | | | | | | |
% 135.15/19.70 | | | | | | | REDUCE: (346), (9866) imply:
% 135.15/19.70 | | | | | | | (9872) ~ (all_52_12 = e0)
% 135.15/19.70 | | | | | | |
% 135.15/19.70 | | | | | | | REDUCE: (45), (9866) imply:
% 135.15/19.70 | | | | | | | (9873) op(e3, e3) = e0
% 135.15/19.70 | | | | | | |
% 135.15/19.70 | | | | | | | BETA: splitting (9867) gives:
% 135.15/19.70 | | | | | | |
% 135.15/19.70 | | | | | | | Case 1:
% 135.15/19.70 | | | | | | | |
% 135.15/19.70 | | | | | | | | (9874) ~ (all_10_0 = e2) & op(e0, e3) = all_10_0 &
% 135.15/19.70 | | | | | | | | $i(all_10_0)
% 135.15/19.70 | | | | | | | |
% 135.15/19.70 | | | | | | | | ALPHA: (9874) implies:
% 135.15/19.70 | | | | | | | | (9875) ~ (all_10_0 = e2)
% 135.15/19.70 | | | | | | | | (9876) op(e0, e3) = all_10_0
% 135.15/19.70 | | | | | | | |
% 135.15/19.70 | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 135.15/19.70 | | | | | | | | all_10_0, e3, e0, simplifying with (159), (9876)
% 135.15/19.70 | | | | | | | | gives:
% 135.15/19.70 | | | | | | | | (9877) all_52_3 = all_10_0
% 135.15/19.70 | | | | | | | |
% 135.15/19.70 | | | | | | | | COMBINE_EQS: (248), (9877) imply:
% 135.15/19.70 | | | | | | | | (9878) all_54_12 = all_10_0
% 135.15/19.70 | | | | | | | |
% 135.15/19.70 | | | | | | | | REDUCE: (140), (9877) imply:
% 135.15/19.70 | | | | | | | | (9879) ~ (all_52_7 = all_10_0)
% 135.15/19.70 | | | | | | | |
% 135.15/19.70 | | | | | | | | SIMP: (9879) implies:
% 135.15/19.70 | | | | | | | | (9880) ~ (all_52_7 = all_10_0)
% 135.15/19.70 | | | | | | | |
% 135.15/19.70 | | | | | | | | REDUCE: (139), (9877) imply:
% 135.15/19.70 | | | | | | | | (9881) ~ (all_52_11 = all_10_0)
% 135.15/19.70 | | | | | | | |
% 135.15/19.70 | | | | | | | | SIMP: (9881) implies:
% 135.15/19.70 | | | | | | | | (9882) ~ (all_52_11 = all_10_0)
% 135.15/19.70 | | | | | | | |
% 135.15/19.70 | | | | | | | | REDUCE: (8979), (9877) imply:
% 135.15/19.70 | | | | | | | | (9883) ~ (all_10_0 = e1)
% 135.15/19.70 | | | | | | | |
% 135.15/19.70 | | | | | | | | REDUCE: (9870), (9877) imply:
% 135.15/19.70 | | | | | | | | (9884) ~ (all_10_0 = e0)
% 135.15/19.70 | | | | | | | |
% 135.15/19.70 | | | | | | | | BETA: splitting (192) gives:
% 135.15/19.70 | | | | | | | |
% 135.15/19.70 | | | | | | | | Case 1:
% 135.15/19.70 | | | | | | | | |
% 135.15/19.70 | | | | | | | | | (9885) all_54_12 = e3
% 135.15/19.70 | | | | | | | | |
% 135.15/19.70 | | | | | | | | | COMBINE_EQS: (9878), (9885) imply:
% 135.15/19.70 | | | | | | | | | (9886) all_10_0 = e3
% 135.15/19.70 | | | | | | | | |
% 135.15/19.70 | | | | | | | | | SIMP: (9886) implies:
% 135.15/19.70 | | | | | | | | | (9887) all_10_0 = e3
% 135.15/19.70 | | | | | | | | |
% 135.15/19.70 | | | | | | | | | REDUCE: (9880), (9887) imply:
% 135.15/19.70 | | | | | | | | | (9888) ~ (all_52_7 = e3)
% 135.15/19.70 | | | | | | | | |
% 135.15/19.70 | | | | | | | | | REDUCE: (9882), (9887) imply:
% 135.15/19.70 | | | | | | | | | (9889) ~ (all_52_11 = e3)
% 135.15/19.70 | | | | | | | | |
% 135.15/19.70 | | | | | | | | | BETA: splitting (211) gives:
% 135.15/19.70 | | | | | | | | |
% 135.15/19.70 | | | | | | | | | Case 1:
% 135.15/19.70 | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | (9890) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 135.15/19.70 | | | | | | | | | | e3 & op(e0, e2) = e3)
% 135.15/19.70 | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | BETA: splitting (9890) gives:
% 135.15/19.70 | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | Case 1:
% 135.15/19.70 | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | (9891) all_57_12 = e3 & op(e0, e3) = e3
% 135.15/19.70 | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | ALPHA: (9891) implies:
% 135.15/19.70 | | | | | | | | | | | (9892) all_57_12 = e3
% 135.15/19.70 | | | | | | | | | | | (9893) op(e0, e3) = e3
% 135.15/19.70 | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | BETA: splitting (49) gives:
% 135.15/19.70 | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | Case 1:
% 135.15/19.70 | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | (9894) ~ (all_12_2 = e1)
% 135.15/19.70 | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | REDUCE: (8978), (9894) imply:
% 135.15/19.70 | | | | | | | | | | | | (9895) $false
% 135.15/19.70 | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | CLOSE: (9895) is inconsistent.
% 135.15/19.70 | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | Case 2:
% 135.15/19.70 | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | (9896) ( ~ (all_12_0 = e2) & op(e1, e0) = all_12_0 &
% 135.15/19.70 | | | | | | | | | | | | $i(all_12_0)) | ( ~ (all_12_1 = e3) & op(e1, e1)
% 135.15/19.70 | | | | | | | | | | | | = all_12_1 & $i(all_12_1))
% 135.15/19.70 | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | BETA: splitting (52) gives:
% 135.15/19.70 | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | Case 1:
% 135.15/19.70 | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | (9897) ~ (all_14_2 = e3)
% 135.15/19.70 | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | REDUCE: (329), (9897) imply:
% 135.15/19.70 | | | | | | | | | | | | | (9898) ~ (all_8_2 = e3)
% 135.15/19.70 | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | BETA: splitting (73) gives:
% 135.15/19.70 | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | Case 1:
% 135.15/19.70 | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | (9899) ~ (all_28_2 = e3)
% 135.15/19.70 | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | REDUCE: (316), (9899) imply:
% 135.15/19.70 | | | | | | | | | | | | | | (9900) ~ (all_6_2 = e3)
% 135.15/19.70 | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 135.15/19.70 | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | Case 1:
% 135.15/19.70 | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | (9901) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 135.15/19.70 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.15/19.70 | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.15/19.70 | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 135.15/19.70 | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.15/19.70 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.15/19.70 | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.15/19.70 | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.15/19.70 | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.15/19.70 | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 135.15/19.70 | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 135.15/19.70 | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 135.15/19.70 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.15/19.70 | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 135.15/19.70 | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 135.15/19.70 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.15/19.70 | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.15/19.70 | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 135.15/19.70 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.15/19.70 | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.15/19.70 | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.15/19.70 | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 135.15/19.70 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.15/19.70 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.15/19.70 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.15/19.70 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 135.15/19.70 | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.15/19.70 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 135.15/19.70 | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | BETA: splitting (9901) gives:
% 135.15/19.70 | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | Case 1:
% 135.15/19.70 | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | (9902) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 135.15/19.70 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.15/19.70 | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.15/19.70 | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 135.15/19.70 | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.15/19.70 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.15/19.70 | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.15/19.70 | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.15/19.70 | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.15/19.70 | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 135.15/19.70 | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 135.15/19.70 | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 135.15/19.70 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.15/19.70 | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 135.15/19.70 | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | BETA: splitting (9902) gives:
% 135.15/19.70 | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | Case 1:
% 135.15/19.70 | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | (9903) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 135.15/19.70 | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.15/19.70 | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 135.15/19.70 | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 135.15/19.70 | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 135.15/19.70 | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 135.15/19.70 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 135.15/19.70 | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | ALPHA: (9903) implies:
% 135.15/19.70 | | | | | | | | | | | | | | | | | (9904) op(e3, e3) = e2
% 135.15/19.70 | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (163), (167), (231), (9868), (9869),
% 135.15/19.70 | | | | | | | | | | | | | | | | | (9892), (9904), (function-axioms) are inconsistent
% 135.15/19.70 | | | | | | | | | | | | | | | | | by sub-proof #25.
% 135.15/19.70 | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | Case 2:
% 135.15/19.70 | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | (9905) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.15/19.70 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 135.15/19.70 | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 135.15/19.70 | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.15/19.70 | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 135.15/19.70 | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.15/19.70 | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 135.15/19.70 | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | ALPHA: (9905) implies:
% 135.15/19.70 | | | | | | | | | | | | | | | | | (9906) op(e3, e3) = e1
% 135.15/19.70 | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9873), (9906), (function-axioms) are
% 135.15/19.70 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #717.
% 135.15/19.70 | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | End of split
% 135.15/19.70 | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | Case 2:
% 135.15/19.70 | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | (9907) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 135.15/19.70 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.15/19.70 | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.15/19.70 | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 135.15/19.70 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.15/19.70 | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.15/19.70 | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.15/19.70 | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 135.15/19.70 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.15/19.70 | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.15/19.70 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.15/19.70 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 135.15/19.70 | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.15/19.70 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 135.15/19.70 | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | REF_CLOSE: (42), (9893), (9898), (9907), (function-axioms)
% 135.15/19.70 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #68.
% 135.15/19.70 | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | End of split
% 135.15/19.70 | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | Case 2:
% 135.15/19.70 | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | (9908) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 135.15/19.70 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.15/19.70 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.15/19.70 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.15/19.70 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 135.15/19.70 | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.15/19.70 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 135.15/19.70 | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 135.15/19.70 | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.15/19.70 | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 135.15/19.70 | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.15/19.70 | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.15/19.70 | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.15/19.70 | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 135.15/19.70 | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 135.15/19.70 | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.15/19.70 | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 135.15/19.70 | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.15/19.70 | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 135.15/19.70 | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 135.15/19.70 | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 135.15/19.70 | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 135.15/19.70 | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.15/19.70 | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.15/19.70 | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 135.15/19.70 | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 135.15/19.70 | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 135.15/19.70 | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 135.15/19.70 | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 135.15/19.70 | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 135.15/19.70 | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 135.15/19.70 | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.15/19.70 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 135.15/19.70 | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 135.15/19.70 | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.15/19.70 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 135.15/19.70 | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 135.15/19.70 | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 135.15/19.70 | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.15/19.70 | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.15/19.70 | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 135.15/19.70 | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.15/19.70 | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 135.15/19.70 | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 135.15/19.70 | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 135.15/19.70 | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 135.15/19.70 | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 135.15/19.70 | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 135.15/19.70 | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 135.15/19.70 | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.15/19.70 | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.15/19.70 | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.15/19.70 | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.15/19.70 | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.15/19.70 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.15/19.70 | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.15/19.70 | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.15/19.70 | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | BETA: splitting (9908) gives:
% 135.15/19.70 | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | Case 1:
% 135.15/19.70 | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | (9909) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 135.15/19.70 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.15/19.70 | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.15/19.70 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.15/19.70 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 135.15/19.70 | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.15/19.70 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 135.15/19.70 | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 135.15/19.70 | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.15/19.70 | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 135.15/19.70 | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.15/19.70 | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.15/19.70 | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.15/19.70 | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 135.15/19.70 | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | BETA: splitting (9909) gives:
% 135.15/19.70 | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | Case 1:
% 135.15/19.70 | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | (9910) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 135.15/19.70 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 135.15/19.70 | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.15/19.70 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.15/19.70 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 135.15/19.70 | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.15/19.70 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 135.15/19.70 | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | ALPHA: (9910) implies:
% 135.15/19.70 | | | | | | | | | | | | | | | | | (9911) op(e1, e1) = e3
% 135.15/19.70 | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (9900), (9911), (function-axioms) are
% 135.15/19.70 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #771.
% 135.15/19.70 | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | Case 2:
% 135.15/19.70 | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | (9912) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 =
% 135.15/19.70 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 135.15/19.70 | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2,
% 135.15/19.70 | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.15/19.70 | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 135.15/19.70 | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.15/19.70 | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 135.15/19.70 | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | ALPHA: (9912) implies:
% 135.15/19.70 | | | | | | | | | | | | | | | | | (9913) op(e2, e2) = e1
% 135.15/19.70 | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (8993), (9913), (function-axioms) are
% 135.15/19.70 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #57.
% 135.15/19.70 | | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | | End of split
% 135.15/19.70 | | | | | | | | | | | | | | | |
% 135.15/19.70 | | | | | | | | | | | | | | | Case 2:
% 135.15/19.70 | | | | | | | | | | | | | | | |
% 135.15/19.71 | | | | | | | | | | | | | | | | (9914) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 135.15/19.71 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.15/19.71 | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 135.15/19.71 | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 135.15/19.71 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.15/19.71 | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.15/19.71 | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.15/19.71 | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.15/19.71 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.15/19.71 | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.15/19.71 | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.15/19.71 | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 135.15/19.71 | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 135.15/19.71 | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.15/19.71 | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.15/19.71 | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 135.15/19.71 | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 135.15/19.71 | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.15/19.71 | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 135.15/19.71 | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.15/19.71 | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 135.15/19.71 | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 135.15/19.71 | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 135.15/19.71 | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.15/19.71 | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.15/19.71 | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 135.15/19.71 | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 135.15/19.71 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.15/19.71 | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 135.15/19.71 | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 135.15/19.71 | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.15/19.71 | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.15/19.71 | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.15/19.71 | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.15/19.71 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.15/19.71 | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 135.15/19.71 | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.15/19.71 | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.15/19.71 | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.15/19.71 | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.15/19.71 | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.15/19.71 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.15/19.71 | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.15/19.71 | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.15/19.71 | | | | | | | | | | | | | | | |
% 135.15/19.71 | | | | | | | | | | | | | | | | BETA: splitting (9914) gives:
% 135.15/19.71 | | | | | | | | | | | | | | | |
% 135.15/19.71 | | | | | | | | | | | | | | | | Case 1:
% 135.15/19.71 | | | | | | | | | | | | | | | | |
% 135.15/19.71 | | | | | | | | | | | | | | | | | (9915) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 135.15/19.71 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 135.15/19.71 | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 135.15/19.71 | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.15/19.71 | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 135.15/19.71 | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 135.15/19.71 | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 135.15/19.71 | | | | | | | | | | | | | | | | |
% 135.15/19.71 | | | | | | | | | | | | | | | | | ALPHA: (9915) implies:
% 135.15/19.71 | | | | | | | | | | | | | | | | | (9916) ~ (all_56_7 = e3)
% 135.15/19.71 | | | | | | | | | | | | | | | | | (9917) op(e0, e3) = all_56_7
% 135.15/19.71 | | | | | | | | | | | | | | | | |
% 135.15/19.71 | | | | | | | | | | | | | | | | | REF_CLOSE: (9893), (9916), (9917), (function-axioms) are
% 135.15/19.71 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #209.
% 135.15/19.71 | | | | | | | | | | | | | | | | |
% 135.15/19.71 | | | | | | | | | | | | | | | | Case 2:
% 135.15/19.71 | | | | | | | | | | | | | | | | |
% 135.15/19.71 | | | | | | | | | | | | | | | | | (9918) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.15/19.71 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.15/19.71 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.15/19.71 | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.15/19.71 | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 135.15/19.71 | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 135.15/19.71 | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.15/19.71 | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.15/19.71 | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 135.15/19.71 | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 135.15/19.71 | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.15/19.71 | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 135.15/19.71 | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.15/19.71 | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 135.15/19.71 | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 135.15/19.71 | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 135.15/19.71 | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.15/19.71 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.15/19.71 | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 135.15/19.71 | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 135.15/19.71 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.15/19.71 | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 135.15/19.71 | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 135.15/19.71 | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.15/19.71 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.15/19.71 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.15/19.71 | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.15/19.71 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.15/19.71 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 135.15/19.71 | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.15/19.71 | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.15/19.71 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.15/19.71 | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.15/19.71 | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.15/19.71 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.15/19.71 | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.15/19.71 | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.15/19.71 | | | | | | | | | | | | | | | | |
% 135.15/19.71 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (39), (157), (160), (194), (334), (364),
% 135.15/19.71 | | | | | | | | | | | | | | | | | (8984), (8991), (8992), (9900), (9918),
% 135.15/19.71 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.15/19.71 | | | | | | | | | | | | | | | | | #30.
% 135.15/19.71 | | | | | | | | | | | | | | | | |
% 135.15/19.71 | | | | | | | | | | | | | | | | End of split
% 135.15/19.71 | | | | | | | | | | | | | | | |
% 135.15/19.71 | | | | | | | | | | | | | | | End of split
% 135.15/19.71 | | | | | | | | | | | | | | |
% 135.15/19.71 | | | | | | | | | | | | | | End of split
% 135.15/19.71 | | | | | | | | | | | | | |
% 135.15/19.71 | | | | | | | | | | | | | Case 2:
% 135.15/19.71 | | | | | | | | | | | | | |
% 135.15/19.71 | | | | | | | | | | | | | | (9919) all_28_2 = e3
% 135.15/19.71 | | | | | | | | | | | | | | (9920) ( ~ (all_28_0 = e2) & op(e3, e1) = all_28_0 &
% 135.15/19.71 | | | | | | | | | | | | | | $i(all_28_0)) | ( ~ (all_28_1 = e0) & op(e3, e3)
% 135.15/19.71 | | | | | | | | | | | | | | = all_28_1 & $i(all_28_1))
% 135.15/19.71 | | | | | | | | | | | | | |
% 135.15/19.71 | | | | | | | | | | | | | | COMBINE_EQS: (316), (9919) imply:
% 135.15/19.71 | | | | | | | | | | | | | | (9921) all_6_2 = e3
% 135.15/19.71 | | | | | | | | | | | | | |
% 135.15/19.71 | | | | | | | | | | | | | | SIMP: (9921) implies:
% 135.15/19.71 | | | | | | | | | | | | | | (9922) all_6_2 = e3
% 135.15/19.71 | | | | | | | | | | | | | |
% 135.15/19.71 | | | | | | | | | | | | | | REDUCE: (359), (9922) imply:
% 135.15/19.71 | | | | | | | | | | | | | | (9923) ~ (all_52_6 = e3)
% 135.15/19.71 | | | | | | | | | | | | | |
% 135.15/19.71 | | | | | | | | | | | | | | REDUCE: (361), (9922) imply:
% 135.15/19.71 | | | | | | | | | | | | | | (9924) ~ (all_52_8 = e3)
% 135.15/19.71 | | | | | | | | | | | | | |
% 135.15/19.71 | | | | | | | | | | | | | | REDUCE: (366), (9922) imply:
% 135.15/19.71 | | | | | | | | | | | | | | (9925) ~ (all_52_14 = e3)
% 135.15/19.71 | | | | | | | | | | | | | |
% 135.15/19.71 | | | | | | | | | | | | | | REDUCE: (39), (9922) imply:
% 135.15/19.71 | | | | | | | | | | | | | | (9926) op(e1, e1) = e3
% 135.15/19.71 | | | | | | | | | | | | | |
% 135.15/19.71 | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 135.15/19.71 | | | | | | | | | | | | | |
% 135.15/19.71 | | | | | | | | | | | | | | Case 1:
% 135.15/19.71 | | | | | | | | | | | | | | |
% 135.15/19.71 | | | | | | | | | | | | | | | (9927) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 135.15/19.71 | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 135.15/19.71 | | | | | | | | | | | | | | |
% 135.15/19.71 | | | | | | | | | | | | | | | BETA: splitting (9927) gives:
% 135.18/19.71 | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | Case 1:
% 135.18/19.71 | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | (9928) all_57_1 = e3 & op(e3, e2) = e3
% 135.18/19.71 | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | ALPHA: (9928) implies:
% 135.18/19.71 | | | | | | | | | | | | | | | | (9929) all_57_1 = e3
% 135.18/19.71 | | | | | | | | | | | | | | | | (9930) op(e3, e2) = e3
% 135.18/19.71 | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 135.18/19.71 | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.71 | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | (9931) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 135.18/19.71 | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 135.18/19.71 | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | BETA: splitting (9931) gives:
% 135.18/19.71 | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.71 | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | (9932) all_57_1 = e1 & op(e3, e2) = e1
% 135.18/19.71 | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | ALPHA: (9932) implies:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | (9933) op(e3, e2) = e1
% 135.18/19.71 | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9930), (9933), (function-axioms) are
% 135.18/19.71 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #413.
% 135.18/19.71 | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.71 | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | (9934) all_57_3 = e1 & op(e2, e2) = e1
% 135.18/19.71 | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | ALPHA: (9934) implies:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | (9935) op(e2, e2) = e1
% 135.18/19.71 | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (8993), (9935), (function-axioms) are
% 135.18/19.71 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #57.
% 135.18/19.71 | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | End of split
% 135.18/19.71 | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.71 | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | (9936) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 135.18/19.71 | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 135.18/19.71 | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | BETA: splitting (9936) gives:
% 135.18/19.71 | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.71 | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | (9937) all_57_7 = e1 & op(e1, e2) = e1
% 135.18/19.71 | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | ALPHA: (9937) implies:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | (9938) all_57_7 = e1
% 135.18/19.71 | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 135.18/19.71 | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | (9939) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 135.18/19.71 | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | BETA: splitting (9939) gives:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | (9940) all_57_0 = e1 & op(e3, e3) = e1
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | ALPHA: (9940) implies:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | (9941) op(e3, e3) = e1
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9873), (9941), (function-axioms) are
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #717.
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | (9942) all_57_1 = e1 & op(e3, e2) = e1
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | ALPHA: (9942) implies:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | (9943) op(e3, e2) = e1
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9930), (9943), (function-axioms) are
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #413.
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.71 | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | (9944) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 135.18/19.71 | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | BETA: splitting (9944) gives:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | (9945) all_57_4 = e1 & op(e3, e1) = e1
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | ALPHA: (9945) implies:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | (9946) all_57_4 = e1
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | (9947) op(e3, e1) = e1
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | (9948) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9948) gives:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | (9949) all_57_6 = e0 & op(e1, e3) = e0
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (9869), (9949), (function-axioms) are
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #73.
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | (9950) all_57_7 = e0 & op(e1, e2) = e0
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9950) implies:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | (9951) all_57_7 = e0
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9938), (9951) imply:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | (9952) e1 = e0
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (9952) imply:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | (9953) $false
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9953) is inconsistent.
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | (9954) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9954) gives:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | (9955) all_57_8 = e0 & op(e1, e1) = e0
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9955) implies:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | (9956) op(e1, e1) = e0
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9926), (9956), (function-axioms) are
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753.
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | (9957) all_57_11 = e0 & op(e1, e0) = e0
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9957) implies:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | (9958) op(e1, e0) = e0
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | (9959) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9959) gives:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (9960) all_57_0 = e2 & op(e3, e3) = e2
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9960) implies:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (9961) op(e3, e3) = e2
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (163), (167), (231), (9868), (9869),
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (9892), (9961), (function-axioms) are inconsistent
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #25.
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (9962) all_57_1 = e2 & op(e3, e2) = e2
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9962) implies:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (9963) all_57_1 = e2
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9929), (9963) imply:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (9964) e3 = e2
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9892), (9964) imply:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (9965) all_57_12 = e2
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (158), (192), (211), (8991), (9875),
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (9878), (9880), (9882), (9883), (9884), (9965),
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | #23.
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | (9966) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9966) gives:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (9967) all_57_4 = e2 & op(e3, e1) = e2
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9967) implies:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (9968) all_57_4 = e2
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9946), (9968) are inconsistent by sub-proof
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | #669.
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (9969) all_57_9 = e2 & op(e3, e0) = e2
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9969) implies:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (9970) all_57_9 = e2
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (9971) op(e3, e0) = e2
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | (9972) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9972) gives:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (9973) all_57_9 = e3 & op(e3, e0) = e3
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9973) implies:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (9974) op(e3, e0) = e3
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (9971), (9974), (function-axioms) are
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #111.
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (9975) all_57_10 = e3 & op(e2, e0) = e3
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9975) implies:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (9976) op(e2, e0) = e3
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9896) gives:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9977) ~ (all_12_0 = e2) & op(e1, e0) = all_12_0 &
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_12_0)
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9977) implies:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9978) ~ (all_12_0 = e2)
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9979) op(e1, e0) = all_12_0
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9920) gives:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9980) ~ (all_28_0 = e2) & op(e3, e1) = all_28_0 &
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_28_0)
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9980) implies:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9981) ~ (all_28_0 = e2)
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9982) op(e3, e1) = all_28_0
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9983) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9983) gives:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9984) all_57_6 = e2 & op(e1, e3) = e2
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9984) implies:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9985) op(e1, e3) = e2
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9986) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9986) gives:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9987) all_57_0 = e1 & op(e3, e3) = e1
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9987) implies:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9988) op(e3, e3) = e1
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (232), (236),
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (9924), (9946), (9970), (9988),
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #163.
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9989) all_57_2 = e1 & op(e2, e3) = e1
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9989) implies:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9990) all_57_2 = e1
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9991) op(e2, e3) = e1
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e0, e1, simplifying with (160), (9958) gives:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9992) all_52_14 = e0
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_12_0, e0, e1, simplifying with (160), (9979)
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9993) all_52_14 = all_12_0
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e2,
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (163), (9985) gives:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9994) all_52_2 = e2
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e0, e2, simplifying with (164), (9976) gives:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9995) all_52_13 = e3
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e1,
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e2, simplifying with (167), (9991) gives:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9996) all_52_1 = e1
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, e3, simplifying with (168), (9971) gives:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9997) all_52_12 = e2
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e1,
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (169), (9947) gives:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9998) all_52_8 = e1
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8,
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_28_0, e1, e3, simplifying with (169), (9982)
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9999) all_52_8 = all_28_0
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9998), (9999) imply:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10000) all_28_0 = e1
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10000) implies:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10001) all_28_0 = e1
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9992), (9993) imply:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10002) all_12_0 = e0
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (9995), (9997) imply:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10003) ~ (e3 = e2)
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (358), (9995) imply:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10004) ~ (all_8_2 = e3)
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9925), (9992) imply:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10005) ~ (e3 = e0)
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8984), (9992) imply:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10006) ~ (e1 = e0)
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9981), (10001) imply:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10007) ~ (e2 = e1)
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9978), (10002) imply:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10008) ~ (e2 = e0)
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10009) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10009) gives:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10010) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (163), (167), (231),
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235), (9868), (9869), (9892), (9990), (9991),
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10010), (function-axioms) are inconsistent by
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #22.
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10011) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (42), (168), (9898), (9971), (10011),
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #110.
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10012) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10012) gives:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10013) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (9958), (9985), (10013),
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #28.
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10014) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10014) gives:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10015) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10015) implies:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10016) op(e2, e0) = e2
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (164), (9976), (10016), (function-axioms) are
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #546.
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10017) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10017) gives:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10018) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10018) implies:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10019) op(e1, e1) = e2
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9926), (10019), (function-axioms) are
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #109.
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10020) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10020) implies:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10021) op(e0, e0) = all_56_31
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10022) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (160), (8984), (8991), (9947), (9958),
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10021), (10022), (function-axioms) are
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #20.
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10023) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (159), (163), (8979), (9985), (10023),
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #47.
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10024) all_57_7 = e2 & op(e1, e2) = e2
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10024) implies:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10025) all_57_7 = e2
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9938), (10025) are inconsistent by sub-proof
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #288.
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10026) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10026) gives:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10027) all_57_8 = e2 & op(e1, e1) = e2
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10027) implies:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10028) op(e1, e1) = e2
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9926), (10028), (function-axioms) are
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #109.
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10029) all_57_11 = e2 & op(e1, e0) = e2
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10029) implies:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10030) op(e1, e0) = e2
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9978), (9979), (10030), (function-axioms) are
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #35.
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10031) ~ (all_28_1 = e0) & op(e3, e3) = all_28_1 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_28_1)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9873), (10031), (function-axioms) are
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #211.
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | (10032) ~ (all_12_1 = e3) & op(e1, e1) = all_12_1 &
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_12_1)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10032) implies:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | (10033) ~ (all_12_1 = e3)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | (10034) op(e1, e1) = all_12_1
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9926), (10033), (10034), (function-axioms) are
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #36.
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | (10035) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (160), (8991), (9925), (10035),
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | #46.
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | (10036) all_57_9 = e1 & op(e3, e0) = e1
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (8982), (10036), (function-axioms) are
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #181.
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.72 | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.72 | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.72 | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | (10037) all_57_13 = e1 & op(e0, e2) = e1
% 135.18/19.72 | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (8980), (10037), (function-axioms) are
% 135.18/19.72 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #178.
% 135.18/19.72 | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | End of split
% 135.18/19.72 | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | End of split
% 135.18/19.72 | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | Case 2:
% 135.18/19.72 | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | (10038) all_57_3 = e3 & op(e2, e2) = e3
% 135.18/19.72 | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | ALPHA: (10038) implies:
% 135.18/19.72 | | | | | | | | | | | | | | | | (10039) op(e2, e2) = e3
% 135.18/19.72 | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | REF_CLOSE: (42), (9898), (10039), (function-axioms) are
% 135.18/19.72 | | | | | | | | | | | | | | | | inconsistent by sub-proof #228.
% 135.18/19.72 | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | End of split
% 135.18/19.72 | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | Case 2:
% 135.18/19.72 | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | (10040) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 135.18/19.72 | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 135.18/19.72 | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (9888), (9923), (10040),
% 135.18/19.72 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.18/19.72 | | | | | | | | | | | | | | | #555.
% 135.18/19.72 | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | End of split
% 135.18/19.72 | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | End of split
% 135.18/19.72 | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | Case 2:
% 135.18/19.72 | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | (10041) all_14_2 = e3
% 135.18/19.72 | | | | | | | | | | | | | (10042) ( ~ (all_14_0 = e1) & op(e3, e2) = all_14_0 &
% 135.18/19.72 | | | | | | | | | | | | | $i(all_14_0)) | ( ~ (all_14_1 = e0) & op(e3, e3)
% 135.18/19.72 | | | | | | | | | | | | | = all_14_1 & $i(all_14_1))
% 135.18/19.72 | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | COMBINE_EQS: (329), (10041) imply:
% 135.18/19.72 | | | | | | | | | | | | | (10043) all_8_2 = e3
% 135.18/19.72 | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | REDUCE: (350), (10043) imply:
% 135.18/19.72 | | | | | | | | | | | | | (10044) ~ (all_52_4 = e3)
% 135.18/19.72 | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | REDUCE: (352), (10043) imply:
% 135.18/19.72 | | | | | | | | | | | | | (10045) ~ (all_52_6 = e3)
% 135.18/19.72 | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | REDUCE: (356), (10043) imply:
% 135.18/19.72 | | | | | | | | | | | | | (10046) ~ (all_52_9 = e3)
% 135.18/19.72 | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | BETA: splitting (10042) gives:
% 135.18/19.72 | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | Case 1:
% 135.18/19.72 | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | (10047) ~ (all_14_0 = e1) & op(e3, e2) = all_14_0 &
% 135.18/19.72 | | | | | | | | | | | | | | $i(all_14_0)
% 135.18/19.72 | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | ALPHA: (10047) implies:
% 135.18/19.72 | | | | | | | | | | | | | | (10048) ~ (all_14_0 = e1)
% 135.18/19.72 | | | | | | | | | | | | | | (10049) op(e3, e2) = all_14_0
% 135.18/19.72 | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 135.18/19.72 | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | Case 1:
% 135.18/19.72 | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | (10050) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 135.18/19.72 | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 135.18/19.72 | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | BETA: splitting (10050) gives:
% 135.18/19.72 | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | Case 1:
% 135.18/19.72 | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | (10051) all_57_1 = e3 & op(e3, e2) = e3
% 135.18/19.72 | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | ALPHA: (10051) implies:
% 135.18/19.72 | | | | | | | | | | | | | | | | (10052) op(e3, e2) = e3
% 135.18/19.72 | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | REF_CLOSE: (170), (10044), (10052), (function-axioms) are
% 135.18/19.72 | | | | | | | | | | | | | | | | inconsistent by sub-proof #738.
% 135.18/19.72 | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | Case 2:
% 135.18/19.72 | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | (10053) all_57_3 = e3 & op(e2, e2) = e3
% 135.18/19.72 | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | ALPHA: (10053) implies:
% 135.18/19.72 | | | | | | | | | | | | | | | | (10054) all_57_3 = e3
% 135.18/19.72 | | | | | | | | | | | | | | | | (10055) op(e2, e2) = e3
% 135.18/19.72 | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4,
% 135.18/19.72 | | | | | | | | | | | | | | | | all_14_0, e2, e3, simplifying with (170), (10049)
% 135.18/19.72 | | | | | | | | | | | | | | | | gives:
% 135.18/19.72 | | | | | | | | | | | | | | | | (10056) all_52_4 = all_14_0
% 135.18/19.72 | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (10056) imply:
% 135.18/19.72 | | | | | | | | | | | | | | | | (10057) all_54_1 = all_14_0
% 135.18/19.72 | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | REDUCE: (136), (10056) imply:
% 135.18/19.72 | | | | | | | | | | | | | | | | (10058) ~ (all_52_6 = all_14_0)
% 135.18/19.72 | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | SIMP: (10058) implies:
% 135.18/19.72 | | | | | | | | | | | | | | | | (10059) ~ (all_52_6 = all_14_0)
% 135.18/19.72 | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | REDUCE: (134), (10056) imply:
% 135.18/19.72 | | | | | | | | | | | | | | | | (10060) ~ (all_52_8 = all_14_0)
% 135.18/19.72 | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | SIMP: (10060) implies:
% 135.18/19.72 | | | | | | | | | | | | | | | | (10061) ~ (all_52_8 = all_14_0)
% 135.18/19.72 | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | REDUCE: (133), (10056) imply:
% 135.18/19.72 | | | | | | | | | | | | | | | | (10062) ~ (all_52_12 = all_14_0)
% 135.18/19.72 | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | SIMP: (10062) implies:
% 135.18/19.72 | | | | | | | | | | | | | | | | (10063) ~ (all_52_12 = all_14_0)
% 135.18/19.72 | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | REDUCE: (10044), (10056) imply:
% 135.18/19.72 | | | | | | | | | | | | | | | | (10064) ~ (all_14_0 = e3)
% 135.18/19.72 | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | REDUCE: (9871), (10056) imply:
% 135.18/19.72 | | | | | | | | | | | | | | | | (10065) ~ (all_14_0 = e0)
% 135.18/19.72 | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 135.18/19.72 | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.72 | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | (10066) all_54_1 = e3
% 135.18/19.72 | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | COMBINE_EQS: (10057), (10066) imply:
% 135.18/19.72 | | | | | | | | | | | | | | | | | (10067) all_14_0 = e3
% 135.18/19.72 | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | REDUCE: (10064), (10067) imply:
% 135.18/19.72 | | | | | | | | | | | | | | | | | (10068) $false
% 135.18/19.72 | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | CLOSE: (10068) is inconsistent.
% 135.18/19.72 | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.72 | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | (10069) ~ (all_54_1 = e3)
% 135.18/19.72 | | | | | | | | | | | | | | | | | (10070) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 135.18/19.72 | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 135.18/19.72 | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.72 | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | (10071) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 135.18/19.72 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 135.18/19.72 | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | BETA: splitting (10071) gives:
% 135.18/19.72 | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | (10072) all_57_1 = e1 & op(e3, e2) = e1
% 135.18/19.72 | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | ALPHA: (10072) implies:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | (10073) all_57_1 = e1
% 135.18/19.72 | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | BETA: splitting (10070) gives:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | (10074) all_54_1 = e2
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10057), (10074) imply:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | (10075) all_14_0 = e2
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | REDUCE: (10061), (10075) imply:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | (10076) ~ (all_52_8 = e2)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | REDUCE: (10063), (10075) imply:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | (10077) ~ (all_52_12 = e2)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | (10078) all_54_3 = e3
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (10078) imply:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | (10079) all_52_12 = e3
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | SIMP: (10079) implies:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | (10080) all_52_12 = e3
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (10080) imply:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | (10081) op(e3, e0) = e3
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | (10082) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10082) gives:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | (10083) all_57_0 = e2 & op(e3, e3) = e2
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10083) implies:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | (10084) op(e3, e3) = e2
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (163), (167), (231), (9868), (9869),
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | (9892), (10084), (function-axioms) are
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #25.
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | (10085) all_57_1 = e2 & op(e3, e2) = e2
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10073), (10085) are inconsistent by
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #616.
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | (10086) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (169), (10076), (10081), (10086),
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | #19.
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | (10087) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (8982), (9872), (10077), (10087) are
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #320.
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | (10088) all_54_1 = e1 | all_54_1 = e0
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10048), (10057), (10065), (10088) are
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #192.
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.72 | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | (10089) all_57_3 = e1 & op(e2, e2) = e1
% 135.18/19.72 | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | ALPHA: (10089) implies:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | (10090) op(e2, e2) = e1
% 135.18/19.72 | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10055), (10090), (function-axioms) are
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #325.
% 135.18/19.72 | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.72 | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.72 | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | (10091) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 135.18/19.72 | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 135.18/19.72 | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | BETA: splitting (10091) gives:
% 135.18/19.72 | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | (10092) all_57_7 = e1 & op(e1, e2) = e1
% 135.18/19.72 | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | ALPHA: (10092) implies:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | (10093) all_57_7 = e1
% 135.18/19.72 | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | |
% 135.18/19.72 | | | | | | | | | | | | | | | | | | | | (10094) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | BETA: splitting (10094) gives:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | (10095) all_57_0 = e1 & op(e3, e3) = e1
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | ALPHA: (10095) implies:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | (10096) op(e3, e3) = e1
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9873), (10096), (function-axioms) are
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #717.
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | (10097) all_57_1 = e1 & op(e3, e2) = e1
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | ALPHA: (10097) implies:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | (10098) all_57_1 = e1
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | (10099) op(e3, e2) = e1
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10070) gives:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | (10100) all_54_1 = e2
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10057), (10100) imply:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | (10101) all_14_0 = e2
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10059), (10101) imply:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | (10102) ~ (all_52_6 = e2)
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | (10103) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10103) gives:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (10104) all_57_1 = e2 & op(e3, e2) = e2
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10098), (10104) are inconsistent by
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #616.
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (10105) all_57_3 = e2 & op(e2, e2) = e2
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10105) implies:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (10106) all_57_3 = e2
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10054), (10106) imply:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (10107) e3 = e2
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10107) implies:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (10108) e3 = e2
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9892), (10108) imply:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (10109) all_57_12 = e2
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (158), (192), (211), (8991), (9875),
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (9878), (9880), (9882), (9883), (9884), (10109),
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | #23.
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | (10110) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10110) gives:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (10111) all_57_7 = e2 & op(e1, e2) = e2
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (10102), (10111), (function-axioms) are
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #515.
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (10112) all_57_13 = e2 & op(e0, e2) = e2
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10112) implies:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (10113) all_57_13 = e2
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | (10114) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10114) gives:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (10115) all_57_1 = e0 & op(e3, e2) = e0
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10115) implies:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (10116) op(e3, e2) = e0
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_14_0,
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (10049), (10099) gives:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (10117) all_14_0 = e1
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (10049), (10116) gives:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (10118) all_14_0 = e0
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10117), (10118) imply:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (10119) e1 = e0
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10119) implies:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (10120) e1 = e0
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (10120) imply:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (10121) $false
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10121) is inconsistent.
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (10122) all_57_3 = e0 & op(e2, e2) = e0
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10054), (10122) are inconsistent by
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #374.
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | (10123) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10123) gives:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (10124) all_57_7 = e0 & op(e1, e2) = e0
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10124) implies:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (10125) all_57_7 = e0
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10093), (10125) are inconsistent by
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #464.
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (10126) all_57_13 = e0 & op(e0, e2) = e0
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10113), (10126) are inconsistent by
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #411.
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | (10127) all_54_1 = e1 | all_54_1 = e0
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10048), (10057), (10065), (10127) are
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #192.
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | End of split
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | (10128) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | BETA: splitting (10128) gives:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | (10129) all_57_4 = e1 & op(e3, e1) = e1
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | ALPHA: (10129) implies:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | (10130) all_57_4 = e1
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | (10131) op(e3, e1) = e1
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10070) gives:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | (10132) all_54_1 = e2
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10057), (10132) imply:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | (10133) all_14_0 = e2
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10059), (10133) imply:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | (10134) ~ (all_52_6 = e2)
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10061), (10133) imply:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | (10135) ~ (all_52_8 = e2)
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10063), (10133) imply:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | (10136) ~ (all_52_12 = e2)
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10064), (10133) imply:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | (10137) ~ (e3 = e2)
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10049), (10133) imply:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | (10138) op(e3, e2) = e2
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | (10139) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10139) gives:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (10140) all_57_12 = e2 & op(e0, e3) = e2
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10140) implies:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (10141) all_57_12 = e2
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (158), (192), (211), (8991), (9875),
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (9878), (9880), (9882), (9883), (9884), (10141),
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | #23.
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (10142) all_57_13 = e2 & op(e0, e2) = e2
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (168), (169), (227),
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (228), (236), (9873), (10054), (10135), (10136),
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (10142), (function-axioms) are inconsistent by
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #193.
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | (10143) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10143) gives:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (10144) all_57_14 = e2 & op(e0, e1) = e2
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10144) implies:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (10145) all_57_14 = e2
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | (10146) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10146) gives:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (10147) all_57_4 = e3 & op(e3, e1) = e3
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10147) implies:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (10148) op(e3, e1) = e3
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (120), (169), (201), (269), (8982), (9872),
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (10136), (10148), (function-axioms) are
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #319.
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (10149) all_57_5 = e3 & op(e2, e1) = e3
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (10046), (10149), (function-axioms) are
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547.
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | (10150) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10150) gives:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (10151) all_57_8 = e3 & op(e1, e1) = e3
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10151) implies:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (10152) op(e1, e1) = e3
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | (10153) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (170), (9873), (10044), (10153),
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | #197.
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | (10154) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10154) gives:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10155) all_57_4 = e3 & op(e3, e1) = e3
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10155) implies:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10156) op(e3, e1) = e3
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (120), (169), (201), (269), (8982), (9872),
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10136), (10156), (function-axioms) are
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #319.
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10157) all_57_9 = e3 & op(e3, e0) = e3
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10157) implies:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10158) all_57_9 = e3
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10159) op(e3, e0) = e3
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10160) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10160) gives:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10161) all_57_6 = e0 & op(e1, e3) = e0
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (9869), (10161), (function-axioms) are
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #73.
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10162) all_57_7 = e0 & op(e1, e2) = e0
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10162) implies:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10163) all_57_7 = e0
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10093), (10163) are inconsistent by
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #464.
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10164) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10164) gives:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10165) all_57_8 = e0 & op(e1, e1) = e0
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10165) implies:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10166) op(e1, e1) = e0
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10152), (10166), (function-axioms) are
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753.
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10167) all_57_11 = e0 & op(e1, e0) = e0
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10167) implies:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10168) all_57_11 = e0
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10169) op(e1, e0) = e0
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10170) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10170) gives:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10171) all_57_9 = e2 & op(e3, e0) = e2
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10171) implies:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10172) op(e3, e0) = e2
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (10159), (10172), (function-axioms)
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #111.
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10173) all_57_10 = e2 & op(e2, e0) = e2
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10173) implies:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10174) all_57_10 = e2
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10175) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10175) gives:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10176) all_57_6 = e2 & op(e1, e3) = e2
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10176) implies:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10177) op(e1, e3) = e2
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10178) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10178) gives:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10179) all_57_0 = e1 & op(e3, e3) = e1
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10179) implies:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10180) op(e3, e3) = e1
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (168), (169), (232),
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236), (238), (10130), (10131), (10135), (10159),
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10180), (function-axioms) are inconsistent by
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #18.
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10181) all_57_2 = e1 & op(e2, e3) = e1
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10181) implies:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10182) all_57_2 = e1
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10183) op(e2, e3) = e1
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10184) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10184) gives:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10185) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (163), (167), (231),
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235), (9868), (9869), (9892), (10182), (10183),
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10185), (function-axioms) are inconsistent by
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #22.
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10186) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9893), (10138), (10186), (function-axioms) are
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #194.
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10187) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10187) gives:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10188) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (10169), (10177), (10188),
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #28.
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10189) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10189) gives:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10190) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10190) implies:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10191) op(e2, e2) = e0
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10055), (10191), (function-axioms) are
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641.
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10192) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10192) gives:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10193) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10193) implies:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10194) op(e1, e1) = e2
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10152), (10194), (function-axioms) are
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #109.
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10195) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (169), (8984), (8991), (10131), (10135),
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10169), (10195), (function-axioms) are
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #17.
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10196) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (159), (163), (8979), (10177), (10196),
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #47.
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10197) all_57_7 = e2 & op(e1, e2) = e2
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (10134), (10197), (function-axioms) are
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #515.
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10198) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (208), (8990), (10152),
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10158), (10174), (10198), (function-axioms) are
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #26.
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10199) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10199) gives:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10200) all_57_11 = e2 & op(e1, e0) = e2
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10200) implies:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10201) all_57_11 = e2
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10168), (10201) are inconsistent by
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #638.
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10202) all_57_15 = e2 & op(e0, e0) = e2
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10202) implies:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10203) all_57_15 = e2
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (208), (209), (9892),
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10145), (10203) are inconsistent by sub-proof
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #434.
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (10204) all_57_14 = e3 & op(e0, e1) = e3
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (9889), (10204), (function-axioms) are
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #652.
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | (10205) all_57_15 = e2 & op(e0, e0) = e2
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10205) implies:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | (10206) op(e0, e0) = e2
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8991), (10206), (function-axioms) are
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #636.
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | (10207) all_54_1 = e1 | all_54_1 = e0
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10048), (10057), (10065), (10207) are
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #192.
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | (10208) all_57_9 = e1 & op(e3, e0) = e1
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (8982), (10208), (function-axioms) are
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #181.
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.74 | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | (10209) all_57_13 = e1 & op(e0, e2) = e1
% 135.21/19.74 | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (8980), (10209), (function-axioms) are
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #178.
% 135.21/19.74 | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.74 | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | End of split
% 135.21/19.74 | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | End of split
% 135.21/19.74 | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | End of split
% 135.21/19.74 | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | Case 2:
% 135.21/19.74 | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | (10210) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 135.21/19.74 | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 135.21/19.74 | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (9888), (10045), (10210),
% 135.21/19.74 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.21/19.74 | | | | | | | | | | | | | | | #555.
% 135.21/19.74 | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | End of split
% 135.21/19.74 | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | Case 2:
% 135.21/19.74 | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | (10211) ~ (all_14_1 = e0) & op(e3, e3) = all_14_1 &
% 135.21/19.74 | | | | | | | | | | | | | | $i(all_14_1)
% 135.21/19.74 | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | REF_CLOSE: (9873), (10211), (function-axioms) are
% 135.21/19.74 | | | | | | | | | | | | | | inconsistent by sub-proof #191.
% 135.21/19.74 | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | End of split
% 135.21/19.74 | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | End of split
% 135.21/19.74 | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | End of split
% 135.21/19.74 | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | Case 2:
% 135.21/19.74 | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | (10212) all_57_13 = e3 & op(e0, e2) = e3
% 135.21/19.74 | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | REF_CLOSE: (158), (9888), (10212), (function-axioms) are
% 135.21/19.74 | | | | | | | | | | | inconsistent by sub-proof #556.
% 135.21/19.74 | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | End of split
% 135.21/19.74 | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | Case 2:
% 135.21/19.74 | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | (10213) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 135.21/19.74 | | | | | | | | | | e3 & op(e0, e0) = e3)
% 135.21/19.74 | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | REF_CLOSE: (8), (157), (8991), (9889), (10213),
% 135.21/19.74 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.21/19.74 | | | | | | | | | | #37.
% 135.21/19.74 | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | End of split
% 135.21/19.74 | | | | | | | | |
% 135.21/19.74 | | | | | | | | Case 2:
% 135.21/19.74 | | | | | | | | |
% 135.21/19.74 | | | | | | | | | (10214) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 135.21/19.74 | | | | | | | | |
% 135.21/19.74 | | | | | | | | | REF_CLOSE: (9875), (9878), (9883), (9884), (10214) are
% 135.21/19.74 | | | | | | | | | inconsistent by sub-proof #24.
% 135.21/19.74 | | | | | | | | |
% 135.21/19.74 | | | | | | | | End of split
% 135.21/19.74 | | | | | | | |
% 135.21/19.74 | | | | | | | Case 2:
% 135.21/19.74 | | | | | | | |
% 135.21/19.74 | | | | | | | | (10215) ~ (all_10_1 = e1) & op(e0, e0) = all_10_1 &
% 135.21/19.74 | | | | | | | | $i(all_10_1)
% 135.21/19.74 | | | | | | | |
% 135.21/19.74 | | | | | | | | REF_CLOSE: (8991), (10215), (function-axioms) are inconsistent
% 135.21/19.74 | | | | | | | | by sub-proof #16.
% 135.21/19.74 | | | | | | | |
% 135.21/19.74 | | | | | | | End of split
% 135.21/19.74 | | | | | | |
% 135.21/19.74 | | | | | | End of split
% 135.21/19.74 | | | | | |
% 135.21/19.74 | | | | | Case 2:
% 135.21/19.74 | | | | | |
% 135.21/19.74 | | | | | | (10216) all_8_2 = e1
% 135.21/19.74 | | | | | | (10217) ( ~ (all_8_0 = e0) & op(e1, e2) = all_8_0 & $i(all_8_0))
% 135.21/19.74 | | | | | | | ( ~ (all_8_1 = e3) & op(e1, e1) = all_8_1 &
% 135.21/19.74 | | | | | | $i(all_8_1))
% 135.21/19.74 | | | | | |
% 135.21/19.74 | | | | | | COMBINE_EQS: (291), (10216) imply:
% 135.21/19.74 | | | | | | (10218) all_48_2 = e1
% 135.21/19.74 | | | | | |
% 135.21/19.74 | | | | | | REDUCE: (347), (10216) imply:
% 135.21/19.74 | | | | | | (10219) ~ (all_52_1 = e1)
% 135.21/19.74 | | | | | |
% 135.21/19.74 | | | | | | REDUCE: (350), (10216) imply:
% 135.21/19.74 | | | | | | (10220) ~ (all_52_4 = e1)
% 135.21/19.74 | | | | | |
% 135.21/19.74 | | | | | | REDUCE: (352), (10216) imply:
% 135.21/19.74 | | | | | | (10221) ~ (all_52_6 = e1)
% 135.21/19.74 | | | | | |
% 135.21/19.74 | | | | | | REDUCE: (356), (10216) imply:
% 135.21/19.74 | | | | | | (10222) ~ (all_52_9 = e1)
% 135.21/19.74 | | | | | |
% 135.21/19.74 | | | | | | REDUCE: (42), (10216) imply:
% 135.21/19.74 | | | | | | (10223) op(e2, e2) = e1
% 135.21/19.74 | | | | | |
% 135.21/19.74 | | | | | | BETA: splitting (46) gives:
% 135.21/19.74 | | | | | |
% 135.21/19.74 | | | | | | Case 1:
% 135.21/19.74 | | | | | | |
% 135.21/19.74 | | | | | | | (10224) ~ (all_10_2 = e0)
% 135.21/19.74 | | | | | | |
% 135.21/19.74 | | | | | | | BETA: splitting (49) gives:
% 135.21/19.74 | | | | | | |
% 135.21/19.74 | | | | | | | Case 1:
% 135.21/19.74 | | | | | | | |
% 135.21/19.74 | | | | | | | | (10225) ~ (all_12_2 = e1)
% 135.21/19.74 | | | | | | | |
% 135.21/19.74 | | | | | | | | REDUCE: (8978), (10225) imply:
% 135.21/19.74 | | | | | | | | (10226) $false
% 135.21/19.74 | | | | | | | |
% 135.21/19.74 | | | | | | | | CLOSE: (10226) is inconsistent.
% 135.21/19.74 | | | | | | | |
% 135.21/19.74 | | | | | | | Case 2:
% 135.21/19.74 | | | | | | | |
% 135.21/19.74 | | | | | | | | (10227) ( ~ (all_12_0 = e2) & op(e1, e0) = all_12_0 &
% 135.21/19.74 | | | | | | | | $i(all_12_0)) | ( ~ (all_12_1 = e3) & op(e1, e1) =
% 135.21/19.74 | | | | | | | | all_12_1 & $i(all_12_1))
% 135.21/19.74 | | | | | | | |
% 135.21/19.74 | | | | | | | | BETA: splitting (55) gives:
% 135.21/19.74 | | | | | | | |
% 135.21/19.74 | | | | | | | | Case 1:
% 135.21/19.74 | | | | | | | | |
% 135.21/19.74 | | | | | | | | | (10228) ~ (all_16_2 = e2)
% 135.21/19.74 | | | | | | | | |
% 135.21/19.74 | | | | | | | | | REDUCE: (327), (10228) imply:
% 135.21/19.74 | | | | | | | | | (10229) ~ (all_10_2 = e2)
% 135.21/19.74 | | | | | | | | |
% 135.21/19.74 | | | | | | | | | BETA: splitting (73) gives:
% 135.21/19.74 | | | | | | | | |
% 135.21/19.74 | | | | | | | | | Case 1:
% 135.21/19.74 | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | (10230) ~ (all_28_2 = e3)
% 135.21/19.74 | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | REDUCE: (316), (10230) imply:
% 135.21/19.74 | | | | | | | | | | (10231) ~ (all_6_2 = e3)
% 135.21/19.74 | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | BETA: splitting (79) gives:
% 135.21/19.74 | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | Case 1:
% 135.21/19.74 | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | (10232) ~ (all_32_2 = e1)
% 135.21/19.74 | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | REDUCE: (312), (10232) imply:
% 135.21/19.74 | | | | | | | | | | | (10233) ~ (all_10_2 = e1)
% 135.21/19.74 | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | BETA: splitting (204) gives:
% 135.21/19.74 | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | Case 1:
% 135.21/19.74 | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | (10234) all_54_0 = e3
% 135.21/19.74 | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | COMBINE_EQS: (278), (10234) imply:
% 135.21/19.74 | | | | | | | | | | | | (10235) all_10_2 = e3
% 135.21/19.74 | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | SIMP: (10235) implies:
% 135.21/19.74 | | | | | | | | | | | | (10236) all_10_2 = e3
% 135.21/19.74 | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | REDUCE: (344), (10236) imply:
% 135.21/19.74 | | | | | | | | | | | | (10237) ~ (all_52_8 = e3)
% 135.21/19.74 | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | REDUCE: (346), (10236) imply:
% 135.21/19.74 | | | | | | | | | | | | (10238) ~ (all_52_12 = e3)
% 135.21/19.74 | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | REDUCE: (45), (10236) imply:
% 135.21/19.74 | | | | | | | | | | | | (10239) op(e3, e3) = e3
% 135.21/19.74 | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | BETA: splitting (234) gives:
% 135.21/19.74 | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | Case 1:
% 135.21/19.74 | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | (10240) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 135.21/19.74 | | | | | | | | | | | | | & op(e3, e2) = e1)
% 135.21/19.74 | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | BETA: splitting (10240) gives:
% 135.21/19.74 | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | Case 1:
% 135.21/19.74 | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | (10241) all_57_0 = e1 & op(e3, e3) = e1
% 135.21/19.74 | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | ALPHA: (10241) implies:
% 135.21/19.74 | | | | | | | | | | | | | | (10242) op(e3, e3) = e1
% 135.21/19.74 | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | REF_CLOSE: (8), (10239), (10242), (function-axioms) are
% 135.21/19.74 | | | | | | | | | | | | | | inconsistent by sub-proof #775.
% 135.21/19.74 | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | Case 2:
% 135.21/19.74 | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | (10243) all_57_1 = e1 & op(e3, e2) = e1
% 135.21/19.74 | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | REF_CLOSE: (170), (10220), (10243), (function-axioms) are
% 135.21/19.74 | | | | | | | | | | | | | | inconsistent by sub-proof #684.
% 135.21/19.74 | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | End of split
% 135.21/19.74 | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | Case 2:
% 135.21/19.74 | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | (10244) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 135.21/19.74 | | | | | | | | | | | | | & op(e3, e0) = e1)
% 135.21/19.74 | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | BETA: splitting (10244) gives:
% 135.21/19.74 | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | Case 1:
% 135.21/19.74 | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | (10245) all_57_4 = e1 & op(e3, e1) = e1
% 135.21/19.74 | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | ALPHA: (10245) implies:
% 135.21/19.74 | | | | | | | | | | | | | | (10246) op(e3, e1) = e1
% 135.21/19.74 | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 135.21/19.74 | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | Case 1:
% 135.21/19.74 | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | (10247) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 135.21/19.74 | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 135.21/19.74 | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | BETA: splitting (10247) gives:
% 135.21/19.74 | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | Case 1:
% 135.21/19.74 | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | (10248) all_57_0 = e1 & op(e3, e3) = e1
% 135.21/19.74 | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | ALPHA: (10248) implies:
% 135.21/19.74 | | | | | | | | | | | | | | | | (10249) op(e3, e3) = e1
% 135.21/19.74 | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10239), (10249), (function-axioms) are
% 135.21/19.74 | | | | | | | | | | | | | | | | inconsistent by sub-proof #775.
% 135.21/19.74 | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | Case 2:
% 135.21/19.74 | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | (10250) all_57_2 = e1 & op(e2, e3) = e1
% 135.21/19.74 | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | REF_CLOSE: (167), (10219), (10250), (function-axioms) are
% 135.21/19.74 | | | | | | | | | | | | | | | | inconsistent by sub-proof #676.
% 135.21/19.74 | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | End of split
% 135.21/19.74 | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | Case 2:
% 135.21/19.74 | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | (10251) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 135.21/19.74 | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 135.21/19.74 | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | BETA: splitting (10251) gives:
% 135.21/19.74 | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | Case 1:
% 135.21/19.74 | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | (10252) all_57_6 = e1 & op(e1, e3) = e1
% 135.21/19.74 | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | ALPHA: (10252) implies:
% 135.21/19.74 | | | | | | | | | | | | | | | | (10253) all_57_6 = e1
% 135.21/19.74 | | | | | | | | | | | | | | | | (10254) op(e1, e3) = e1
% 135.21/19.74 | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1,
% 135.21/19.74 | | | | | | | | | | | | | | | | e3, e1, simplifying with (163), (10254) gives:
% 135.21/19.74 | | | | | | | | | | | | | | | | (10255) all_52_2 = e1
% 135.21/19.74 | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e1,
% 135.21/19.74 | | | | | | | | | | | | | | | | e1, e3, simplifying with (169), (10246) gives:
% 135.21/19.74 | | | | | | | | | | | | | | | | (10256) all_52_8 = e1
% 135.21/19.74 | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | REDUCE: (143), (10255) imply:
% 135.21/19.74 | | | | | | | | | | | | | | | | (10257) ~ (all_52_6 = e1)
% 135.21/19.74 | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | REDUCE: (141), (10255) imply:
% 135.21/19.74 | | | | | | | | | | | | | | | | (10258) ~ (all_52_14 = e1)
% 135.21/19.74 | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | REDUCE: (361), (10256) imply:
% 135.21/19.74 | | | | | | | | | | | | | | | | (10259) ~ (all_6_2 = e1)
% 135.21/19.74 | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | SIMP: (10259) implies:
% 135.21/19.74 | | | | | | | | | | | | | | | | (10260) ~ (all_6_2 = e1)
% 135.21/19.74 | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | REDUCE: (10237), (10256) imply:
% 135.21/19.74 | | | | | | | | | | | | | | | | (10261) ~ (e3 = e1)
% 135.21/19.74 | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 135.21/19.74 | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.74 | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | (10262) all_54_10 = e3
% 135.21/19.74 | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (10231), (10262) are inconsistent by
% 135.21/19.74 | | | | | | | | | | | | | | | | | sub-proof #742.
% 135.21/19.74 | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.74 | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | (10263) ~ (all_54_10 = e3)
% 135.21/19.74 | | | | | | | | | | | | | | | | | (10264) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 135.21/19.74 | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | BETA: splitting (10264) gives:
% 135.21/19.74 | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.74 | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | (10265) all_54_10 = e2
% 135.21/19.74 | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (8992), (10265) are inconsistent by
% 135.21/19.74 | | | | | | | | | | | | | | | | | | sub-proof #741.
% 135.21/19.74 | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.74 | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | (10266) ~ (all_54_10 = e2)
% 135.21/19.74 | | | | | | | | | | | | | | | | | | (10267) all_54_10 = e1 | all_54_10 = e0
% 135.21/19.74 | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | BETA: splitting (10267) gives:
% 135.21/19.74 | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | (10268) all_54_10 = e1
% 135.21/19.74 | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (10260), (10268) are inconsistent by
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | sub-proof #736.
% 135.21/19.74 | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | (10269) all_54_10 = e0
% 135.21/19.74 | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (10269) imply:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | (10270) all_6_2 = e0
% 135.21/19.74 | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | SIMP: (10270) implies:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | (10271) all_6_2 = e0
% 135.21/19.74 | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | REDUCE: (359), (10271) imply:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | (10272) ~ (all_52_6 = e0)
% 135.21/19.74 | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | REDUCE: (364), (10271) imply:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | (10273) ~ (all_52_11 = e0)
% 135.21/19.74 | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | REDUCE: (10231), (10271) imply:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | (10274) ~ (e3 = e0)
% 135.21/19.74 | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | REDUCE: (8992), (10271) imply:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | (10275) ~ (e2 = e0)
% 135.21/19.74 | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | REDUCE: (10260), (10271) imply:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | (10276) ~ (e1 = e0)
% 135.21/19.74 | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | REDUCE: (39), (10271) imply:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | (10277) op(e1, e1) = e0
% 135.21/19.74 | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | (10278) ~ (all_48_2 = e1)
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | REDUCE: (10218), (10278) imply:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | (10279) $false
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | CLOSE: (10279) is inconsistent.
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | (10280) ( ~ (all_48_0 = e3) & op(e1, e2) = all_48_0 &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | $i(all_48_0)) | ( ~ (all_48_1 = e0) & op(e1, e1)
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | = all_48_1 & $i(all_48_1))
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | (10281) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10281) gives:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | (10282) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (10239), (10282), (function-axioms) are
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #623.
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | (10283) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (168), (10223), (10238), (10283),
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | #190.
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | (10284) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10284) gives:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | (10285) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10285) gives:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | (10286) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10286) implies:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | (10287) op(e1, e1) = e3
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10277), (10287), (function-axioms) are
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753.
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | (10288) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2,
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10288) implies:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | (10289) ~ (all_56_29 = e0)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | (10290) ~ (all_56_13 = e2)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | (10291) op(e1, e0) = all_56_29
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | (10292) op(e1, e1) = all_56_21
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | (10293) op(e1, e2) = all_56_13
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | (10294) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10294) gives:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | (10295) all_57_6 = e0 & op(e1, e3) = e0
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10295) implies:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | (10296) all_57_6 = e0
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10253), (10296) imply:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | (10297) e1 = e0
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (10297) imply:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | (10298) $false
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10298) is inconsistent.
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | (10299) all_57_7 = e0 & op(e1, e2) = e0
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (10272), (10299), (function-axioms) are
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #505.
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | (10300) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10300) gives:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | (10301) all_57_8 = e0 & op(e1, e1) = e0
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21, e1, e1, simplifying with (10277),
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | (10292) gives:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | (10302) all_56_21 = e0
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6,
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13, e2, e1, simplifying with (162), (10293)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | (10303) all_56_13 = all_52_6
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10290), (10303) imply:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | (10304) ~ (all_52_6 = e2)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10280) gives:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | (10305) ~ (all_48_0 = e3) & op(e1, e2) = all_48_0 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_48_0)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10305) implies:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | (10306) ~ (all_48_0 = e3)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | (10307) op(e1, e2) = all_48_0
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (10308) all_54_9 = e3
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (10308) imply:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (10309) all_52_6 = e3
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10309) implies:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (10310) all_52_6 = e3
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (162), (10310) imply:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (10311) op(e1, e2) = e3
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10306), (10307), (10311), (function-axioms) are
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #188.
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (10312) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10312) gives:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10313) all_54_9 = e2
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (10304), (10313) are inconsistent by
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #582.
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10314) all_54_9 = e1 | all_54_9 = e0
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (10221), (10272), (10314) are inconsistent
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #168.
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | (10315) ~ (all_48_1 = e0) & op(e1, e1) = all_48_1 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_48_1)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10277), (10315), (function-axioms) are
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #187.
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | (10316) all_57_11 = e0 & op(e1, e0) = e0
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10316) implies:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | (10317) op(e1, e0) = e0
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10289), (10291), (10317), (function-axioms) are
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #45.
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | (10318) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10318) gives:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | (10319) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10319) implies:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | (10320) op(e2, e2) = e0
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10223), (10320), (function-axioms) are
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675.
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | (10321) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10321) gives:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | (10322) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10322) implies:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | (10323) op(e1, e1) = e2
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10277), (10323), (function-axioms) are
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #98.
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | (10324) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (157), (160), (8984), (8991), (10246),
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | (10273), (10324), (function-axioms) are
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #15.
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.75 | | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.75 | | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | | End of split
% 135.21/19.75 | | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | End of split
% 135.21/19.75 | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | Case 2:
% 135.21/19.75 | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | (10325) all_57_12 = e1 & op(e0, e3) = e1
% 135.21/19.75 | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | | REF_CLOSE: (159), (8979), (10325), (function-axioms) are
% 135.21/19.75 | | | | | | | | | | | | | | | | inconsistent by sub-proof #48.
% 135.21/19.75 | | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | End of split
% 135.21/19.75 | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | End of split
% 135.21/19.75 | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | Case 2:
% 135.21/19.75 | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | (10326) all_57_9 = e1 & op(e3, e0) = e1
% 135.21/19.75 | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | REF_CLOSE: (168), (8982), (10326), (function-axioms) are
% 135.21/19.75 | | | | | | | | | | | | | | inconsistent by sub-proof #181.
% 135.21/19.75 | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | End of split
% 135.21/19.75 | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | End of split
% 135.21/19.75 | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | Case 2:
% 135.21/19.75 | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | (10327) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 135.21/19.75 | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | REF_CLOSE: (278), (10224), (10229), (10233), (10327) are
% 135.21/19.75 | | | | | | | | | | | | inconsistent by sub-proof #777.
% 135.21/19.75 | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | End of split
% 135.21/19.75 | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | Case 2:
% 135.21/19.75 | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | (10328) all_32_2 = e1
% 135.21/19.75 | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | COMBINE_EQS: (312), (10328) imply:
% 135.21/19.75 | | | | | | | | | | | (10329) all_10_2 = e1
% 135.21/19.75 | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | SIMP: (10329) implies:
% 135.21/19.75 | | | | | | | | | | | (10330) all_10_2 = e1
% 135.21/19.75 | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | REDUCE: (338), (10330) imply:
% 135.21/19.75 | | | | | | | | | | | (10331) ~ (all_52_2 = e1)
% 135.21/19.75 | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | REDUCE: (45), (10330) imply:
% 135.21/19.75 | | | | | | | | | | | (10332) op(e3, e3) = e1
% 135.21/19.75 | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | BETA: splitting (216) gives:
% 135.21/19.75 | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | Case 1:
% 135.21/19.75 | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | (10333) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 135.21/19.75 | | | | | | | | | | | | & op(e1, e2) = e1)
% 135.21/19.75 | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | BETA: splitting (10333) gives:
% 135.21/19.75 | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | Case 1:
% 135.21/19.75 | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | (10334) all_57_6 = e1 & op(e1, e3) = e1
% 135.21/19.75 | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | ALPHA: (10334) implies:
% 135.21/19.75 | | | | | | | | | | | | | (10335) op(e1, e3) = e1
% 135.21/19.75 | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | REF_CLOSE: (163), (10331), (10335), (function-axioms) are
% 135.21/19.75 | | | | | | | | | | | | | inconsistent by sub-proof #725.
% 135.21/19.75 | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | Case 2:
% 135.21/19.75 | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | (10336) all_57_7 = e1 & op(e1, e2) = e1
% 135.21/19.75 | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | ALPHA: (10336) implies:
% 135.21/19.75 | | | | | | | | | | | | | (10337) op(e1, e2) = e1
% 135.21/19.75 | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | REF_CLOSE: (162), (10221), (10337), (function-axioms) are
% 135.21/19.75 | | | | | | | | | | | | | inconsistent by sub-proof #65.
% 135.21/19.75 | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | End of split
% 135.21/19.75 | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | Case 2:
% 135.21/19.75 | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | (10338) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 135.21/19.75 | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 135.21/19.75 | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | BETA: splitting (10338) gives:
% 135.21/19.75 | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | Case 1:
% 135.21/19.75 | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | (10339) all_57_8 = e1 & op(e1, e1) = e1
% 135.21/19.75 | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | ALPHA: (10339) implies:
% 135.21/19.75 | | | | | | | | | | | | | (10340) op(e1, e1) = e1
% 135.21/19.75 | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, e1,
% 135.21/19.75 | | | | | | | | | | | | | e1, e1, simplifying with (39), (10340) gives:
% 135.21/19.75 | | | | | | | | | | | | | (10341) all_6_2 = e1
% 135.21/19.75 | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | REDUCE: (10231), (10341) imply:
% 135.21/19.75 | | | | | | | | | | | | | (10342) ~ (e3 = e1)
% 135.21/19.75 | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | REDUCE: (8992), (10341) imply:
% 135.21/19.75 | | | | | | | | | | | | | (10343) ~ (e2 = e1)
% 135.21/19.75 | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | BETA: splitting (206) gives:
% 135.21/19.75 | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | Case 1:
% 135.21/19.75 | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | (10344) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 135.21/19.75 | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.21/19.75 | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.21/19.75 | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 135.21/19.75 | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.75 | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.21/19.75 | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.21/19.75 | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.21/19.75 | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.21/19.75 | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 135.21/19.75 | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 135.21/19.75 | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.75 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.21/19.75 | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 135.21/19.75 | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 135.21/19.75 | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.21/19.75 | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.21/19.75 | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.75 | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.75 | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.21/19.75 | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.21/19.75 | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 135.21/19.75 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.75 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.75 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.75 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 135.21/19.75 | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.75 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 135.21/19.75 | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | BETA: splitting (10344) gives:
% 135.21/19.75 | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | Case 1:
% 135.21/19.75 | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | (10345) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 135.21/19.75 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.21/19.75 | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.21/19.75 | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 135.21/19.75 | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.75 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.21/19.75 | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.21/19.75 | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.21/19.75 | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.21/19.75 | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 135.21/19.75 | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 135.21/19.75 | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.75 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.21/19.75 | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 135.21/19.75 | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | REF_CLOSE: (6), (10332), (10340), (10345), (function-axioms)
% 135.21/19.75 | | | | | | | | | | | | | | | are inconsistent by sub-proof #509.
% 135.21/19.75 | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | Case 2:
% 135.21/19.75 | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | (10346) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 135.21/19.75 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.21/19.75 | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.21/19.75 | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.75 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.75 | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.21/19.75 | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.21/19.75 | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 135.21/19.75 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.75 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.75 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.75 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 135.21/19.75 | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.75 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 135.21/19.75 | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (10223), (10332), (10346),
% 135.21/19.75 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.21/19.75 | | | | | | | | | | | | | | | #175.
% 135.21/19.75 | | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | | End of split
% 135.21/19.75 | | | | | | | | | | | | | |
% 135.21/19.75 | | | | | | | | | | | | | Case 2:
% 135.21/19.75 | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | (10347) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 135.21/19.76 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.76 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.76 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.76 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 135.21/19.76 | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.76 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 135.21/19.76 | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 135.21/19.76 | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.21/19.76 | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 135.21/19.76 | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.21/19.76 | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.21/19.76 | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.21/19.76 | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 135.21/19.76 | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 135.21/19.76 | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.21/19.76 | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 135.21/19.76 | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.21/19.76 | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 135.21/19.76 | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 135.21/19.76 | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 135.21/19.76 | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 135.21/19.76 | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.21/19.76 | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.21/19.76 | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 135.21/19.76 | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 135.21/19.76 | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 135.21/19.76 | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 135.21/19.76 | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 135.21/19.76 | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 135.21/19.76 | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 135.21/19.76 | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.76 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 135.21/19.76 | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 135.21/19.76 | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.76 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 135.21/19.76 | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 135.21/19.76 | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 135.21/19.76 | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.21/19.76 | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.21/19.76 | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 135.21/19.76 | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.21/19.76 | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 135.21/19.76 | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 135.21/19.76 | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 135.21/19.76 | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 135.21/19.76 | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 135.21/19.76 | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 135.21/19.76 | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 135.21/19.76 | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.21/19.76 | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.21/19.76 | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.21/19.76 | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.21/19.76 | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.76 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.21/19.76 | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.21/19.76 | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.21/19.76 | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | BETA: splitting (10347) gives:
% 135.21/19.76 | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | Case 1:
% 135.21/19.76 | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | (10348) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 135.21/19.76 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.76 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.76 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.76 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 135.21/19.76 | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.76 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 135.21/19.76 | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 135.21/19.76 | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.21/19.76 | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 135.21/19.76 | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.21/19.76 | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.21/19.76 | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.21/19.76 | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 135.21/19.76 | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | BETA: splitting (10348) gives:
% 135.21/19.76 | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | Case 1:
% 135.21/19.76 | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | (10349) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 135.21/19.76 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 135.21/19.76 | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.76 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.76 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 135.21/19.76 | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.76 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 135.21/19.76 | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | ALPHA: (10349) implies:
% 135.21/19.76 | | | | | | | | | | | | | | | | (10350) op(e1, e1) = e3
% 135.21/19.76 | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (10340), (10350), (function-axioms) are
% 135.21/19.76 | | | | | | | | | | | | | | | | inconsistent by sub-proof #662.
% 135.21/19.76 | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | Case 2:
% 135.21/19.76 | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | (10351) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 =
% 135.21/19.76 | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 135.21/19.76 | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2,
% 135.21/19.76 | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.21/19.76 | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 135.21/19.76 | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.21/19.76 | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 135.21/19.76 | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | ALPHA: (10351) implies:
% 135.21/19.76 | | | | | | | | | | | | | | | | (10352) ~ (all_56_21 = e1)
% 135.21/19.76 | | | | | | | | | | | | | | | | (10353) op(e1, e1) = all_56_21
% 135.21/19.76 | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | REF_CLOSE: (10340), (10352), (10353), (function-axioms) are
% 135.21/19.76 | | | | | | | | | | | | | | | | inconsistent by sub-proof #510.
% 135.21/19.76 | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | End of split
% 135.21/19.76 | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | Case 2:
% 135.21/19.76 | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | (10354) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 135.21/19.76 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.21/19.76 | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 135.21/19.76 | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.76 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.76 | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.21/19.76 | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.21/19.76 | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.21/19.76 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.21/19.76 | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.21/19.76 | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.21/19.76 | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 135.21/19.76 | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 135.21/19.76 | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.21/19.76 | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.21/19.76 | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 135.21/19.76 | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 135.21/19.76 | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.21/19.76 | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 135.21/19.76 | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.21/19.76 | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 135.21/19.76 | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 135.21/19.76 | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 135.21/19.76 | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.21/19.76 | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.21/19.76 | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 135.21/19.76 | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.76 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.21/19.76 | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 135.21/19.76 | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 135.21/19.76 | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.21/19.76 | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.21/19.76 | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.21/19.76 | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.76 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.76 | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 135.21/19.76 | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.21/19.76 | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.21/19.76 | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.21/19.76 | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.21/19.76 | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.76 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.21/19.76 | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.21/19.76 | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.21/19.76 | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | BETA: splitting (10354) gives:
% 135.21/19.76 | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | Case 1:
% 135.21/19.76 | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | (10355) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 135.21/19.76 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 135.21/19.76 | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 135.21/19.76 | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.21/19.76 | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 135.21/19.76 | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 135.21/19.76 | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 135.21/19.76 | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | ALPHA: (10355) implies:
% 135.21/19.76 | | | | | | | | | | | | | | | | (10356) op(e2, e2) = e0
% 135.21/19.76 | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10223), (10356), (function-axioms) are
% 135.21/19.76 | | | | | | | | | | | | | | | | inconsistent by sub-proof #675.
% 135.21/19.76 | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | Case 2:
% 135.21/19.76 | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | (10357) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.21/19.76 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.21/19.76 | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.21/19.76 | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.21/19.76 | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 135.21/19.76 | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 135.21/19.76 | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.21/19.76 | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.21/19.76 | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 135.21/19.76 | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 135.21/19.76 | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.21/19.76 | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 135.21/19.76 | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.21/19.76 | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 135.21/19.76 | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 135.21/19.76 | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 135.21/19.76 | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.21/19.76 | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.21/19.76 | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 135.21/19.76 | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.76 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.21/19.76 | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 135.21/19.76 | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 135.21/19.76 | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.21/19.76 | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.21/19.76 | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.21/19.76 | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.76 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.76 | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 135.21/19.76 | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.21/19.76 | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.21/19.76 | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.21/19.76 | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.21/19.76 | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.76 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.21/19.76 | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.21/19.76 | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.21/19.76 | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | BETA: splitting (10357) gives:
% 135.21/19.76 | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.76 | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | (10358) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.21/19.76 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 135.21/19.76 | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 135.21/19.76 | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 135.21/19.76 | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | ALPHA: (10358) implies:
% 135.21/19.76 | | | | | | | | | | | | | | | | | (10359) op(e1, e1) = e2
% 135.21/19.76 | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (8992), (10359), (function-axioms) are
% 135.21/19.76 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 135.21/19.76 | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.76 | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | (10360) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 135.21/19.76 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 135.21/19.76 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.21/19.76 | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 135.21/19.76 | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 135.21/19.76 | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 135.21/19.76 | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 135.21/19.76 | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.21/19.76 | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.21/19.76 | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 135.21/19.76 | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 135.21/19.76 | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.21/19.76 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.21/19.76 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.21/19.76 | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.76 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 135.21/19.76 | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 135.21/19.76 | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.21/19.76 | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 135.21/19.76 | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 135.21/19.76 | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 135.21/19.76 | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | ALPHA: (10360) implies:
% 135.21/19.76 | | | | | | | | | | | | | | | | | (10361) op(e0, e0) = all_56_31
% 135.21/19.76 | | | | | | | | | | | | | | | | | (10362) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 135.21/19.76 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.76 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 135.21/19.76 | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 135.21/19.76 | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 135.21/19.76 | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 135.21/19.76 | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.21/19.76 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.21/19.76 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 135.21/19.76 | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.21/19.76 | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 135.21/19.76 | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 135.21/19.76 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.21/19.76 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 135.21/19.76 | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.21/19.76 | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 135.21/19.76 | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 135.21/19.76 | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 135.21/19.76 | | | | | | | | | | | | | | | | | all_56_31, e0, e0, simplifying with (8991),
% 135.21/19.76 | | | | | | | | | | | | | | | | | (10361) gives:
% 135.21/19.76 | | | | | | | | | | | | | | | | | (10363) all_56_31 = e1
% 135.21/19.76 | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | BETA: splitting (10362) gives:
% 135.21/19.76 | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.76 | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | (10364) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.76 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 135.21/19.76 | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 135.21/19.76 | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27))
% 135.21/19.76 | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (10363), (10364) are inconsistent by
% 135.21/19.76 | | | | | | | | | | | | | | | | | | sub-proof #32.
% 135.21/19.76 | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.76 | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | (10365) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.76 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 135.21/19.76 | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 135.21/19.76 | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (8984), (10340), (10365), (function-axioms)
% 135.21/19.76 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #182.
% 135.21/19.76 | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | End of split
% 135.21/19.76 | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | End of split
% 135.21/19.76 | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | End of split
% 135.21/19.76 | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | End of split
% 135.21/19.76 | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | End of split
% 135.21/19.76 | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | Case 2:
% 135.21/19.76 | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | (10366) all_57_11 = e1 & op(e1, e0) = e1
% 135.21/19.76 | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | ALPHA: (10366) implies:
% 135.21/19.76 | | | | | | | | | | | | | (10367) op(e1, e0) = e1
% 135.21/19.76 | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | REF_CLOSE: (160), (8984), (10367), (function-axioms) are
% 135.21/19.76 | | | | | | | | | | | | | inconsistent by sub-proof #327.
% 135.21/19.76 | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | End of split
% 135.21/19.76 | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | End of split
% 135.21/19.76 | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | End of split
% 135.21/19.76 | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | Case 2:
% 135.21/19.76 | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | (10368) all_28_2 = e3
% 135.21/19.76 | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | COMBINE_EQS: (316), (10368) imply:
% 135.21/19.76 | | | | | | | | | | (10369) all_6_2 = e3
% 135.21/19.76 | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | REDUCE: (348), (10369) imply:
% 135.21/19.76 | | | | | | | | | | (10370) ~ (all_52_2 = e3)
% 135.21/19.76 | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | REDUCE: (359), (10369) imply:
% 135.21/19.76 | | | | | | | | | | (10371) ~ (all_52_6 = e3)
% 135.21/19.76 | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | REDUCE: (361), (10369) imply:
% 135.21/19.76 | | | | | | | | | | (10372) ~ (all_52_8 = e3)
% 135.21/19.76 | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | REDUCE: (366), (10369) imply:
% 135.21/19.76 | | | | | | | | | | (10373) ~ (all_52_14 = e3)
% 135.21/19.76 | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | REDUCE: (39), (10369) imply:
% 135.21/19.76 | | | | | | | | | | (10374) op(e1, e1) = e3
% 135.21/19.76 | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | BETA: splitting (10227) gives:
% 135.21/19.76 | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | Case 1:
% 135.21/19.76 | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | (10375) ~ (all_12_0 = e2) & op(e1, e0) = all_12_0 &
% 135.21/19.76 | | | | | | | | | | | $i(all_12_0)
% 135.21/19.76 | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | ALPHA: (10375) implies:
% 135.21/19.76 | | | | | | | | | | | (10376) op(e1, e0) = all_12_0
% 135.21/19.76 | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | BETA: splitting (10217) gives:
% 135.21/19.76 | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | Case 1:
% 135.21/19.76 | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | (10377) ~ (all_8_0 = e0) & op(e1, e2) = all_8_0 &
% 135.21/19.76 | | | | | | | | | | | | $i(all_8_0)
% 135.21/19.76 | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | ALPHA: (10377) implies:
% 135.21/19.76 | | | | | | | | | | | | (10378) ~ (all_8_0 = e0)
% 135.21/19.76 | | | | | | | | | | | | (10379) op(e1, e2) = all_8_0
% 135.21/19.76 | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | BETA: splitting (220) gives:
% 135.21/19.76 | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | Case 1:
% 135.21/19.76 | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | (10380) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 135.21/19.76 | | | | | | | | | | | | | & op(e2, e1) = e1)
% 135.21/19.76 | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | BETA: splitting (10380) gives:
% 135.21/19.76 | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | Case 1:
% 135.21/19.76 | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | (10381) all_57_4 = e1 & op(e3, e1) = e1
% 135.21/19.76 | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | ALPHA: (10381) implies:
% 135.21/19.76 | | | | | | | | | | | | | | (10382) all_57_4 = e1
% 135.21/19.76 | | | | | | | | | | | | | | (10383) op(e3, e1) = e1
% 135.21/19.76 | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 135.21/19.76 | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | Case 1:
% 135.21/19.76 | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | (10384) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 135.21/19.76 | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 135.21/19.76 | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | REF_CLOSE: (162), (163), (10370), (10371), (10384),
% 135.21/19.76 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.21/19.76 | | | | | | | | | | | | | | | #323.
% 135.21/19.76 | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | Case 2:
% 135.21/19.76 | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | (10385) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 135.21/19.76 | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 135.21/19.76 | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | BETA: splitting (10385) gives:
% 135.21/19.76 | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | Case 1:
% 135.21/19.76 | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | (10386) all_57_8 = e3 & op(e1, e1) = e3
% 135.21/19.76 | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 135.21/19.76 | | | | | | | | | | | | | | | | all_12_0, e0, e1, simplifying with (160), (10376)
% 135.21/19.76 | | | | | | | | | | | | | | | | gives:
% 135.21/19.76 | | | | | | | | | | | | | | | | (10387) all_52_14 = all_12_0
% 135.21/19.76 | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6,
% 135.21/19.76 | | | | | | | | | | | | | | | | all_8_0, e2, e1, simplifying with (162), (10379)
% 135.21/19.76 | | | | | | | | | | | | | | | | gives:
% 135.21/19.76 | | | | | | | | | | | | | | | | (10388) all_52_6 = all_8_0
% 135.21/19.76 | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e1,
% 135.21/19.76 | | | | | | | | | | | | | | | | e1, e3, simplifying with (169), (10383) gives:
% 135.21/19.76 | | | | | | | | | | | | | | | | (10389) all_52_8 = e1
% 135.21/19.76 | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (10387) imply:
% 135.21/19.76 | | | | | | | | | | | | | | | | (10390) all_54_11 = all_12_0
% 135.21/19.76 | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (10388) imply:
% 135.21/19.76 | | | | | | | | | | | | | | | | (10391) all_54_9 = all_8_0
% 135.21/19.76 | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | REDUCE: (136), (10388) imply:
% 135.21/19.76 | | | | | | | | | | | | | | | | (10392) ~ (all_52_4 = all_8_0)
% 135.21/19.76 | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | REDUCE: (126), (10387), (10388) imply:
% 135.21/19.76 | | | | | | | | | | | | | | | | (10393) ~ (all_12_0 = all_8_0)
% 135.21/19.76 | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | SIMP: (10393) implies:
% 135.21/19.76 | | | | | | | | | | | | | | | | (10394) ~ (all_12_0 = all_8_0)
% 135.21/19.76 | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | REDUCE: (10371), (10388) imply:
% 135.21/19.76 | | | | | | | | | | | | | | | | (10395) ~ (all_8_0 = e3)
% 135.21/19.76 | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | REDUCE: (10221), (10388) imply:
% 135.21/19.76 | | | | | | | | | | | | | | | | (10396) ~ (all_8_0 = e1)
% 135.21/19.76 | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | REDUCE: (344), (10389) imply:
% 135.21/19.76 | | | | | | | | | | | | | | | | (10397) ~ (all_10_2 = e1)
% 135.21/19.76 | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | SIMP: (10397) implies:
% 135.21/19.76 | | | | | | | | | | | | | | | | (10398) ~ (all_10_2 = e1)
% 135.21/19.76 | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | REDUCE: (10373), (10387) imply:
% 135.21/19.76 | | | | | | | | | | | | | | | | (10399) ~ (all_12_0 = e3)
% 135.21/19.76 | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | REDUCE: (8984), (10387) imply:
% 135.21/19.76 | | | | | | | | | | | | | | | | (10400) ~ (all_12_0 = e1)
% 135.21/19.76 | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 135.21/19.76 | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.76 | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | (10401) all_54_11 = e3
% 135.21/19.76 | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | REF_CLOSE: (10390), (10399), (10401) are inconsistent by
% 135.21/19.76 | | | | | | | | | | | | | | | | | sub-proof #52.
% 135.21/19.76 | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.76 | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | (10402) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 135.21/19.76 | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 135.21/19.76 | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.76 | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | (10403) all_54_0 = e3
% 135.21/19.76 | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (10403) imply:
% 135.21/19.76 | | | | | | | | | | | | | | | | | | (10404) all_10_2 = e3
% 135.21/19.76 | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | SIMP: (10404) implies:
% 135.21/19.76 | | | | | | | | | | | | | | | | | | (10405) all_10_2 = e3
% 135.21/19.76 | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | REDUCE: (346), (10405) imply:
% 135.21/19.76 | | | | | | | | | | | | | | | | | | (10406) ~ (all_52_12 = e3)
% 135.21/19.76 | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | REDUCE: (45), (10405) imply:
% 135.21/19.76 | | | | | | | | | | | | | | | | | | (10407) op(e3, e3) = e3
% 135.21/19.76 | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 135.21/19.76 | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.76 | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | (10408) all_54_9 = e3
% 135.21/19.76 | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10391), (10408) imply:
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | (10409) all_8_0 = e3
% 135.21/19.76 | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | SIMP: (10409) implies:
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | (10410) all_8_0 = e3
% 135.21/19.76 | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | REDUCE: (10395), (10410) imply:
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | (10411) $false
% 135.21/19.76 | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | CLOSE: (10411) is inconsistent.
% 135.21/19.76 | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.76 | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | (10412) ~ (all_54_9 = e3)
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | (10413) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 135.21/19.76 | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | BETA: splitting (10413) gives:
% 135.21/19.76 | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | (10414) all_54_9 = e2
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10391), (10414) imply:
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | (10415) all_8_0 = e2
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | REDUCE: (10392), (10415) imply:
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | (10416) ~ (all_52_4 = e2)
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | REDUCE: (10394), (10415) imply:
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | (10417) ~ (all_12_0 = e2)
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | REDUCE: (10395), (10415) imply:
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | (10418) ~ (e3 = e2)
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | REDUCE: (10379), (10415) imply:
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | (10419) op(e1, e2) = e2
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | (10420) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10420) gives:
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | (10421) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10421) gives:
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | (10422) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10422) implies:
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | (10423) op(e3, e3) = e2
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10407), (10423), (function-axioms) are
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #778.
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | (10424) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10424) implies:
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | (10425) op(e3, e3) = e1
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (170), (232),
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | (236), (238), (10372), (10382), (10416), (10425),
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | #162.
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | (10426) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (168), (10223), (10406), (10426),
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | #190.
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | (10427) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10427) gives:
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | (10428) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10383), (10419), (10428), (function-axioms) are
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #132.
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | (10429) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10429) gives:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | (10430) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10430) implies:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | (10431) op(e2, e2) = e0
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10223), (10431), (function-axioms) are
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675.
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | (10432) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10432) gives:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | (10433) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10433) implies:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | (10434) op(e1, e1) = e2
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10374), (10434), (function-axioms) are
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #109.
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | (10435) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10435) implies:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | (10436) op(e0, e0) = all_56_31
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | (10437) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10402) gives:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | (10438) all_54_11 = e2
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10390), (10417), (10438) are inconsistent by
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #51.
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | (10439) all_54_11 = e1 | all_54_11 = e0
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10439) gives:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | (10440) all_54_11 = e1
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10390), (10400), (10440) are inconsistent by
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #50.
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | (10441) all_54_11 = e0
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10390), (10441) imply:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | (10442) all_12_0 = e0
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10442) implies:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | (10443) all_12_0 = e0
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10376), (10443) imply:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | (10444) op(e1, e0) = e0
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (160), (8984), (8991), (10383), (10436),
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | (10437), (10444), (function-axioms) are
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #20.
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | (10445) all_54_9 = e1 | all_54_9 = e0
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10378), (10391), (10396), (10445) are
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #155.
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.77 | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.77 | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.77 | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | (10446) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 135.21/19.77 | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (10224), (10229), (10398), (10446) are
% 135.21/19.77 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #777.
% 135.21/19.77 | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | End of split
% 135.21/19.77 | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | End of split
% 135.21/19.77 | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | Case 2:
% 135.21/19.77 | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | (10447) all_57_11 = e3 & op(e1, e0) = e3
% 135.21/19.77 | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | REF_CLOSE: (160), (10373), (10447), (function-axioms) are
% 135.21/19.77 | | | | | | | | | | | | | | | | inconsistent by sub-proof #750.
% 135.21/19.77 | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | End of split
% 135.21/19.77 | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | End of split
% 135.21/19.77 | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | Case 2:
% 135.21/19.77 | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | (10448) all_57_5 = e1 & op(e2, e1) = e1
% 135.21/19.77 | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | REF_CLOSE: (165), (10222), (10448), (function-axioms) are
% 135.21/19.77 | | | | | | | | | | | | | | inconsistent by sub-proof #161.
% 135.21/19.77 | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | End of split
% 135.21/19.77 | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | Case 2:
% 135.21/19.77 | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | (10449) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 135.21/19.77 | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 135.21/19.77 | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | BETA: splitting (10449) gives:
% 135.21/19.77 | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | Case 1:
% 135.21/19.77 | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | (10450) all_57_8 = e1 & op(e1, e1) = e1
% 135.21/19.77 | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | ALPHA: (10450) implies:
% 135.21/19.77 | | | | | | | | | | | | | | (10451) op(e1, e1) = e1
% 135.21/19.77 | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (10374), (10451), (function-axioms) are
% 135.21/19.77 | | | | | | | | | | | | | | inconsistent by sub-proof #662.
% 135.21/19.77 | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | Case 2:
% 135.21/19.77 | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | (10452) all_57_14 = e1 & op(e0, e1) = e1
% 135.21/19.77 | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | ALPHA: (10452) implies:
% 135.21/19.77 | | | | | | | | | | | | | | (10453) op(e0, e1) = e1
% 135.21/19.77 | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 135.21/19.77 | | | | | | | | | | | | | | e1, e1, e0, simplifying with (157), (10453) gives:
% 135.21/19.77 | | | | | | | | | | | | | | (10454) all_52_11 = e1
% 135.21/19.77 | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | REDUCE: (8981), (10454) imply:
% 135.21/19.77 | | | | | | | | | | | | | | (10455) $false
% 135.21/19.77 | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | CLOSE: (10455) is inconsistent.
% 135.21/19.77 | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | End of split
% 135.21/19.77 | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | End of split
% 135.21/19.77 | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | Case 2:
% 135.21/19.77 | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | (10456) ~ (all_8_1 = e3) & op(e1, e1) = all_8_1 &
% 135.21/19.77 | | | | | | | | | | | | $i(all_8_1)
% 135.21/19.77 | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | REF_CLOSE: (10374), (10456), (function-axioms) are
% 135.21/19.77 | | | | | | | | | | | | inconsistent by sub-proof #128.
% 135.21/19.77 | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | End of split
% 135.21/19.77 | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | Case 2:
% 135.21/19.77 | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | (10457) ~ (all_12_1 = e3) & op(e1, e1) = all_12_1 &
% 135.21/19.77 | | | | | | | | | | | $i(all_12_1)
% 135.21/19.77 | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | ALPHA: (10457) implies:
% 135.21/19.77 | | | | | | | | | | | (10458) ~ (all_12_1 = e3)
% 135.21/19.77 | | | | | | | | | | | (10459) op(e1, e1) = all_12_1
% 135.21/19.77 | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | REF_CLOSE: (10374), (10458), (10459), (function-axioms) are
% 135.21/19.77 | | | | | | | | | | | inconsistent by sub-proof #36.
% 135.21/19.77 | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | End of split
% 135.21/19.77 | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | End of split
% 135.21/19.77 | | | | | | | | |
% 135.21/19.77 | | | | | | | | Case 2:
% 135.21/19.77 | | | | | | | | |
% 135.21/19.77 | | | | | | | | | (10460) all_16_2 = e2
% 135.21/19.77 | | | | | | | | |
% 135.21/19.77 | | | | | | | | | COMBINE_EQS: (327), (10460) imply:
% 135.21/19.77 | | | | | | | | | (10461) all_10_2 = e2
% 135.21/19.77 | | | | | | | | |
% 135.21/19.77 | | | | | | | | | COMBINE_EQS: (299), (10461) imply:
% 135.21/19.77 | | | | | | | | | (10462) all_38_2 = e2
% 135.21/19.77 | | | | | | | | |
% 135.21/19.77 | | | | | | | | | REDUCE: (336), (10461) imply:
% 135.21/19.77 | | | | | | | | | (10463) ~ (all_52_1 = e2)
% 135.21/19.77 | | | | | | | | |
% 135.21/19.77 | | | | | | | | | REDUCE: (340), (10461) imply:
% 135.21/19.77 | | | | | | | | | (10464) ~ (all_52_3 = e2)
% 135.21/19.77 | | | | | | | | |
% 135.21/19.77 | | | | | | | | | REDUCE: (344), (10461) imply:
% 135.21/19.77 | | | | | | | | | (10465) ~ (all_52_8 = e2)
% 135.21/19.77 | | | | | | | | |
% 135.21/19.77 | | | | | | | | | REDUCE: (346), (10461) imply:
% 135.21/19.77 | | | | | | | | | (10466) ~ (all_52_12 = e2)
% 135.21/19.77 | | | | | | | | |
% 135.21/19.77 | | | | | | | | | REDUCE: (45), (10461) imply:
% 135.21/19.77 | | | | | | | | | (10467) op(e3, e3) = e2
% 135.21/19.77 | | | | | | | | |
% 135.21/19.77 | | | | | | | | | BETA: splitting (234) gives:
% 135.21/19.77 | | | | | | | | |
% 135.21/19.77 | | | | | | | | | Case 1:
% 135.21/19.77 | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | (10468) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 135.21/19.77 | | | | | | | | | | & op(e3, e2) = e1)
% 135.21/19.77 | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | REF_CLOSE: (6), (170), (10220), (10467), (10468),
% 135.21/19.77 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.21/19.77 | | | | | | | | | | #378.
% 135.21/19.77 | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | Case 2:
% 135.21/19.77 | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | (10469) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 135.21/19.77 | | | | | | | | | | & op(e3, e0) = e1)
% 135.21/19.77 | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | BETA: splitting (10469) gives:
% 135.21/19.77 | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | Case 1:
% 135.21/19.77 | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | (10470) all_57_4 = e1 & op(e3, e1) = e1
% 135.21/19.77 | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | ALPHA: (10470) implies:
% 135.21/19.77 | | | | | | | | | | | (10471) all_57_4 = e1
% 135.21/19.77 | | | | | | | | | | | (10472) op(e3, e1) = e1
% 135.21/19.77 | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | BETA: splitting (88) gives:
% 135.21/19.77 | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | Case 1:
% 135.21/19.77 | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | (10473) ~ (all_38_2 = e2)
% 135.21/19.77 | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | REDUCE: (10462), (10473) imply:
% 135.21/19.77 | | | | | | | | | | | | (10474) $false
% 135.21/19.77 | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | CLOSE: (10474) is inconsistent.
% 135.21/19.77 | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | Case 2:
% 135.21/19.77 | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | (10475) ( ~ (all_38_0 = e0) & op(e2, e3) = all_38_0 &
% 135.21/19.77 | | | | | | | | | | | | $i(all_38_0)) | ( ~ (all_38_1 = e1) & op(e2, e2)
% 135.21/19.77 | | | | | | | | | | | | = all_38_1 & $i(all_38_1))
% 135.21/19.77 | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | BETA: splitting (233) gives:
% 135.21/19.77 | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | Case 1:
% 135.21/19.77 | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | (10476) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 135.21/19.77 | | | | | | | | | | | | | & op(e2, e3) = e1)
% 135.21/19.77 | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | BETA: splitting (10476) gives:
% 135.21/19.77 | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | Case 1:
% 135.21/19.77 | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | (10477) all_57_0 = e1 & op(e3, e3) = e1
% 135.21/19.77 | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | ALPHA: (10477) implies:
% 135.21/19.77 | | | | | | | | | | | | | | (10478) op(e3, e3) = e1
% 135.21/19.77 | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (168), (169), (232),
% 135.21/19.77 | | | | | | | | | | | | | | (236), (238), (10465), (10471), (10472), (10478),
% 135.21/19.77 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.21/19.77 | | | | | | | | | | | | | | #14.
% 135.21/19.77 | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | Case 2:
% 135.21/19.77 | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | (10479) all_57_2 = e1 & op(e2, e3) = e1
% 135.21/19.77 | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | REF_CLOSE: (167), (10219), (10479), (function-axioms) are
% 135.21/19.77 | | | | | | | | | | | | | | inconsistent by sub-proof #676.
% 135.21/19.77 | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | End of split
% 135.21/19.77 | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | Case 2:
% 135.21/19.77 | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | (10480) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 135.21/19.77 | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 135.21/19.77 | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | BETA: splitting (10480) gives:
% 135.21/19.77 | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | Case 1:
% 135.21/19.77 | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | (10481) all_57_6 = e1 & op(e1, e3) = e1
% 135.21/19.77 | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | ALPHA: (10481) implies:
% 135.21/19.77 | | | | | | | | | | | | | | (10482) op(e1, e3) = e1
% 135.21/19.77 | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | BETA: splitting (10475) gives:
% 135.21/19.77 | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | Case 1:
% 135.21/19.77 | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | (10483) ~ (all_38_0 = e0) & op(e2, e3) = all_38_0 &
% 135.21/19.77 | | | | | | | | | | | | | | | $i(all_38_0)
% 135.21/19.77 | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | ALPHA: (10483) implies:
% 135.21/19.77 | | | | | | | | | | | | | | | (10484) ~ (all_38_0 = e0)
% 135.21/19.77 | | | | | | | | | | | | | | | (10485) op(e2, e3) = all_38_0
% 135.21/19.77 | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1,
% 135.21/19.77 | | | | | | | | | | | | | | | e3, e1, simplifying with (163), (10482) gives:
% 135.21/19.77 | | | | | | | | | | | | | | | (10486) all_52_2 = e1
% 135.21/19.77 | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 135.21/19.77 | | | | | | | | | | | | | | | all_38_0, e3, e2, simplifying with (167), (10485)
% 135.21/19.77 | | | | | | | | | | | | | | | gives:
% 135.21/19.77 | | | | | | | | | | | | | | | (10487) all_52_1 = all_38_0
% 135.21/19.77 | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e1,
% 135.21/19.77 | | | | | | | | | | | | | | | e1, e3, simplifying with (169), (10472) gives:
% 135.21/19.77 | | | | | | | | | | | | | | | (10488) all_52_8 = e1
% 135.21/19.77 | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | COMBINE_EQS: (268), (10487) imply:
% 135.21/19.77 | | | | | | | | | | | | | | | (10489) all_54_4 = all_38_0
% 135.21/19.77 | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | REDUCE: (148), (10487) imply:
% 135.21/19.77 | | | | | | | | | | | | | | | (10490) ~ (all_52_3 = all_38_0)
% 135.21/19.77 | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | SIMP: (10490) implies:
% 135.21/19.77 | | | | | | | | | | | | | | | (10491) ~ (all_52_3 = all_38_0)
% 135.21/19.77 | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | REDUCE: (145), (10487) imply:
% 135.21/19.77 | | | | | | | | | | | | | | | (10492) ~ (all_52_13 = all_38_0)
% 135.21/19.77 | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | SIMP: (10492) implies:
% 135.21/19.77 | | | | | | | | | | | | | | | (10493) ~ (all_52_13 = all_38_0)
% 135.21/19.77 | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | REDUCE: (10463), (10487) imply:
% 135.21/19.77 | | | | | | | | | | | | | | | (10494) ~ (all_38_0 = e2)
% 135.21/19.77 | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | REDUCE: (10219), (10487) imply:
% 135.21/19.77 | | | | | | | | | | | | | | | (10495) ~ (all_38_0 = e1)
% 135.21/19.77 | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | REDUCE: (144), (10486) imply:
% 135.21/19.77 | | | | | | | | | | | | | | | (10496) ~ (all_52_3 = e1)
% 135.21/19.77 | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | REDUCE: (141), (10486) imply:
% 135.21/19.77 | | | | | | | | | | | | | | | (10497) ~ (all_52_14 = e1)
% 135.21/19.77 | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | REDUCE: (121), (10488) imply:
% 135.21/19.77 | | | | | | | | | | | | | | | (10498) ~ (all_52_11 = e1)
% 135.21/19.77 | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | REDUCE: (120), (10488) imply:
% 135.21/19.77 | | | | | | | | | | | | | | | (10499) ~ (all_52_12 = e1)
% 135.21/19.77 | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | REDUCE: (10465), (10488) imply:
% 135.21/19.77 | | | | | | | | | | | | | | | (10500) ~ (e2 = e1)
% 135.21/19.77 | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 135.21/19.77 | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | Case 1:
% 135.21/19.77 | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | (10501) all_54_4 = e3
% 135.21/19.77 | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | COMBINE_EQS: (10489), (10501) imply:
% 135.21/19.77 | | | | | | | | | | | | | | | | (10502) all_38_0 = e3
% 135.21/19.77 | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | SIMP: (10502) implies:
% 135.21/19.77 | | | | | | | | | | | | | | | | (10503) all_38_0 = e3
% 135.21/19.77 | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | REDUCE: (10491), (10503) imply:
% 135.21/19.77 | | | | | | | | | | | | | | | | (10504) ~ (all_52_3 = e3)
% 135.21/19.77 | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | REDUCE: (10493), (10503) imply:
% 135.21/19.77 | | | | | | | | | | | | | | | | (10505) ~ (all_52_13 = e3)
% 135.21/19.77 | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | REDUCE: (10485), (10503) imply:
% 135.21/19.77 | | | | | | | | | | | | | | | | (10506) op(e2, e3) = e3
% 135.21/19.77 | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 135.21/19.77 | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.77 | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | (10507) all_54_12 = e3
% 135.21/19.77 | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (10504), (10507) are inconsistent by
% 135.21/19.77 | | | | | | | | | | | | | | | | | sub-proof #424.
% 135.21/19.77 | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.77 | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | (10508) ~ (all_54_12 = e3)
% 135.21/19.77 | | | | | | | | | | | | | | | | | (10509) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 135.21/19.77 | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | BETA: splitting (10509) gives:
% 135.21/19.77 | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.77 | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | (10510) all_54_12 = e2
% 135.21/19.77 | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (10464), (10510) are inconsistent by
% 135.21/19.77 | | | | | | | | | | | | | | | | | | sub-proof #423.
% 135.21/19.77 | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.77 | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | (10511) ~ (all_54_12 = e2)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | (10512) all_54_12 = e1 | all_54_12 = e0
% 135.21/19.77 | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | BETA: splitting (10512) gives:
% 135.21/19.77 | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | (10513) all_54_12 = e1
% 135.21/19.77 | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (8979), (10513) are inconsistent by
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | sub-proof #99.
% 135.21/19.77 | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | (10514) all_54_12 = e0
% 135.21/19.77 | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (10514) imply:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | (10515) all_52_3 = e0
% 135.21/19.77 | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | SIMP: (10515) implies:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | (10516) all_52_3 = e0
% 135.21/19.77 | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | REDUCE: (139), (10516) imply:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | (10517) ~ (all_52_11 = e0)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | SIMP: (10517) implies:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | (10518) ~ (all_52_11 = e0)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | REDUCE: (10504), (10516) imply:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | (10519) ~ (e3 = e0)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | REDUCE: (10464), (10516) imply:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | (10520) ~ (e2 = e0)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | REDUCE: (8979), (10516) imply:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | (10521) ~ (e1 = e0)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | (10522) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | BETA: splitting (10522) gives:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | (10523) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10523) gives:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | (10524) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10524) implies:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | (10525) ~ (all_56_3 = e3)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | (10526) op(e2, e3) = all_56_3
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10506), (10525), (10526), (function-axioms) are
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #347.
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | (10527) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10527) implies:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | (10528) op(e3, e3) = e1
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (168), (169), (232),
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | (236), (238), (10465), (10471), (10472), (10528),
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | #14.
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | (10529) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (10223), (10467), (10529),
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | #136.
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | (10530) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | BETA: splitting (10530) gives:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.77 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | (10531) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10531) gives:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10532) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10532) implies:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10533) ~ (all_56_17 = e1)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10534) op(e3, e1) = all_56_17
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10472), (10533), (10534), (function-axioms) are
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #349.
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10535) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2,
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10535) implies:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10536) ~ (all_56_21 = e1)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10537) ~ (all_56_5 = e3)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10538) op(e1, e0) = all_56_29
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10539) op(e1, e1) = all_56_21
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10540) op(e1, e3) = all_56_5
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10541) op(e2, e1) = e2
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | all_56_29, e0, e1, simplifying with (160), (10538)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | gives:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10542) all_56_29 = all_52_14
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | all_56_21, e1, e1, simplifying with (39), (10539)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | gives:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10543) all_56_21 = all_6_2
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2,
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (165), (10541) gives:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10544) all_52_9 = e2
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10536), (10543) imply:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10545) ~ (all_6_2 = e1)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (10544) imply:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10546) ~ (all_52_11 = e2)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | SIMP: (10546) implies:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10547) ~ (all_52_11 = e2)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (10544) imply:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10548) ~ (all_52_13 = e2)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | SIMP: (10548) implies:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10549) ~ (all_52_13 = e2)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (10544) imply:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10550) ~ (all_6_2 = e2)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | (10551) all_54_7 = e3
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (10551) imply:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | (10552) all_52_13 = e3
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10505), (10552) imply:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | (10553) $false
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10553) is inconsistent.
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | (10554) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | (10555) all_54_14 = e3
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (10555) imply:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | (10556) all_52_11 = e3
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10556) implies:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | (10557) all_52_11 = e3
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (364), (10557) imply:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | (10558) ~ (all_6_2 = e3)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10558) implies:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | (10559) ~ (all_6_2 = e3)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | (10560) all_54_10 = e3
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (10559), (10560) are inconsistent by
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #742.
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | (10561) ~ (all_54_10 = e3)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | (10562) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10562) gives:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | (10563) all_54_10 = e2
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (8992), (10563) are inconsistent by
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #741.
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | (10564) all_54_10 = e1 | all_54_10 = e0
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10554) gives:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | (10565) all_54_7 = e2
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (10549), (10565) are inconsistent by
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #337.
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | (10566) all_54_7 = e1 | all_54_7 = e0
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10566) gives:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10567) all_54_7 = e1
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (8983), (10567) are inconsistent by
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #314.
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10568) all_54_7 = e0
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (10568) imply:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10569) all_52_13 = e0
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10569) implies:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10570) all_52_13 = e0
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (10570) imply:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10571) ~ (all_52_12 = e0)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10572) all_54_3 = e3
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (10572) imply:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10573) all_52_12 = e3
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (10573) imply:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10574) ~ (all_52_14 = e3)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10574) implies:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10575) ~ (all_52_14 = e3)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (103), (160), (218), (334), (10218),
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10537), (10540), (10545), (10559), (10564),
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10575), (function-axioms) are inconsistent by
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #186.
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10576) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (8982), (10466), (10571), (10576) are
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #320.
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | (10577) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (8981), (10518), (10547), (10577) are
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #526.
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | (10578) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10578) gives:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10579) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10579) implies:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10580) op(e2, e2) = e0
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10223), (10580), (function-axioms) are
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675.
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10581) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10581) gives:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | (10582) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10582) implies:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | (10583) op(e1, e1) = e2
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (8992), (10583), (function-axioms) are
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | (10584) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (157), (160), (8984), (8991), (10472),
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | (10518), (10584), (function-axioms) are
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #15.
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.78 | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.78 | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | End of split
% 135.21/19.78 | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | End of split
% 135.21/19.78 | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | Case 2:
% 135.21/19.78 | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | (10585) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 135.21/19.78 | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | REF_CLOSE: (10484), (10489), (10494), (10495), (10585) are
% 135.21/19.78 | | | | | | | | | | | | | | | | inconsistent by sub-proof #126.
% 135.21/19.78 | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | End of split
% 135.21/19.78 | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | Case 2:
% 135.21/19.78 | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | (10586) ~ (all_38_1 = e1) & op(e2, e2) = all_38_1 &
% 135.21/19.78 | | | | | | | | | | | | | | | $i(all_38_1)
% 135.21/19.78 | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | REF_CLOSE: (10223), (10586), (function-axioms) are
% 135.21/19.78 | | | | | | | | | | | | | | | inconsistent by sub-proof #125.
% 135.21/19.78 | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | End of split
% 135.21/19.78 | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | Case 2:
% 135.21/19.78 | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | (10587) all_57_12 = e1 & op(e0, e3) = e1
% 135.21/19.78 | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | REF_CLOSE: (159), (8979), (10587), (function-axioms) are
% 135.21/19.78 | | | | | | | | | | | | | | inconsistent by sub-proof #48.
% 135.21/19.78 | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | End of split
% 135.21/19.78 | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | End of split
% 135.21/19.78 | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | End of split
% 135.21/19.78 | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | Case 2:
% 135.21/19.78 | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | (10588) all_57_9 = e1 & op(e3, e0) = e1
% 135.21/19.78 | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | REF_CLOSE: (168), (8982), (10588), (function-axioms) are
% 135.21/19.78 | | | | | | | | | | | inconsistent by sub-proof #181.
% 135.21/19.78 | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | End of split
% 135.21/19.78 | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | End of split
% 135.21/19.78 | | | | | | | | |
% 135.21/19.78 | | | | | | | | End of split
% 135.21/19.78 | | | | | | | |
% 135.21/19.78 | | | | | | | End of split
% 135.21/19.78 | | | | | | |
% 135.21/19.78 | | | | | | Case 2:
% 135.21/19.78 | | | | | | |
% 135.21/19.78 | | | | | | | (10589) all_10_2 = e0
% 135.21/19.78 | | | | | | | (10590) ( ~ (all_10_0 = e2) & op(e0, e3) = all_10_0 &
% 135.21/19.78 | | | | | | | $i(all_10_0)) | ( ~ (all_10_1 = e1) & op(e0, e0) =
% 135.21/19.78 | | | | | | | all_10_1 & $i(all_10_1))
% 135.21/19.78 | | | | | | |
% 135.21/19.78 | | | | | | | REDUCE: (336), (10589) imply:
% 135.21/19.78 | | | | | | | (10591) ~ (all_52_1 = e0)
% 135.21/19.78 | | | | | | |
% 135.21/19.78 | | | | | | | REDUCE: (338), (10589) imply:
% 135.21/19.78 | | | | | | | (10592) ~ (all_52_2 = e0)
% 135.21/19.78 | | | | | | |
% 135.21/19.78 | | | | | | | REDUCE: (340), (10589) imply:
% 135.21/19.78 | | | | | | | (10593) ~ (all_52_3 = e0)
% 135.21/19.78 | | | | | | |
% 135.21/19.78 | | | | | | | REDUCE: (342), (10589) imply:
% 135.21/19.78 | | | | | | | (10594) ~ (all_52_4 = e0)
% 135.21/19.78 | | | | | | |
% 135.21/19.78 | | | | | | | REDUCE: (344), (10589) imply:
% 135.21/19.78 | | | | | | | (10595) ~ (all_52_8 = e0)
% 135.21/19.78 | | | | | | |
% 135.21/19.78 | | | | | | | REDUCE: (45), (10589) imply:
% 135.21/19.78 | | | | | | | (10596) op(e3, e3) = e0
% 135.21/19.78 | | | | | | |
% 135.21/19.78 | | | | | | | BETA: splitting (234) gives:
% 135.21/19.78 | | | | | | |
% 135.21/19.78 | | | | | | | Case 1:
% 135.21/19.78 | | | | | | | |
% 135.21/19.78 | | | | | | | | (10597) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 &
% 135.21/19.78 | | | | | | | | op(e3, e2) = e1)
% 135.21/19.78 | | | | | | | |
% 135.21/19.78 | | | | | | | | REF_CLOSE: (4), (170), (10220), (10596), (10597),
% 135.21/19.78 | | | | | | | | (function-axioms) are inconsistent by sub-proof #117.
% 135.21/19.78 | | | | | | | |
% 135.21/19.78 | | | | | | | Case 2:
% 135.21/19.78 | | | | | | | |
% 135.21/19.78 | | | | | | | | (10598) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 &
% 135.21/19.78 | | | | | | | | op(e3, e0) = e1)
% 135.21/19.78 | | | | | | | |
% 135.21/19.78 | | | | | | | | BETA: splitting (10598) gives:
% 135.21/19.78 | | | | | | | |
% 135.21/19.78 | | | | | | | | Case 1:
% 135.21/19.78 | | | | | | | | |
% 135.21/19.78 | | | | | | | | | (10599) all_57_4 = e1 & op(e3, e1) = e1
% 135.21/19.78 | | | | | | | | |
% 135.21/19.78 | | | | | | | | | ALPHA: (10599) implies:
% 135.21/19.78 | | | | | | | | | (10600) all_57_4 = e1
% 135.21/19.78 | | | | | | | | | (10601) op(e3, e1) = e1
% 135.21/19.78 | | | | | | | | |
% 135.21/19.78 | | | | | | | | | BETA: splitting (233) gives:
% 135.21/19.78 | | | | | | | | |
% 135.21/19.78 | | | | | | | | | Case 1:
% 135.21/19.78 | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | (10602) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 135.21/19.78 | | | | | | | | | | & op(e2, e3) = e1)
% 135.21/19.78 | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | BETA: splitting (10602) gives:
% 135.21/19.78 | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | Case 1:
% 135.21/19.78 | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | (10603) all_57_0 = e1 & op(e3, e3) = e1
% 135.21/19.78 | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | ALPHA: (10603) implies:
% 135.21/19.78 | | | | | | | | | | | (10604) op(e3, e3) = e1
% 135.21/19.78 | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (236),
% 135.21/19.78 | | | | | | | | | | | (238), (10594), (10600), (10604),
% 135.21/19.78 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.21/19.78 | | | | | | | | | | | #667.
% 135.21/19.78 | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | Case 2:
% 135.21/19.78 | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | (10605) all_57_2 = e1 & op(e2, e3) = e1
% 135.21/19.78 | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | REF_CLOSE: (167), (10219), (10605), (function-axioms) are
% 135.21/19.78 | | | | | | | | | | | inconsistent by sub-proof #676.
% 135.21/19.78 | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | End of split
% 135.21/19.78 | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | Case 2:
% 135.21/19.78 | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | (10606) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 135.21/19.78 | | | | | | | | | | e1 & op(e0, e3) = e1)
% 135.21/19.78 | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | BETA: splitting (10606) gives:
% 135.21/19.78 | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | Case 1:
% 135.21/19.78 | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | (10607) all_57_6 = e1 & op(e1, e3) = e1
% 135.21/19.78 | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | ALPHA: (10607) implies:
% 135.21/19.78 | | | | | | | | | | | (10608) op(e1, e3) = e1
% 135.21/19.78 | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | BETA: splitting (10590) gives:
% 135.21/19.78 | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | Case 1:
% 135.21/19.78 | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | (10609) ~ (all_10_0 = e2) & op(e0, e3) = all_10_0 &
% 135.21/19.78 | | | | | | | | | | | | $i(all_10_0)
% 135.21/19.78 | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | ALPHA: (10609) implies:
% 135.21/19.78 | | | | | | | | | | | | (10610) ~ (all_10_0 = e2)
% 135.21/19.78 | | | | | | | | | | | | (10611) op(e0, e3) = all_10_0
% 135.21/19.78 | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 135.21/19.78 | | | | | | | | | | | | all_10_0, e3, e0, simplifying with (159), (10611)
% 135.21/19.78 | | | | | | | | | | | | gives:
% 135.21/19.78 | | | | | | | | | | | | (10612) all_52_3 = all_10_0
% 135.21/19.78 | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1,
% 135.21/19.78 | | | | | | | | | | | | e3, e1, simplifying with (163), (10608) gives:
% 135.21/19.78 | | | | | | | | | | | | (10613) all_52_2 = e1
% 135.21/19.78 | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e1,
% 135.21/19.78 | | | | | | | | | | | | e1, e3, simplifying with (169), (10601) gives:
% 135.21/19.78 | | | | | | | | | | | | (10614) all_52_8 = e1
% 135.21/19.78 | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | COMBINE_EQS: (248), (10612) imply:
% 135.21/19.78 | | | | | | | | | | | | (10615) all_54_12 = all_10_0
% 135.21/19.78 | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | REDUCE: (148), (10612) imply:
% 135.21/19.78 | | | | | | | | | | | | (10616) ~ (all_52_1 = all_10_0)
% 135.21/19.78 | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | REDUCE: (141), (10613) imply:
% 135.21/19.78 | | | | | | | | | | | | (10617) ~ (all_52_14 = e1)
% 135.21/19.78 | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | REDUCE: (140), (10612) imply:
% 135.21/19.78 | | | | | | | | | | | | (10618) ~ (all_52_7 = all_10_0)
% 135.21/19.78 | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | SIMP: (10618) implies:
% 135.21/19.78 | | | | | | | | | | | | (10619) ~ (all_52_7 = all_10_0)
% 135.21/19.78 | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | REDUCE: (139), (10612) imply:
% 135.21/19.78 | | | | | | | | | | | | (10620) ~ (all_52_11 = all_10_0)
% 135.21/19.78 | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | SIMP: (10620) implies:
% 135.21/19.78 | | | | | | | | | | | | (10621) ~ (all_52_11 = all_10_0)
% 135.21/19.78 | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | REDUCE: (8979), (10612) imply:
% 135.21/19.78 | | | | | | | | | | | | (10622) ~ (all_10_0 = e1)
% 135.21/19.78 | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | REDUCE: (10593), (10612) imply:
% 135.21/19.78 | | | | | | | | | | | | (10623) ~ (all_10_0 = e0)
% 135.21/19.78 | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | BETA: splitting (192) gives:
% 135.21/19.78 | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | Case 1:
% 135.21/19.78 | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | (10624) all_54_12 = e3
% 135.21/19.78 | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | COMBINE_EQS: (10615), (10624) imply:
% 135.21/19.78 | | | | | | | | | | | | | (10625) all_10_0 = e3
% 135.21/19.78 | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | SIMP: (10625) implies:
% 135.21/19.78 | | | | | | | | | | | | | (10626) all_10_0 = e3
% 135.21/19.78 | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | REDUCE: (10616), (10626) imply:
% 135.21/19.78 | | | | | | | | | | | | | (10627) ~ (all_52_1 = e3)
% 135.21/19.78 | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | REDUCE: (10619), (10626) imply:
% 135.21/19.78 | | | | | | | | | | | | | (10628) ~ (all_52_7 = e3)
% 135.21/19.78 | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | REDUCE: (10621), (10626) imply:
% 135.21/19.78 | | | | | | | | | | | | | (10629) ~ (all_52_11 = e3)
% 135.21/19.78 | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | BETA: splitting (211) gives:
% 135.21/19.78 | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | Case 1:
% 135.21/19.78 | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | (10630) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 135.21/19.78 | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 135.21/19.78 | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | BETA: splitting (10630) gives:
% 135.21/19.78 | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | Case 1:
% 135.21/19.78 | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | (10631) all_57_12 = e3 & op(e0, e3) = e3
% 135.21/19.78 | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | ALPHA: (10631) implies:
% 135.21/19.78 | | | | | | | | | | | | | | | (10632) all_57_12 = e3
% 135.21/19.78 | | | | | | | | | | | | | | | (10633) op(e0, e3) = e3
% 135.21/19.78 | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 135.21/19.78 | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | Case 1:
% 135.21/19.78 | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | (10634) all_54_4 = e3
% 135.21/19.78 | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | REF_CLOSE: (268), (10627), (10634) are inconsistent by
% 135.21/19.78 | | | | | | | | | | | | | | | | sub-proof #481.
% 135.21/19.78 | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | Case 2:
% 135.21/19.78 | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | (10635) ~ (all_54_4 = e3)
% 135.21/19.78 | | | | | | | | | | | | | | | | (10636) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 135.21/19.78 | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | BETA: splitting (10636) gives:
% 135.21/19.78 | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.78 | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | (10637) all_54_4 = e2
% 135.21/19.78 | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (10637) imply:
% 135.21/19.78 | | | | | | | | | | | | | | | | | (10638) all_52_1 = e2
% 135.21/19.78 | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | SIMP: (10638) implies:
% 135.21/19.78 | | | | | | | | | | | | | | | | | (10639) all_52_1 = e2
% 135.21/19.78 | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | REDUCE: (146), (10639) imply:
% 135.21/19.78 | | | | | | | | | | | | | | | | | (10640) ~ (all_52_9 = e2)
% 135.21/19.78 | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | SIMP: (10640) implies:
% 135.21/19.78 | | | | | | | | | | | | | | | | | (10641) ~ (all_52_9 = e2)
% 135.21/19.78 | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | REDUCE: (10627), (10639) imply:
% 135.21/19.78 | | | | | | | | | | | | | | | | | (10642) ~ (e3 = e2)
% 135.21/19.78 | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 135.21/19.78 | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.78 | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | (10643) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 135.21/19.78 | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 135.21/19.78 | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | BETA: splitting (10643) gives:
% 135.21/19.78 | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | (10644) all_57_4 = e2 & op(e3, e1) = e2
% 135.21/19.78 | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | ALPHA: (10644) implies:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | (10645) all_57_4 = e2
% 135.21/19.78 | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10600), (10645) are inconsistent by
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | sub-proof #669.
% 135.21/19.78 | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | (10646) all_57_5 = e2 & op(e2, e1) = e2
% 135.21/19.78 | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | ALPHA: (10646) implies:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | (10647) op(e2, e1) = e2
% 135.21/19.78 | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (10641), (10647), (function-axioms) are
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #770.
% 135.21/19.78 | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.78 | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.78 | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | (10648) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 135.21/19.78 | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | BETA: splitting (10648) gives:
% 135.21/19.78 | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | (10649) all_57_8 = e2 & op(e1, e1) = e2
% 135.21/19.78 | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | ALPHA: (10649) implies:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | (10650) op(e1, e1) = e2
% 135.21/19.78 | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (8992), (10650), (function-axioms) are
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 135.21/19.78 | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | (10651) all_57_14 = e2 & op(e0, e1) = e2
% 135.21/19.78 | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | ALPHA: (10651) implies:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | (10652) all_57_14 = e2
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | (10653) op(e0, e1) = e2
% 135.21/19.78 | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | (10654) all_57_15 = e0 & op(e0, e0) = e0
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | ALPHA: (10654) implies:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | (10655) op(e0, e0) = e0
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8991), (10655), (function-axioms) are
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #220.
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | (10656) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | ALPHA: (10656) implies:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | (10657) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | (10658) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10658) gives:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10659) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10659) gives:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | (10660) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10660) implies:
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | (10661) op(e3, e3) = e2
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (163), (167), (231), (10591), (10592),
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | (10632), (10661), (function-axioms) are
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #25.
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | (10662) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10662) implies:
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | (10663) op(e3, e3) = e1
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (236),
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | (238), (10594), (10600), (10663),
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | #667.
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | (10664) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10223), (10633), (10664), (function-axioms)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #115.
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | (10665) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10665) gives:
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | (10666) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (10601), (10641), (10666),
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | #348.
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | (10667) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10667) gives:
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | (10668) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10668) implies:
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | (10669) op(e2, e2) = e0
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10223), (10669), (function-axioms) are
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675.
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | (10670) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10670) gives:
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (10671) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10671) implies:
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (10672) op(e1, e1) = e2
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (8992), (10672), (function-axioms) are
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767.
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (10673) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10673) implies:
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (10674) op(e0, e0) = all_56_31
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (10675) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10675) gives:
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | (10676) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27))
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10676) gives:
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | (10677) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10677) implies:
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | (10678) op(e0, e3) = e0
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (10593), (10678), (function-axioms) are
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #219.
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | (10679) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10679) implies:
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | (10680) all_56_31 = e2
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10674), (10680) imply:
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | (10681) op(e0, e0) = e2
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (209), (10632), (10652),
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | (10657), (10681), (function-axioms) are
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #284.
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | (10682) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10682) gives:
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | (10683) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10683) implies:
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | (10684) op(e1, e0) = e1
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (8984), (10684), (function-axioms) are
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #327.
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | (10685) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10685) implies:
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | (10686) op(e0, e1) = e0
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10653), (10686), (function-axioms) are
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #660.
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.79 | | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.79 | | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | End of split
% 135.21/19.79 | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.79 | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | (10687) all_54_4 = e1 | all_54_4 = e0
% 135.21/19.79 | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (163), (268), (10591), (10608), (10687),
% 135.21/19.79 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.21/19.79 | | | | | | | | | | | | | | | | | #243.
% 135.21/19.79 | | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | End of split
% 135.21/19.79 | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | End of split
% 135.21/19.79 | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | Case 2:
% 135.21/19.79 | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | (10688) all_57_13 = e3 & op(e0, e2) = e3
% 135.21/19.79 | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | REF_CLOSE: (158), (10628), (10688), (function-axioms) are
% 135.21/19.79 | | | | | | | | | | | | | | | inconsistent by sub-proof #556.
% 135.21/19.79 | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | End of split
% 135.21/19.79 | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | Case 2:
% 135.21/19.79 | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | (10689) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 135.21/19.79 | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 135.21/19.79 | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | REF_CLOSE: (8), (157), (8991), (10629), (10689),
% 135.21/19.79 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.21/19.79 | | | | | | | | | | | | | | #37.
% 135.21/19.79 | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | End of split
% 135.21/19.79 | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | Case 2:
% 135.21/19.79 | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | (10690) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 135.21/19.79 | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | REF_CLOSE: (10610), (10615), (10622), (10623), (10690) are
% 135.21/19.79 | | | | | | | | | | | | | inconsistent by sub-proof #24.
% 135.21/19.79 | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | End of split
% 135.21/19.79 | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | Case 2:
% 135.21/19.79 | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | (10691) ~ (all_10_1 = e1) & op(e0, e0) = all_10_1 &
% 135.21/19.79 | | | | | | | | | | | | $i(all_10_1)
% 135.21/19.79 | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | REF_CLOSE: (8991), (10691), (function-axioms) are
% 135.21/19.79 | | | | | | | | | | | | inconsistent by sub-proof #16.
% 135.21/19.79 | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | End of split
% 135.21/19.79 | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | Case 2:
% 135.21/19.79 | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | (10692) all_57_12 = e1 & op(e0, e3) = e1
% 135.21/19.79 | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | REF_CLOSE: (159), (8979), (10692), (function-axioms) are
% 135.21/19.79 | | | | | | | | | | | inconsistent by sub-proof #48.
% 135.21/19.79 | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | End of split
% 135.21/19.79 | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | End of split
% 135.21/19.79 | | | | | | | | |
% 135.21/19.79 | | | | | | | | Case 2:
% 135.21/19.79 | | | | | | | | |
% 135.21/19.79 | | | | | | | | | (10693) all_57_9 = e1 & op(e3, e0) = e1
% 135.21/19.79 | | | | | | | | |
% 135.21/19.79 | | | | | | | | | REF_CLOSE: (168), (8982), (10693), (function-axioms) are
% 135.21/19.79 | | | | | | | | | inconsistent by sub-proof #181.
% 135.21/19.79 | | | | | | | | |
% 135.21/19.79 | | | | | | | | End of split
% 135.21/19.79 | | | | | | | |
% 135.21/19.79 | | | | | | | End of split
% 135.21/19.79 | | | | | | |
% 135.21/19.79 | | | | | | End of split
% 135.21/19.79 | | | | | |
% 135.21/19.79 | | | | | End of split
% 135.21/19.79 | | | | |
% 135.21/19.79 | | | | Case 2:
% 135.21/19.79 | | | | |
% 135.21/19.79 | | | | | (10694) all_6_2 = e2
% 135.21/19.79 | | | | | (10695) ( ~ (all_6_0 = e0) & op(e2, e1) = all_6_0 & $i(all_6_0)) |
% 135.21/19.79 | | | | | ( ~ (all_6_1 = e3) & op(e2, e2) = all_6_1 & $i(all_6_1))
% 135.21/19.79 | | | | |
% 135.21/19.79 | | | | | COMBINE_EQS: (324), (10694) imply:
% 135.21/19.79 | | | | | (10696) all_18_2 = e2
% 135.21/19.79 | | | | |
% 135.21/19.79 | | | | | REDUCE: (348), (10694) imply:
% 135.21/19.79 | | | | | (10697) ~ (all_52_2 = e2)
% 135.21/19.79 | | | | |
% 135.21/19.79 | | | | | REDUCE: (359), (10694) imply:
% 135.21/19.79 | | | | | (10698) ~ (all_52_6 = e2)
% 135.21/19.79 | | | | |
% 135.21/19.79 | | | | | REDUCE: (361), (10694) imply:
% 135.21/19.79 | | | | | (10699) ~ (all_52_8 = e2)
% 135.21/19.79 | | | | |
% 135.21/19.79 | | | | | REDUCE: (364), (10694) imply:
% 135.21/19.79 | | | | | (10700) ~ (all_52_11 = e2)
% 135.21/19.79 | | | | |
% 135.21/19.79 | | | | | REDUCE: (366), (10694) imply:
% 135.21/19.79 | | | | | (10701) ~ (all_52_14 = e2)
% 135.21/19.79 | | | | |
% 135.21/19.79 | | | | | REDUCE: (39), (10694) imply:
% 135.21/19.79 | | | | | (10702) op(e1, e1) = e2
% 135.21/19.79 | | | | |
% 135.21/19.79 | | | | | BETA: splitting (8977) gives:
% 135.21/19.79 | | | | |
% 135.21/19.79 | | | | | Case 1:
% 135.21/19.79 | | | | | |
% 135.21/19.79 | | | | | | (10703) ~ (all_4_0 = e3) & op(e1, e0) = all_4_0 & $i(all_4_0)
% 135.21/19.79 | | | | | |
% 135.21/19.79 | | | | | | ALPHA: (10703) implies:
% 135.21/19.79 | | | | | | (10704) ~ (all_4_0 = e3)
% 135.21/19.79 | | | | | | (10705) op(e1, e0) = all_4_0
% 135.21/19.79 | | | | | |
% 135.21/19.79 | | | | | | BETA: splitting (217) gives:
% 135.21/19.79 | | | | | |
% 135.21/19.79 | | | | | | Case 1:
% 135.21/19.79 | | | | | | |
% 135.21/19.79 | | | | | | | (10706) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 &
% 135.21/19.79 | | | | | | | op(e1, e2) = e2)
% 135.21/19.79 | | | | | | |
% 135.21/19.79 | | | | | | | BETA: splitting (10706) gives:
% 135.21/19.79 | | | | | | |
% 135.21/19.79 | | | | | | | Case 1:
% 135.21/19.79 | | | | | | | |
% 135.21/19.79 | | | | | | | | (10707) all_57_6 = e2 & op(e1, e3) = e2
% 135.21/19.79 | | | | | | | |
% 135.21/19.79 | | | | | | | | REF_CLOSE: (163), (10697), (10707), (function-axioms) are
% 135.21/19.79 | | | | | | | | inconsistent by sub-proof #341.
% 135.21/19.79 | | | | | | | |
% 135.21/19.79 | | | | | | | Case 2:
% 135.21/19.79 | | | | | | | |
% 135.21/19.79 | | | | | | | | (10708) all_57_7 = e2 & op(e1, e2) = e2
% 135.21/19.79 | | | | | | | |
% 135.21/19.79 | | | | | | | | REF_CLOSE: (162), (10698), (10708), (function-axioms) are
% 135.21/19.79 | | | | | | | | inconsistent by sub-proof #515.
% 135.21/19.79 | | | | | | | |
% 135.21/19.79 | | | | | | | End of split
% 135.21/19.79 | | | | | | |
% 135.21/19.79 | | | | | | Case 2:
% 135.21/19.79 | | | | | | |
% 135.21/19.79 | | | | | | | (10709) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 &
% 135.21/19.79 | | | | | | | op(e1, e0) = e2)
% 135.21/19.79 | | | | | | |
% 135.21/19.79 | | | | | | | BETA: splitting (10709) gives:
% 135.21/19.79 | | | | | | |
% 135.21/19.79 | | | | | | | Case 1:
% 135.21/19.79 | | | | | | | |
% 135.21/19.79 | | | | | | | | (10710) all_57_8 = e2 & op(e1, e1) = e2
% 135.21/19.79 | | | | | | | |
% 135.21/19.79 | | | | | | | | ALPHA: (10710) implies:
% 135.21/19.79 | | | | | | | | (10711) all_57_8 = e2
% 135.21/19.79 | | | | | | | |
% 135.21/19.79 | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 135.21/19.79 | | | | | | | | all_4_0, e0, e1, simplifying with (160), (10705)
% 135.21/19.79 | | | | | | | | gives:
% 135.21/19.79 | | | | | | | | (10712) all_52_14 = all_4_0
% 135.21/19.79 | | | | | | | |
% 135.21/19.79 | | | | | | | | COMBINE_EQS: (249), (10712) imply:
% 135.21/19.79 | | | | | | | | (10713) all_54_11 = all_4_0
% 135.21/19.79 | | | | | | | |
% 135.21/19.79 | | | | | | | | REDUCE: (141), (10712) imply:
% 135.21/19.79 | | | | | | | | (10714) ~ (all_52_2 = all_4_0)
% 135.21/19.79 | | | | | | | |
% 135.21/19.79 | | | | | | | | REDUCE: (126), (10712) imply:
% 135.21/19.79 | | | | | | | | (10715) ~ (all_52_6 = all_4_0)
% 135.21/19.79 | | | | | | | |
% 135.21/19.79 | | | | | | | | REDUCE: (112), (10712) imply:
% 135.21/19.79 | | | | | | | | (10716) ~ (all_52_12 = all_4_0)
% 135.21/19.79 | | | | | | | |
% 135.21/19.79 | | | | | | | | REDUCE: (110), (10712) imply:
% 135.21/19.79 | | | | | | | | (10717) ~ (all_52_13 = all_4_0)
% 135.21/19.79 | | | | | | | |
% 135.21/19.79 | | | | | | | | REDUCE: (10701), (10712) imply:
% 135.21/19.79 | | | | | | | | (10718) ~ (all_4_0 = e2)
% 135.21/19.79 | | | | | | | |
% 135.21/19.79 | | | | | | | | REDUCE: (8984), (10712) imply:
% 135.21/19.79 | | | | | | | | (10719) ~ (all_4_0 = e1)
% 135.21/19.79 | | | | | | | |
% 135.21/19.79 | | | | | | | | BETA: splitting (193) gives:
% 135.21/19.79 | | | | | | | |
% 135.21/19.79 | | | | | | | | Case 1:
% 135.21/19.79 | | | | | | | | |
% 135.21/19.79 | | | | | | | | | (10720) all_54_11 = e3
% 135.21/19.79 | | | | | | | | |
% 135.21/19.79 | | | | | | | | | COMBINE_EQS: (10713), (10720) imply:
% 135.21/19.79 | | | | | | | | | (10721) all_4_0 = e3
% 135.21/19.79 | | | | | | | | |
% 135.21/19.79 | | | | | | | | | SIMP: (10721) implies:
% 135.21/19.79 | | | | | | | | | (10722) all_4_0 = e3
% 135.21/19.79 | | | | | | | | |
% 135.21/19.79 | | | | | | | | | REDUCE: (10704), (10722) imply:
% 135.21/19.79 | | | | | | | | | (10723) $false
% 135.21/19.79 | | | | | | | | |
% 135.21/19.79 | | | | | | | | | CLOSE: (10723) is inconsistent.
% 135.21/19.79 | | | | | | | | |
% 135.21/19.79 | | | | | | | | Case 2:
% 135.21/19.79 | | | | | | | | |
% 135.21/19.79 | | | | | | | | | (10724) ~ (all_54_11 = e3)
% 135.21/19.79 | | | | | | | | | (10725) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 135.21/19.79 | | | | | | | | |
% 135.21/19.79 | | | | | | | | | BETA: splitting (10725) gives:
% 135.21/19.79 | | | | | | | | |
% 135.21/19.79 | | | | | | | | | Case 1:
% 135.21/19.79 | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | (10726) all_54_11 = e2
% 135.21/19.79 | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | COMBINE_EQS: (10713), (10726) imply:
% 135.21/19.79 | | | | | | | | | | (10727) all_4_0 = e2
% 135.21/19.79 | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | SIMP: (10727) implies:
% 135.21/19.79 | | | | | | | | | | (10728) all_4_0 = e2
% 135.21/19.79 | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | REDUCE: (10718), (10728) imply:
% 135.21/19.79 | | | | | | | | | | (10729) $false
% 135.21/19.79 | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | CLOSE: (10729) is inconsistent.
% 135.21/19.79 | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | Case 2:
% 135.21/19.79 | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | (10730) ~ (all_54_11 = e2)
% 135.21/19.79 | | | | | | | | | | (10731) all_54_11 = e1 | all_54_11 = e0
% 135.21/19.79 | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | BETA: splitting (10731) gives:
% 135.21/19.79 | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | Case 1:
% 135.21/19.79 | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | (10732) all_54_11 = e1
% 135.21/19.79 | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | COMBINE_EQS: (10713), (10732) imply:
% 135.21/19.79 | | | | | | | | | | | (10733) all_4_0 = e1
% 135.21/19.79 | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | SIMP: (10733) implies:
% 135.21/19.79 | | | | | | | | | | | (10734) all_4_0 = e1
% 135.21/19.79 | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | REDUCE: (10719), (10734) imply:
% 135.21/19.79 | | | | | | | | | | | (10735) $false
% 135.21/19.79 | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | CLOSE: (10735) is inconsistent.
% 135.21/19.79 | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | Case 2:
% 135.21/19.79 | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | (10736) all_54_11 = e0
% 135.21/19.79 | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | COMBINE_EQS: (10713), (10736) imply:
% 135.21/19.79 | | | | | | | | | | | (10737) all_4_0 = e0
% 135.21/19.79 | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | SIMP: (10737) implies:
% 135.21/19.79 | | | | | | | | | | | (10738) all_4_0 = e0
% 135.21/19.79 | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | REDUCE: (10714), (10738) imply:
% 135.21/19.79 | | | | | | | | | | | (10739) ~ (all_52_2 = e0)
% 135.21/19.79 | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | REDUCE: (10715), (10738) imply:
% 135.21/19.79 | | | | | | | | | | | (10740) ~ (all_52_6 = e0)
% 135.21/19.79 | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | REDUCE: (10716), (10738) imply:
% 135.21/19.79 | | | | | | | | | | | (10741) ~ (all_52_12 = e0)
% 135.21/19.79 | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | REDUCE: (10717), (10738) imply:
% 135.21/19.79 | | | | | | | | | | | (10742) ~ (all_52_13 = e0)
% 135.21/19.79 | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | REDUCE: (10704), (10738) imply:
% 135.21/19.79 | | | | | | | | | | | (10743) ~ (e3 = e0)
% 135.21/19.79 | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | REDUCE: (10718), (10738) imply:
% 135.21/19.79 | | | | | | | | | | | (10744) ~ (e2 = e0)
% 135.21/19.79 | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | REDUCE: (10719), (10738) imply:
% 135.21/19.79 | | | | | | | | | | | (10745) ~ (e1 = e0)
% 135.21/19.79 | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | BETA: splitting (215) gives:
% 135.21/19.79 | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | Case 1:
% 135.21/19.79 | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | (10746) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 135.21/19.79 | | | | | | | | | | | | & op(e1, e2) = e0)
% 135.21/19.79 | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | BETA: splitting (10746) gives:
% 135.21/19.79 | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | Case 1:
% 135.21/19.79 | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | (10747) all_57_6 = e0 & op(e1, e3) = e0
% 135.21/19.79 | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | REF_CLOSE: (163), (10739), (10747), (function-axioms) are
% 135.21/19.79 | | | | | | | | | | | | | inconsistent by sub-proof #73.
% 135.21/19.79 | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | Case 2:
% 135.21/19.79 | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | (10748) all_57_7 = e0 & op(e1, e2) = e0
% 135.21/19.79 | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | REF_CLOSE: (162), (10740), (10748), (function-axioms) are
% 135.21/19.79 | | | | | | | | | | | | | inconsistent by sub-proof #505.
% 135.21/19.79 | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | End of split
% 135.21/19.79 | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | Case 2:
% 135.21/19.79 | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | (10749) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 135.21/19.79 | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 135.21/19.79 | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | BETA: splitting (10749) gives:
% 135.21/19.79 | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | Case 1:
% 135.21/19.79 | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | (10750) all_57_8 = e0 & op(e1, e1) = e0
% 135.21/19.79 | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | ALPHA: (10750) implies:
% 135.21/19.79 | | | | | | | | | | | | | (10751) op(e1, e1) = e0
% 135.21/19.79 | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | REF_CLOSE: (5), (10702), (10751), (function-axioms) are
% 135.21/19.79 | | | | | | | | | | | | | inconsistent by sub-proof #98.
% 135.21/19.79 | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | Case 2:
% 135.21/19.79 | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | (10752) all_57_11 = e0 & op(e1, e0) = e0
% 135.21/19.79 | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | ALPHA: (10752) implies:
% 135.21/19.79 | | | | | | | | | | | | | (10753) all_57_11 = e0
% 135.21/19.79 | | | | | | | | | | | | | (10754) op(e1, e0) = e0
% 135.21/19.79 | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | BETA: splitting (43) gives:
% 135.21/19.79 | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | Case 1:
% 135.21/19.79 | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | (10755) ~ (all_8_2 = e1)
% 135.21/19.79 | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 135.21/19.79 | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | Case 1:
% 135.21/19.79 | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | (10756) ~ (all_10_2 = e0)
% 135.21/19.79 | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 135.21/19.79 | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | Case 1:
% 135.21/19.79 | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | (10757) ~ (all_14_2 = e3)
% 135.21/19.79 | | | | | | | | | | | | | | | |
% 135.21/19.79 | | | | | | | | | | | | | | | | REDUCE: (329), (10757) imply:
% 135.21/19.80 | | | | | | | | | | | | | | | | (10758) ~ (all_8_2 = e3)
% 135.21/19.80 | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 135.21/19.80 | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.80 | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | (10759) ~ (all_16_2 = e2)
% 135.21/19.80 | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | REDUCE: (327), (10759) imply:
% 135.21/19.80 | | | | | | | | | | | | | | | | | (10760) ~ (all_10_2 = e2)
% 135.21/19.80 | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | BETA: splitting (58) gives:
% 135.21/19.80 | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.80 | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | (10761) ~ (all_18_2 = e2)
% 135.21/19.80 | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | REDUCE: (10696), (10761) imply:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | (10762) $false
% 135.21/19.80 | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | CLOSE: (10762) is inconsistent.
% 135.21/19.80 | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.80 | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | (10763) ( ~ (all_18_0 = e3) & op(e2, e1) = all_18_0 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | $i(all_18_0)) | ( ~ (all_18_1 = e0) & op(e2, e2)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | = all_18_1 & $i(all_18_1))
% 135.21/19.80 | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 135.21/19.80 | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | (10764) ~ (all_30_2 = e0)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | REDUCE: (309), (10764) imply:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | (10765) ~ (all_8_2 = e0)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | (10766) all_54_5 = e3
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (10766) imply:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | (10767) all_8_2 = e3
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | REDUCE: (10758), (10767) imply:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | (10768) $false
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | CLOSE: (10768) is inconsistent.
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | (10769) ~ (all_54_5 = e3)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | (10770) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (42), (45), (158), (160), (164), (199),
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | (206), (267), (354), (358), (8984), (8991),
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | (10702), (10754), (10755), (10756), (10758),
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | (10760), (10765), (10770), (function-axioms) are
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #38.
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.80 | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | (10771) all_30_2 = e0
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | (10772) ( ~ (all_30_0 = e3) & op(e0, e2) = all_30_0 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | $i(all_30_0)) | ( ~ (all_30_1 = e1) & op(e0, e0)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | = all_30_1 & $i(all_30_1))
% 135.21/19.80 | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (309), (10771) imply:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | (10773) all_8_2 = e0
% 135.21/19.80 | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | SIMP: (10773) implies:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | (10774) all_8_2 = e0
% 135.21/19.80 | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | REDUCE: (347), (10774) imply:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | (10775) ~ (all_52_1 = e0)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | REDUCE: (42), (10774) imply:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | (10776) op(e2, e2) = e0
% 135.21/19.80 | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | BETA: splitting (10763) gives:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | (10777) ~ (all_18_0 = e3) & op(e2, e1) = all_18_0 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | $i(all_18_0)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | ALPHA: (10777) implies:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | (10778) ~ (all_18_0 = e3)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | (10779) op(e2, e1) = all_18_0
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | (10780) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (167), (10756), (10775), (10780),
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | #142.
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | (10781) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10781) gives:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | (10782) all_57_6 = e0 & op(e1, e3) = e0
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (10739), (10782), (function-axioms) are
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #73.
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | (10783) all_57_12 = e0 & op(e0, e3) = e0
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10783) implies:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | (10784) all_57_12 = e0
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | (10785) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10785) gives:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | (10786) all_57_0 = e2 & op(e3, e3) = e2
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10786) implies:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | (10787) op(e3, e3) = e2
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (10760), (10787), (function-axioms) are
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #536.
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | (10788) all_57_2 = e2 & op(e2, e3) = e2
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10788) implies:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | (10789) all_57_2 = e2
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | (10790) op(e2, e3) = e2
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | (10791) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10791) gives:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | (10792) all_57_12 = e2 & op(e0, e3) = e2
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10792) implies:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | (10793) all_57_12 = e2
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10784), (10793) are inconsistent by
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #682.
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | (10794) all_57_13 = e2 & op(e0, e2) = e2
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10794) implies:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | (10795) all_57_13 = e2
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | (10796) op(e0, e2) = e2
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (10797) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (10776), (10790), (10797),
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | #93.
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (10798) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10798) gives:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10799) all_57_5 = e1 & op(e2, e1) = e1
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10799) implies:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10800) all_57_5 = e1
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10801) op(e2, e1) = e1
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10802) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (10776), (10789), (10802),
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #94.
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10803) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10803) gives:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10804) all_57_5 = e3 & op(e2, e1) = e3
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10804) implies:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10805) all_57_5 = e3
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10800), (10805) are inconsistent by
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #88.
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10806) all_57_10 = e3 & op(e2, e0) = e3
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10806) implies:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10807) op(e2, e0) = e3
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10772) gives:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10808) ~ (all_30_0 = e3) & op(e0, e2) = all_30_0 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_30_0)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10808) implies:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10809) ~ (all_30_0 = e3)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10810) op(e0, e2) = all_30_0
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10811) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10811) gives:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10812) all_57_9 = e2 & op(e3, e0) = e2
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10812) implies:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10813) op(e3, e0) = e2
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e2,
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (158), (10796) gives:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10814) all_52_7 = e2
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7,
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_30_0, e2, e0, simplifying with (158), (10810)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10815) all_52_7 = all_30_0
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e0, e2, simplifying with (164), (10807) gives:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10816) all_52_13 = e3
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e1,
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (165), (10801) gives:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10817) all_52_9 = e1
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_18_0, e1, e2, simplifying with (165), (10779)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10818) all_52_9 = all_18_0
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, e3, simplifying with (168), (10813) gives:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10819) all_52_12 = e2
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10814), (10815) imply:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10820) all_30_0 = e2
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10817), (10818) imply:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10821) all_18_0 = e1
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (346), (10819) imply:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10822) ~ (all_10_2 = e2)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10809), (10820) imply:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10823) ~ (e3 = e2)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10778), (10821) imply:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10824) ~ (e3 = e1)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10825) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10825) gives:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10826) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (10754), (10760), (10826), (function-axioms)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #44.
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10827) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (168), (10776), (10813), (10827),
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #13.
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10828) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10828) gives:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10829) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10702), (10754), (10829), (function-axioms)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #42.
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10830) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10830) gives:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10831) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10831) implies:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10832) op(e2, e0) = e2
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (164), (10807), (10832), (function-axioms)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #546.
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10833) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (42), (158), (160), (199), (267), (354),
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8984), (8991), (10754), (10755), (10758),
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10801), (10833), (function-axioms) are
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #12.
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10834) all_57_10 = e2 & op(e2, e0) = e2
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10834) implies:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10835) op(e2, e0) = e2
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (164), (10807), (10835), (function-axioms)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #546.
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10836) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10836) gives:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10837) all_57_11 = e2 & op(e1, e0) = e2
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (10701), (10837), (function-axioms) are
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #514.
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10838) all_57_15 = e2 & op(e0, e0) = e2
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10838) implies:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10839) all_57_15 = e2
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10840) op(e0, e0) = e2
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10841) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10841) gives:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10842) all_57_12 = e3 & op(e0, e3) = e3
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10842) implies:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10843) all_57_12 = e3
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (208), (209), (10795),
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10839), (10843) are inconsistent by sub-proof
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #11.
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10844) all_57_13 = e3 & op(e0, e2) = e3
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10844) implies:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10845) all_57_13 = e3
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10795), (10845) are inconsistent by
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #408.
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10846) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10846) gives:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10847) all_57_14 = e3 & op(e0, e1) = e3
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10847) implies:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10848) all_57_14 = e3
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10849) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10849) gives:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10850) all_57_12 = e1 & op(e0, e3) = e1
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10850) implies:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10851) all_57_12 = e1
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (208), (10795), (10839), (10848),
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10851) are inconsistent by sub-proof #398.
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10852) all_57_13 = e1 & op(e0, e2) = e1
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (8980), (10852), (function-axioms) are
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #178.
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10853) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10853) gives:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10854) all_57_14 = e1 & op(e0, e1) = e1
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10848), (10854) are inconsistent by
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #247.
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8991), (10840), (function-axioms) are
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #636.
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10855) all_57_15 = e3 & op(e0, e0) = e3
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10855) implies:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10856) op(e0, e0) = e3
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10840), (10856), (function-axioms) are
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #634.
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10857) ~ (all_30_1 = e1) & op(e0, e0) = all_30_1 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_30_1)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8991), (10857), (function-axioms) are
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #53.
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10858) all_57_10 = e1 & op(e2, e0) = e1
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10858) implies:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10859) op(e2, e0) = e1
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8983), (10859), (function-axioms) are
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #180.
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | (10860) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (157), (8991), (10700), (10860),
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | #34.
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | (10861) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10861) gives:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | (10862) all_57_6 = e2 & op(e1, e3) = e2
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (10697), (10862), (function-axioms) are
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #341.
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | (10863) all_57_12 = e2 & op(e0, e3) = e2
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10863) implies:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | (10864) all_57_12 = e2
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10784), (10864) are inconsistent by
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #682.
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | (10865) ~ (all_18_1 = e0) & op(e2, e2) = all_18_1 &
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | $i(all_18_1)
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10776), (10865), (function-axioms) are
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #103.
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.80 | | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.80 | | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | End of split
% 135.21/19.80 | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.80 | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | (10866) all_16_2 = e2
% 135.21/19.80 | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | COMBINE_EQS: (327), (10866) imply:
% 135.21/19.80 | | | | | | | | | | | | | | | | | (10867) all_10_2 = e2
% 135.21/19.80 | | | | | | | | | | | | | | | | |
% 135.21/19.80 | | | | | | | | | | | | | | | | | REDUCE: (342), (10867) imply:
% 135.21/19.81 | | | | | | | | | | | | | | | | | (10868) ~ (all_52_4 = e2)
% 135.21/19.81 | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | REDUCE: (346), (10867) imply:
% 135.21/19.81 | | | | | | | | | | | | | | | | | (10869) ~ (all_52_12 = e2)
% 135.21/19.81 | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | REDUCE: (45), (10867) imply:
% 135.21/19.81 | | | | | | | | | | | | | | | | | (10870) op(e3, e3) = e2
% 135.21/19.81 | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | (10871) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 135.21/19.81 | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | BETA: splitting (10871) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | (10872) all_57_9 = e2 & op(e3, e0) = e2
% 135.21/19.81 | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (10869), (10872), (function-axioms) are
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #460.
% 135.21/19.81 | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | (10873) all_57_10 = e2 & op(e2, e0) = e2
% 135.21/19.81 | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | ALPHA: (10873) implies:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | (10874) op(e2, e0) = e2
% 135.21/19.81 | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | (10875) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | BETA: splitting (10875) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | (10876) all_57_9 = e3 & op(e3, e0) = e3
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | ALPHA: (10876) implies:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | (10877) all_57_9 = e3
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | (10878) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10878) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | (10879) all_57_12 = e2 & op(e0, e3) = e2
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10879) implies:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | (10880) all_57_12 = e2
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | (10870), (10880), (function-axioms) are
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #290.
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | (10881) all_57_13 = e2 & op(e0, e2) = e2
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10881) implies:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | (10882) all_57_13 = e2
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | (10883) op(e0, e2) = e2
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | (10884) all_54_3 = e3
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (10884) imply:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | (10885) all_52_12 = e3
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (10885) imply:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | (10886) ~ (all_52_4 = e3)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (10885) imply:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | (10887) ~ (all_52_8 = e3)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (10885) imply:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | (10888) ~ (all_52_13 = e3)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10888) implies:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | (10889) ~ (all_52_13 = e3)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | (10890) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10890) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (10891) all_57_1 = e3 & op(e3, e2) = e3
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10891) implies:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (10892) op(e3, e2) = e3
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (10886), (10892), (function-axioms) are
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #738.
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (10893) all_57_3 = e3 & op(e2, e2) = e3
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10893) implies:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (10894) op(e2, e2) = e3
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (10758), (10894), (function-axioms) are
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #228.
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | (10895) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10895) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (10896) all_57_7 = e3 & op(e1, e2) = e3
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10896) implies:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (10897) all_57_7 = e3
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (10898) op(e1, e2) = e3
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | (10899) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10899) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10900) all_57_1 = e1 & op(e3, e2) = e1
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10900) implies:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10901) all_57_1 = e1
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10902) op(e3, e2) = e1
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10903) all_54_7 = e3
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (10889), (10903) are inconsistent by
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #338.
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10904) ~ (all_54_7 = e3)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10905) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10905) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10906) all_54_7 = e2
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (10906) imply:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10907) all_52_13 = e2
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10907) implies:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10908) all_52_13 = e2
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (358), (10908) imply:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10909) ~ (all_8_2 = e2)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10909) implies:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10910) ~ (all_8_2 = e2)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10889), (10908) imply:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10911) ~ (e3 = e2)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10912) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (10870), (10902), (10912),
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #333.
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10913) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10913) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10914) all_57_4 = e0 & op(e3, e1) = e0
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10914) implies:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10915) op(e3, e1) = e0
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10916) all_54_5 = e3
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (10758), (10916) are inconsistent by
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #554.
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10917) ~ (all_54_5 = e3)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10918) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10919) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10919) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10920) all_57_1 = e0 & op(e3, e2) = e0
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10920) implies:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10921) op(e3, e2) = e0
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10902), (10921), (function-axioms) are
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #730.
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10922) all_57_3 = e0 & op(e2, e2) = e0
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10922) implies:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10923) all_57_3 = e0
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10918) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10924) all_54_5 = e2
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (10910), (10924) are inconsistent by
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #340.
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10925) ~ (all_54_5 = e2)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10926) all_54_5 = e1 | all_54_5 = e0
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10927) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10927) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10928) all_57_4 = e1 & op(e3, e1) = e1
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10928) implies:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10929) op(e3, e1) = e1
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10915), (10929), (function-axioms) are
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #343.
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10930) all_57_5 = e1 & op(e2, e1) = e1
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10930) implies:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10931) op(e2, e1) = e1
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10926) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10932) all_54_5 = e1
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (10755), (10932) are inconsistent by
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #339.
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10933) all_54_5 = e0
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (10933) imply:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10934) all_8_2 = e0
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10934) implies:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10935) all_8_2 = e0
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (350), (10935) imply:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10936) ~ (all_52_4 = e0)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10937) all_54_1 = e3
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (10937) imply:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10938) all_52_4 = e3
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10886), (10938) imply:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10939) $false
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10939) is inconsistent.
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10940) ~ (all_54_1 = e3)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10941) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10941) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10942) all_54_1 = e2
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (10942) imply:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10943) all_52_4 = e2
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10868), (10943) imply:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10944) $false
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10944) is inconsistent.
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10945) ~ (all_54_1 = e2)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10946) all_54_1 = e1 | all_54_1 = e0
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10946) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10947) all_54_1 = e1
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (10947) imply:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10948) all_52_4 = e1
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (10948) imply:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10949) ~ (all_52_8 = e1)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10949) implies:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10950) ~ (all_52_8 = e1)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10868), (10948) imply:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10951) ~ (e2 = e1)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10952) all_54_2 = e3
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (10952) imply:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10953) all_52_8 = e3
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10887), (10953) imply:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10954) $false
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10954) is inconsistent.
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10955) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10955) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10956) all_54_2 = e2
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (10956) imply:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10957) all_52_8 = e2
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10699), (10957) imply:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10958) $false
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10958) is inconsistent.
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10959) ~ (all_54_2 = e2)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10960) all_54_2 = e1 | all_54_2 = e0
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10961) all_54_9 = e3
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (10961) imply:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10962) all_52_6 = e3
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (10962) imply:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10963) ~ (all_52_7 = e3)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10963) implies:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10964) ~ (all_52_7 = e3)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10960) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10965) all_54_2 = e1
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (10965) imply:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10966) all_52_8 = e1
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10950), (10966) imply:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10967) $false
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10967) is inconsistent.
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10968) all_54_2 = e0
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (10968) imply:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10969) all_52_8 = e0
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (10969) imply:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10970) ~ (all_52_11 = e0)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10970) implies:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10971) ~ (all_52_11 = e0)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10972) all_54_14 = e3
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (10972) imply:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10973) all_52_11 = e3
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10973) implies:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10974) all_52_11 = e3
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (10974) imply:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10975) ~ (all_52_3 = e3)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (10974) imply:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10976) ~ (all_52_9 = e3)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10977) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10977) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10978) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10978) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10979) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10979) implies:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10980) ~ (all_56_19 = e1)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10981) op(e2, e1) = all_56_19
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10931), (10980), (10981), (function-axioms) are
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #106.
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10982) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10982) implies:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10983) op(e3, e3) = e1
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (236),
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (10886), (10901), (10902), (10983),
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #610.
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10984) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10984) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10985) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3,
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10985) implies:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10986) ~ (all_56_15 = e2)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10987) op(e0, e2) = all_56_15
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10883), (10986), (10987), (function-axioms) are
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #609.
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10988) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2,
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10988) implies:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10989) op(e2, e2) = e3
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (45), (117), (145), (146), (157),
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (158), (159), (160), (164), (165), (167), (169),
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197), (198), (206), (211), (219), (220), (222),
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223), (224), (259), (260), (8983), (8984),
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8991), (10695), (10700), (10702), (10711),
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10742), (10754), (10756), (10889), (10964),
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10975), (10976), (10989), (function-axioms) are
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #7.
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10990) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10990) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10991) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10702), (10754), (10991), (function-axioms)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #42.
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10992) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10992) gives:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10993) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10993) implies:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10994) ~ (all_56_15 = e2)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10995) op(e0, e2) = all_56_15
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10883), (10994), (10995), (function-axioms) are
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #609.
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10996) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (42), (158), (160), (199), (267), (354),
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8984), (8991), (10754), (10755), (10758),
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10931), (10996), (function-axioms) are
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #12.
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10997) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (8981), (10700), (10971), (10997) are
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #526.
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10998) ~ (all_54_9 = e3)
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (257), (10998) imply:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10999) ~ (all_52_6 = e3)
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (10898), (10999), (function-axioms) are
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #654.
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11000) all_54_1 = e0
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (11000) imply:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11001) all_52_4 = e0
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10936), (11001) imply:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11002) $false
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11002) is inconsistent.
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11003) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11003) gives:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11004) all_57_8 = e1 & op(e1, e1) = e1
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10711), (11004) are inconsistent by
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #85.
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11005) all_57_14 = e1 & op(e0, e1) = e1
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11005) implies:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11006) all_57_14 = e1
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11007) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11007) gives:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11008) all_57_12 = e3 & op(e0, e3) = e3
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11008) implies:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11009) all_57_12 = e3
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10926) gives:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11010) all_54_5 = e1
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (10755), (11010) are inconsistent by
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #339.
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11011) all_54_5 = e0
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (11011) imply:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11012) all_8_2 = e0
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11012) implies:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11013) all_8_2 = e0
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (347), (11013) imply:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11014) ~ (all_52_1 = e0)
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (163), (167), (231), (10739), (10870),
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11009), (11014), (function-axioms) are
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #25.
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11015) all_57_13 = e3 & op(e0, e2) = e3
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (228), (229), (10897),
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10923), (11015) are inconsistent by sub-proof
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #388.
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11016) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8991), (11006), (11016), (function-axioms)
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #6.
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11017) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (162), (10740), (10882), (11017),
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #170.
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11018) all_57_9 = e0 & op(e3, e0) = e0
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (10741), (11018), (function-axioms) are
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #618.
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11019) all_54_7 = e1 | all_54_7 = e0
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (8983), (10742), (11019) are inconsistent
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #313.
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11020) all_57_3 = e1 & op(e2, e2) = e1
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11020) implies:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11021) op(e2, e2) = e1
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (10755), (11021), (function-axioms) are
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #57.
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (11022) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11022) gives:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11023) all_57_7 = e1 & op(e1, e2) = e1
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10897), (11023) are inconsistent by
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #603.
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11024) all_57_13 = e1 & op(e0, e2) = e1
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (8980), (11024), (function-axioms) are
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #178.
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (11025) all_57_13 = e3 & op(e0, e2) = e3
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11025) implies:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (11026) all_57_13 = e3
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10882), (11026) imply:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (11027) e3 = e2
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11027) implies:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (11028) e3 = e2
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10877), (11028) imply:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (11029) all_57_9 = e2
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (234),
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (10870), (10886), (11029),
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | #250.
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (11030) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (8982), (10741), (10869), (11030) are
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #320.
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | (11031) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (157), (8991), (10700), (11031),
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | #34.
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | (11032) all_57_10 = e3 & op(e2, e0) = e3
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | ALPHA: (11032) implies:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | (11033) op(e2, e0) = e3
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (164), (10874), (11033), (function-axioms)
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #546.
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | (11034) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | BETA: splitting (11034) gives:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | (11035) all_57_11 = e3 & op(e1, e0) = e3
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10753), (11035) are inconsistent by
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | sub-proof #5.
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | (11036) all_57_15 = e3 & op(e0, e0) = e3
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | ALPHA: (11036) implies:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | (11037) op(e0, e0) = e3
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8991), (11037), (function-axioms) are
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #606.
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.82 | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.82 | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.82 | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | (11038) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 135.30/19.82 | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 135.30/19.82 | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | BETA: splitting (11038) gives:
% 135.30/19.82 | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | (11039) all_57_11 = e2 & op(e1, e0) = e2
% 135.30/19.82 | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (10701), (11039), (function-axioms) are
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #514.
% 135.30/19.82 | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | (11040) all_57_15 = e2 & op(e0, e0) = e2
% 135.30/19.82 | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | ALPHA: (11040) implies:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | (11041) op(e0, e0) = e2
% 135.30/19.82 | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8991), (11041), (function-axioms) are
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #636.
% 135.30/19.82 | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.82 | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | End of split
% 135.30/19.82 | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | End of split
% 135.30/19.82 | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | Case 2:
% 135.30/19.82 | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | (11042) all_14_2 = e3
% 135.30/19.82 | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | COMBINE_EQS: (329), (11042) imply:
% 135.30/19.82 | | | | | | | | | | | | | | | | (11043) all_8_2 = e3
% 135.30/19.82 | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | REDUCE: (352), (11043) imply:
% 135.30/19.82 | | | | | | | | | | | | | | | | (11044) ~ (all_52_6 = e3)
% 135.30/19.82 | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | REDUCE: (354), (11043) imply:
% 135.30/19.82 | | | | | | | | | | | | | | | | (11045) ~ (all_52_7 = e3)
% 135.30/19.82 | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | REDUCE: (356), (11043) imply:
% 135.30/19.82 | | | | | | | | | | | | | | | | (11046) ~ (all_52_9 = e3)
% 135.30/19.82 | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | REDUCE: (358), (11043) imply:
% 135.30/19.82 | | | | | | | | | | | | | | | | (11047) ~ (all_52_13 = e3)
% 135.30/19.82 | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | REDUCE: (42), (11043) imply:
% 135.30/19.82 | | | | | | | | | | | | | | | | (11048) op(e2, e2) = e3
% 135.30/19.82 | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 135.30/19.82 | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.82 | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | (11049) all_54_9 = e3
% 135.30/19.82 | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (11044), (11049) are inconsistent by
% 135.30/19.82 | | | | | | | | | | | | | | | | | sub-proof #64.
% 135.30/19.82 | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.82 | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | (11050) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 135.30/19.82 | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | BETA: splitting (11050) gives:
% 135.30/19.82 | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.82 | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | (11051) all_54_9 = e2
% 135.30/19.82 | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (10698), (11051) are inconsistent by
% 135.30/19.82 | | | | | | | | | | | | | | | | | | sub-proof #582.
% 135.30/19.82 | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.82 | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | (11052) all_54_9 = e1 | all_54_9 = e0
% 135.30/19.82 | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | BETA: splitting (11052) gives:
% 135.30/19.82 | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | (11053) all_54_9 = e1
% 135.30/19.82 | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (11053) imply:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | (11054) all_52_6 = e1
% 135.30/19.82 | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | SIMP: (11054) implies:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | (11055) all_52_6 = e1
% 135.30/19.82 | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | REDUCE: (143), (11055) imply:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | (11056) ~ (all_52_2 = e1)
% 135.30/19.82 | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | (11057) all_54_8 = e3
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (11057) imply:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | (11058) all_52_2 = e3
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | SIMP: (11058) implies:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | (11059) all_52_2 = e3
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (11059) imply:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | (11060) ~ (all_52_3 = e3)
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | SIMP: (11060) implies:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | (11061) ~ (all_52_3 = e3)
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (45), (117), (145), (146), (157),
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | (158), (159), (160), (164), (165), (167), (169),
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | (197), (198), (206), (211), (219), (220), (222),
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | (223), (224), (259), (260), (8983), (8984),
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | (8991), (10695), (10700), (10702), (10711),
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | (10742), (10754), (10756), (11045), (11046),
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | (11047), (11048), (11061), (function-axioms) are
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #7.
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | (11062) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (10697), (10739), (11056), (11062) are
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #429.
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.82 | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | (11063) all_54_9 = e0
% 135.30/19.82 | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (10740), (11063) are inconsistent by
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | sub-proof #568.
% 135.30/19.82 | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.82 | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | End of split
% 135.30/19.82 | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | End of split
% 135.30/19.82 | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | End of split
% 135.30/19.82 | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | Case 2:
% 135.30/19.82 | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | (11064) all_10_2 = e0
% 135.30/19.82 | | | | | | | | | | | | | | | (11065) ( ~ (all_10_0 = e2) & op(e0, e3) = all_10_0 &
% 135.30/19.82 | | | | | | | | | | | | | | | $i(all_10_0)) | ( ~ (all_10_1 = e1) & op(e0, e0)
% 135.30/19.82 | | | | | | | | | | | | | | | = all_10_1 & $i(all_10_1))
% 135.30/19.82 | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | REDUCE: (340), (11064) imply:
% 135.30/19.82 | | | | | | | | | | | | | | | (11066) ~ (all_52_3 = e0)
% 135.30/19.82 | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | REDUCE: (342), (11064) imply:
% 135.30/19.82 | | | | | | | | | | | | | | | (11067) ~ (all_52_4 = e0)
% 135.30/19.82 | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | REDUCE: (45), (11064) imply:
% 135.30/19.82 | | | | | | | | | | | | | | | (11068) op(e3, e3) = e0
% 135.30/19.82 | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (136), (139), (140),
% 135.30/19.82 | | | | | | | | | | | | | | | (143), (144), (157), (158), (159), (160), (162),
% 135.30/19.82 | | | | | | | | | | | | | | | (163), (164), (168), (170), (192), (195), (196),
% 135.30/19.82 | | | | | | | | | | | | | | | (206), (208), (209), (210), (211), (213), (218),
% 135.30/19.82 | | | | | | | | | | | | | | | (224), (226), (227), (228), (231), (232), (233),
% 135.30/19.82 | | | | | | | | | | | | | | | (235), (237), (238), (248), (257), (258), (8979),
% 135.30/19.82 | | | | | | | | | | | | | | | (8980), (8983), (8984), (8991), (10697), (10698),
% 135.30/19.82 | | | | | | | | | | | | | | | (10700), (10701), (10702), (10739), (10740),
% 135.30/19.82 | | | | | | | | | | | | | | | (10753), (10754), (11065), (11066), (11067),
% 135.30/19.82 | | | | | | | | | | | | | | | (11068), (function-axioms) are inconsistent by
% 135.30/19.82 | | | | | | | | | | | | | | | sub-proof #2.
% 135.30/19.82 | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | End of split
% 135.30/19.82 | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | Case 2:
% 135.30/19.82 | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | (11069) all_8_2 = e1
% 135.30/19.82 | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | COMBINE_EQS: (291), (11069) imply:
% 135.30/19.82 | | | | | | | | | | | | | | (11070) all_48_2 = e1
% 135.30/19.82 | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | REDUCE: (352), (11069) imply:
% 135.30/19.82 | | | | | | | | | | | | | | (11071) ~ (all_52_6 = e1)
% 135.30/19.82 | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | REDUCE: (356), (11069) imply:
% 135.30/19.82 | | | | | | | | | | | | | | (11072) ~ (all_52_9 = e1)
% 135.30/19.82 | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | REDUCE: (42), (11069) imply:
% 135.30/19.82 | | | | | | | | | | | | | | (11073) op(e2, e2) = e1
% 135.30/19.82 | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 135.30/19.82 | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | Case 1:
% 135.30/19.82 | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | (11074) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 135.30/19.82 | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 135.30/19.82 | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | BETA: splitting (11074) gives:
% 135.30/19.82 | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | Case 1:
% 135.30/19.82 | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | (11075) all_57_4 = e1 & op(e3, e1) = e1
% 135.30/19.82 | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | ALPHA: (11075) implies:
% 135.30/19.82 | | | | | | | | | | | | | | | | (11076) op(e3, e1) = e1
% 135.30/19.82 | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 135.30/19.82 | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.82 | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | (11077) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 135.30/19.82 | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 135.30/19.82 | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | BETA: splitting (11077) gives:
% 135.30/19.82 | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.82 | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | (11078) all_57_6 = e1 & op(e1, e3) = e1
% 135.30/19.82 | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | ALPHA: (11078) implies:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | (11079) all_57_6 = e1
% 135.30/19.82 | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 135.30/19.82 | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | (11080) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 135.30/19.82 | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | BETA: splitting (11080) gives:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | (11081) all_57_6 = e3 & op(e1, e3) = e3
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | ALPHA: (11081) implies:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | (11082) all_57_6 = e3
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11079), (11082) are inconsistent by
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | sub-proof #575.
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | (11083) all_57_7 = e3 & op(e1, e2) = e3
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | ALPHA: (11083) implies:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | (11084) op(e1, e2) = e3
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | (11085) all_54_9 = e3
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (11085) imply:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | (11086) all_52_6 = e3
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | SIMP: (11086) implies:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | (11087) all_52_6 = e3
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (11087) imply:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | (11088) ~ (all_52_2 = e3)
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (11087) imply:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | (11089) ~ (all_52_4 = e3)
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | (11090) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11090) gives:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | (11091) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11091) gives:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (11092) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11092) implies:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (11093) op(e3, e2) = e3
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (11089), (11093), (function-axioms) are
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #738.
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (11094) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11094) implies:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (11095) ~ (all_56_29 = e0)
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (11096) op(e1, e0) = all_56_29
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10754), (11095), (11096), (function-axioms) are
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #45.
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | (11097) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11097) gives:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (11098) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3,
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11098) implies:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (11099) op(e0, e0) = all_56_31
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (11100) op(e0, e1) = all_56_23
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (11101) op(e0, e2) = all_56_15
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (11102) op(e0, e3) = all_56_7
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (11103) op(e3, e0) = e3
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (11104) op(e3, e3) = e0
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | (11105) all_54_8 = e3
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (11105) imply:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | (11106) all_52_2 = e3
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11088), (11106) imply:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | (11107) $false
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11107) is inconsistent.
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | (11108) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11108) gives:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (11109) all_54_8 = e2
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (11109) imply:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (11110) all_52_2 = e2
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10697), (11110) imply:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (11111) $false
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11111) is inconsistent.
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (11112) ~ (all_54_8 = e2)
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (11113) all_54_8 = e1 | all_54_8 = e0
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (11114) ~ (all_48_2 = e1)
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11070), (11114) imply:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (11115) $false
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11115) is inconsistent.
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (11116) ( ~ (all_48_0 = e3) & op(e1, e2) = all_48_0 &
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_48_0)) | ( ~ (all_48_1 = e0) & op(e1, e1)
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_48_1 & $i(all_48_1))
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11116) gives:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11117) ~ (all_48_0 = e3) & op(e1, e2) = all_48_0 &
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_48_0)
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11117) implies:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11118) ~ (all_48_0 = e3)
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11119) op(e1, e2) = all_48_0
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11084), (11118), (11119), (function-axioms) are
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #188.
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11120) ~ (all_48_1 = e0) & op(e1, e1) = all_48_1 &
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_48_1)
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11120) implies:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11121) ~ (all_48_1 = e0)
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11122) op(e1, e1) = all_48_1
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11113) gives:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11123) all_54_8 = e1
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (11123) imply:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11124) all_52_2 = e1
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11124) implies:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11125) all_52_2 = e1
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (11125) imply:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11126) ~ (all_52_3 = e1)
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (338), (11125) imply:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11127) ~ (all_10_2 = e1)
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11127) implies:
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11128) ~ (all_10_2 = e1)
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31, e0, e0, simplifying with (8991),
% 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11099) gives:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11129) all_56_31 = e1
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23, e1, e0, simplifying with (157), (11100)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11130) all_56_23 = all_52_11
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7,
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15, e2, e0, simplifying with (158), (11101)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11131) all_56_15 = all_52_7
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_7, e3, e0, simplifying with (159), (11102)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11132) all_56_7 = all_52_3
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_48_1,
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e1, simplifying with (10702), (11122) gives:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11133) all_48_1 = e2
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e0, e3, simplifying with (168), (11103) gives:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11134) all_52_12 = e3
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e1,
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (169), (11076) gives:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11135) all_52_8 = e1
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e0,
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (45), (11104) gives:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11136) all_10_2 = e0
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (340), (11136) imply:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11137) ~ (all_52_3 = e0)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (342), (11136) imply:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11138) ~ (all_52_4 = e0)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10699), (11135) imply:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11139) ~ (e2 = e1)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11140) ~ (all_10_2 = e0)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11136), (11140) imply:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11141) $false
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11141) is inconsistent.
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11142) ( ~ (all_10_0 = e2) & op(e0, e3) = all_10_0 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_10_0)) | ( ~ (all_10_1 = e1) & op(e0, e0)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_10_1 & $i(all_10_1))
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (136), (139), (140),
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (143), (144), (157), (158), (159), (160), (162),
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (163), (164), (168), (170), (192), (195), (196),
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206), (208), (209), (210), (211), (213), (218),
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224), (226), (227), (228), (231), (232), (233),
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235), (237), (238), (248), (257), (258), (8979),
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8980), (8983), (8984), (8991), (10697), (10698),
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10700), (10701), (10702), (10739), (10740),
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10753), (10754), (11104), (11137), (11138),
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11142), (function-axioms) are inconsistent by
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #2.
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11143) all_54_8 = e0
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (10739), (11143) are inconsistent by
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #475.
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | (11144) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2,
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11144) implies:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | (11145) op(e2, e2) = e3
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11073), (11145), (function-axioms) are
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #325.
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | (11146) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11146) gives:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | (11147) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10702), (10754), (11147), (function-axioms)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #42.
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | (11148) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11148) gives:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | (11149) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11149) implies:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | (11150) op(e2, e2) = e0
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11073), (11150), (function-axioms) are
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675.
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | (11151) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11151) gives:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | (11152) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11152) implies:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | (11153) op(e1, e2) = e1
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (11071), (11153), (function-axioms) are
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #65.
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | (11154) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (169), (8984), (8991), (10699), (10754),
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | (11076), (11154), (function-axioms) are
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #17.
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | (11155) ~ (all_54_9 = e3)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | REDUCE: (257), (11155) imply:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | (11156) ~ (all_52_6 = e3)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (11084), (11156), (function-axioms) are
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #654.
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | (11157) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | BETA: splitting (11157) gives:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | (11158) all_57_8 = e3 & op(e1, e1) = e3
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | ALPHA: (11158) implies:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | (11159) op(e1, e1) = e3
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10702), (11159), (function-axioms) are
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #109.
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | (11160) all_57_11 = e3 & op(e1, e0) = e3
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10753), (11160) are inconsistent by
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | sub-proof #5.
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.83 | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | (11161) all_57_7 = e1 & op(e1, e2) = e1
% 135.30/19.83 | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | ALPHA: (11161) implies:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | (11162) op(e1, e2) = e1
% 135.30/19.83 | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (11071), (11162), (function-axioms) are
% 135.30/19.83 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #65.
% 135.30/19.83 | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.83 | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | (11163) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 135.30/19.83 | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 135.30/19.83 | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (160), (8984), (10711), (11163),
% 135.30/19.83 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.30/19.83 | | | | | | | | | | | | | | | | | #1.
% 135.30/19.83 | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | Case 2:
% 135.30/19.83 | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | (11164) all_57_5 = e1 & op(e2, e1) = e1
% 135.30/19.83 | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | REF_CLOSE: (165), (11072), (11164), (function-axioms) are
% 135.30/19.83 | | | | | | | | | | | | | | | | inconsistent by sub-proof #161.
% 135.30/19.83 | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | Case 2:
% 135.30/19.83 | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | (11165) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 135.30/19.83 | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 135.30/19.83 | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | BETA: splitting (11165) gives:
% 135.30/19.83 | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | Case 1:
% 135.30/19.83 | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | (11166) all_57_8 = e1 & op(e1, e1) = e1
% 135.30/19.83 | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10711), (11166) are inconsistent by
% 135.30/19.83 | | | | | | | | | | | | | | | | sub-proof #574.
% 135.30/19.83 | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | Case 2:
% 135.30/19.83 | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | (11167) all_57_14 = e1 & op(e0, e1) = e1
% 135.30/19.83 | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | ALPHA: (11167) implies:
% 135.30/19.83 | | | | | | | | | | | | | | | | (11168) all_57_14 = e1
% 135.30/19.83 | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 135.30/19.83 | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.83 | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | (11169) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 135.30/19.83 | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 135.30/19.83 | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | BETA: splitting (11169) gives:
% 135.30/19.83 | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.83 | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | (11170) all_57_6 = e1 & op(e1, e3) = e1
% 135.30/19.83 | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | ALPHA: (11170) implies:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | (11171) all_57_6 = e1
% 135.30/19.83 | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 135.30/19.83 | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | (11172) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | BETA: splitting (11172) gives:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | (11173) all_57_6 = e3 & op(e1, e3) = e3
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | ALPHA: (11173) implies:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | (11174) all_57_6 = e3
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11171), (11174) are inconsistent by
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | sub-proof #575.
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | (11175) all_57_7 = e3 & op(e1, e2) = e3
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | ALPHA: (11175) implies:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | (11176) op(e1, e2) = e3
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | (11177) all_54_9 = e3
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (11177) imply:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | (11178) all_52_6 = e3
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | SIMP: (11178) implies:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | (11179) all_52_6 = e3
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (11179) imply:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | (11180) ~ (all_52_7 = e3)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | SIMP: (11180) implies:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | (11181) ~ (all_52_7 = e3)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | (11182) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11182) gives:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | (11183) all_57_12 = e3 & op(e0, e3) = e3
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11183) implies:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | (11184) all_57_12 = e3
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | (11185) all_57_15 = e0 & op(e0, e0) = e0
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11185) implies:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | (11186) op(e0, e0) = e0
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8991), (11186), (function-axioms) are
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #220.
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | (11187) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11187) implies:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | (11188) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11188) gives:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | (11189) all_57_12 = e0 & op(e0, e3) = e0
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11189) implies:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | (11190) all_57_12 = e0
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11184), (11190) are inconsistent by
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #492.
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | (11191) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11191) gives:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | (11192) all_57_13 = e0 & op(e0, e2) = e0
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11192) implies:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | (11193) all_57_13 = e0
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | (11194) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11194) gives:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11195) all_57_12 = e2 & op(e0, e3) = e2
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11184), (11195) are inconsistent by
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #196.
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11196) all_57_13 = e2 & op(e0, e2) = e2
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11196) implies:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11197) all_57_13 = e2
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11193), (11197) are inconsistent by
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #404.
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | (11198) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (157), (8991), (10700), (11198),
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | #34.
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | (11199) all_57_14 = e0 & op(e0, e1) = e0
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11168), (11199) are inconsistent by
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #483.
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | (11200) all_57_13 = e3 & op(e0, e2) = e3
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (11181), (11200), (function-axioms) are
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #556.
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | (11201) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8991), (11168), (11201), (function-axioms)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #6.
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | (11202) ~ (all_54_9 = e3)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | REDUCE: (257), (11202) imply:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | (11203) ~ (all_52_6 = e3)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (11176), (11203), (function-axioms) are
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #654.
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | (11204) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 135.30/19.83 | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (10702), (10753), (11204),
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.30/19.83 | | | | | | | | | | | | | | | | | | | #3.
% 135.30/19.83 | | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.83 | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | (11205) all_57_7 = e1 & op(e1, e2) = e1
% 135.30/19.83 | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | ALPHA: (11205) implies:
% 135.30/19.83 | | | | | | | | | | | | | | | | | | (11206) op(e1, e2) = e1
% 135.30/19.83 | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (11071), (11206), (function-axioms) are
% 135.30/19.83 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #65.
% 135.30/19.83 | | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.83 | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | (11207) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 135.30/19.83 | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 135.30/19.83 | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (160), (8984), (10711), (11207),
% 135.30/19.83 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.30/19.83 | | | | | | | | | | | | | | | | | #1.
% 135.30/19.83 | | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | | |
% 135.30/19.83 | | | | | | | | | End of split
% 135.30/19.83 | | | | | | | | |
% 135.30/19.83 | | | | | | | | End of split
% 135.30/19.83 | | | | | | | |
% 135.30/19.83 | | | | | | | Case 2:
% 135.30/19.83 | | | | | | | |
% 135.30/19.83 | | | | | | | | (11208) all_57_11 = e2 & op(e1, e0) = e2
% 135.30/19.83 | | | | | | | |
% 135.30/19.83 | | | | | | | | REF_CLOSE: (160), (10701), (11208), (function-axioms) are
% 135.30/19.83 | | | | | | | | inconsistent by sub-proof #514.
% 135.30/19.83 | | | | | | | |
% 135.30/19.83 | | | | | | | End of split
% 135.30/19.83 | | | | | | |
% 135.30/19.83 | | | | | | End of split
% 135.30/19.83 | | | | | |
% 135.30/19.83 | | | | | Case 2:
% 135.30/19.83 | | | | | |
% 135.30/19.83 | | | | | | (11209) ~ (all_4_1 = e2) & op(e1, e1) = all_4_1 & $i(all_4_1)
% 135.30/19.83 | | | | | |
% 135.30/19.83 | | | | | | ALPHA: (11209) implies:
% 135.30/19.83 | | | | | | (11210) ~ (all_4_1 = e2)
% 135.30/19.83 | | | | | | (11211) op(e1, e1) = all_4_1
% 135.30/19.83 | | | | | |
% 135.30/19.83 | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_4_1, e1,
% 135.30/19.83 | | | | | | e1, simplifying with (10702), (11211) gives:
% 135.30/19.83 | | | | | | (11212) all_4_1 = e2
% 135.30/19.83 | | | | | |
% 135.30/19.83 | | | | | | REDUCE: (11210), (11212) imply:
% 135.30/19.83 | | | | | | (11213) $false
% 135.30/19.83 | | | | | |
% 135.30/19.83 | | | | | | CLOSE: (11213) is inconsistent.
% 135.30/19.83 | | | | | |
% 135.30/19.83 | | | | | End of split
% 135.30/19.83 | | | | |
% 135.30/19.83 | | | | End of split
% 135.30/19.83 | | | |
% 135.30/19.83 | | | End of split
% 135.30/19.83 | | |
% 135.30/19.83 | | End of split
% 135.30/19.83 | |
% 135.30/19.83 | End of split
% 135.30/19.83 |
% 135.30/19.83 End of proof
% 135.30/19.83
% 135.30/19.83 Sub-proof #1 shows that the following formulas are inconsistent:
% 135.30/19.83 ----------------------------------------------------------------
% 135.30/19.84 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.30/19.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.30/19.84 (2) ~ (e2 = e1)
% 135.30/19.84 (3) all_57_8 = e2
% 135.30/19.84 (4) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 135.30/19.84 (5) ~ (all_52_14 = e1)
% 135.30/19.84 (6) op(e1, e0) = all_52_14
% 135.30/19.84
% 135.30/19.84 Begin of proof
% 135.30/19.84 |
% 135.30/19.84 | BETA: splitting (4) gives:
% 135.30/19.84 |
% 135.30/19.84 | Case 1:
% 135.30/19.84 | |
% 135.30/19.84 | | (7) all_57_8 = e1 & op(e1, e1) = e1
% 135.30/19.84 | |
% 135.30/19.84 | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #574.
% 135.30/19.84 | |
% 135.30/19.84 | Case 2:
% 135.30/19.84 | |
% 135.30/19.84 | | (8) all_57_11 = e1 & op(e1, e0) = e1
% 135.30/19.84 | |
% 135.30/19.84 | | ALPHA: (8) implies:
% 135.30/19.84 | | (9) op(e1, e0) = e1
% 135.30/19.84 | |
% 135.30/19.84 | | REF_CLOSE: (1), (5), (6), (9) are inconsistent by sub-proof #327.
% 135.30/19.84 | |
% 135.30/19.84 | End of split
% 135.30/19.84 |
% 135.30/19.84 End of proof
% 135.30/19.84
% 135.30/19.84 Sub-proof #2 shows that the following formulas are inconsistent:
% 135.30/19.84 ----------------------------------------------------------------
% 135.30/19.84 (1) ~ (all_52_3 = all_52_7)
% 135.30/19.84 (2) ~ (all_52_4 = e0)
% 135.30/19.84 (3) op(e2, e0) = all_52_13
% 135.30/19.84 (4) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 135.30/19.84 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 135.30/19.84 (5) ~ (all_52_11 = e2)
% 135.30/19.84 (6) ~ (e2 = e0)
% 135.30/19.84 (7) ~ (all_52_2 = e2)
% 135.30/19.84 (8) ~ (all_52_3 = all_52_11)
% 135.30/19.84 (9) all_54_12 = all_52_3
% 135.30/19.84 (10) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 135.30/19.84 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 135.30/19.84 (11) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 135.30/19.84 | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 135.30/19.84 e3)
% 135.30/19.84 (12) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 135.30/19.84 (13) ~ (all_52_13 = e1)
% 135.30/19.84 (14) ~ (all_52_2 = all_52_3)
% 135.30/19.84 (15) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 135.30/19.84 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 135.30/19.84 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.30/19.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.30/19.84 (17) ~ (e2 = e1)
% 135.30/19.84 (18) ~ (all_52_6 = e2)
% 135.30/19.84 (19) ~ (e3 = e0)
% 135.30/19.84 (20) ~ (all_52_4 = all_52_6)
% 135.30/19.84 (21) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 135.30/19.84 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 135.30/19.84 e2)
% 135.30/19.84 (22) ~ (e3 = e2)
% 135.30/19.84 (23) op(e0, e0) = e1
% 135.30/19.84 (24) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 135.30/19.84 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 135.30/19.84 (25) ~ (all_52_14 = e2)
% 135.30/19.84 (26) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 135.30/19.84 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 135.30/19.84 (27) op(e0, e1) = all_52_11
% 135.30/19.84 (28) op(e0, e2) = all_52_7
% 135.30/19.84 (29) op(e1, e1) = e2
% 135.30/19.84 (30) ~ (all_52_6 = e0)
% 135.30/19.84 (31) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 135.30/19.84 (32) all_54_9 = all_52_6
% 135.30/19.84 (33) ~ (all_52_2 = e0)
% 135.30/19.84 (34) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.30/19.84 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.30/19.84 op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.30/19.84 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.30/19.84 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 135.30/19.84 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.30/19.84 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 135.30/19.84 = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.30/19.84 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.30/19.84 $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~
% 135.30/19.84 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.30/19.84 (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) =
% 135.30/19.84 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0,
% 135.30/19.84 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 135.30/19.84 $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3)
% 135.30/19.84 & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 135.30/19.84 op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17
% 135.30/19.84 & op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 135.30/19.84 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 135.30/19.84 (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 135.30/19.84 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.30/19.84 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0)
% 135.30/19.84 = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) &
% 135.30/19.84 $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 &
% 135.30/19.84 all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.30/19.84 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 135.30/19.84 = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.30/19.84 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.30/19.84 $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~
% 135.30/19.84 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.30/19.84 (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 135.30/19.84 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0,
% 135.30/19.84 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 135.30/19.84 $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3)
% 135.30/19.84 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.30/19.84 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.30/19.84 all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2
% 135.30/19.84 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.30/19.84 (op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 =
% 135.30/19.84 e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.30/19.84 & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) =
% 135.30/19.84 all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.30/19.84 op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.30/19.84 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 135.30/19.84 e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.30/19.84 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 135.30/19.84 e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.30/19.84 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.30/19.84 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.30/19.84 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.30/19.84 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.30/19.84 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 135.30/19.84 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 135.30/19.84 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 135.30/19.84 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.30/19.84 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 135.30/19.84 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.30/19.84 $i(all_56_29))))
% 135.30/19.84 (35) op(e1, e2) = all_52_6
% 135.30/19.84 (36) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 135.30/19.84 (37) ~ (all_52_2 = all_52_6)
% 135.30/19.84 (38) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 135.30/19.84 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 135.30/19.84 e1)
% 135.30/19.84 (39) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 135.30/19.84 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 135.30/19.84 (40) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 135.30/19.84 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 135.30/19.84 (41) ~ (all_52_3 = e1)
% 135.30/19.84 (42) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 135.30/19.84 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 135.30/19.84 (43) ~ (all_52_7 = e1)
% 135.30/19.84 (44) op(e1, e3) = all_52_2
% 135.30/19.84 (45) ( ~ (all_10_0 = e2) & op(e0, e3) = all_10_0 & $i(all_10_0)) | ( ~
% 135.30/19.84 (all_10_1 = e1) & op(e0, e0) = all_10_1 & $i(all_10_1))
% 135.30/19.84 (46) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 135.30/19.84 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 135.30/19.84 (47) op(e3, e2) = all_52_4
% 135.30/19.84 (48) op(e0, e3) = all_52_3
% 135.30/19.84 (49) op(e3, e0) = all_52_12
% 135.30/19.84 (50) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 135.30/19.84 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 135.30/19.84 (51) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 135.30/19.84 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 135.30/19.84 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 135.30/19.84 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 135.30/19.84 (52) ~ (all_52_14 = e1)
% 135.30/19.84 (53) all_57_11 = e0
% 135.30/19.84 (54) op(e3, e3) = e0
% 135.30/19.84 (55) ~ (e3 = e1)
% 135.30/19.84 (56) ~ (e1 = e0)
% 135.30/19.84 (57) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 135.30/19.84 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 135.30/19.84 (58) all_54_8 = all_52_2
% 135.30/19.84 (59) ~ (all_52_3 = e0)
% 135.30/19.84 (60) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 135.30/19.84 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 135.30/19.84 (61) op(e1, e0) = all_52_14
% 135.30/19.84 (62) op(e1, e0) = e0
% 135.30/19.84
% 135.30/19.84 Begin of proof
% 135.30/19.84 |
% 135.30/19.84 | BETA: splitting (45) gives:
% 135.30/19.84 |
% 135.30/19.84 | Case 1:
% 135.30/19.84 | |
% 135.30/19.84 | | (63) ~ (all_10_0 = e2) & op(e0, e3) = all_10_0 & $i(all_10_0)
% 135.30/19.84 | |
% 135.30/19.84 | | ALPHA: (63) implies:
% 135.30/19.84 | | (64) ~ (all_10_0 = e2)
% 135.30/19.84 | | (65) op(e0, e3) = all_10_0
% 135.30/19.84 | |
% 135.30/19.84 | | GROUND_INST: instantiating (16) with all_52_3, all_10_0, e3, e0, simplifying
% 135.30/19.84 | | with (48), (65) gives:
% 135.30/19.84 | | (66) all_52_3 = all_10_0
% 135.30/19.84 | |
% 135.30/19.84 | | COMBINE_EQS: (9), (66) imply:
% 135.30/19.84 | | (67) all_54_12 = all_10_0
% 135.30/19.84 | |
% 135.30/19.84 | | REDUCE: (14), (66) imply:
% 135.30/19.84 | | (68) ~ (all_52_2 = all_10_0)
% 135.30/19.84 | |
% 135.30/19.84 | | REDUCE: (1), (66) imply:
% 135.30/19.84 | | (69) ~ (all_52_7 = all_10_0)
% 135.30/19.84 | |
% 135.30/19.84 | | SIMP: (69) implies:
% 135.30/19.84 | | (70) ~ (all_52_7 = all_10_0)
% 135.30/19.84 | |
% 135.30/19.84 | | REDUCE: (8), (66) imply:
% 135.30/19.84 | | (71) ~ (all_52_11 = all_10_0)
% 135.30/19.84 | |
% 135.30/19.84 | | SIMP: (71) implies:
% 135.30/19.84 | | (72) ~ (all_52_11 = all_10_0)
% 135.30/19.84 | |
% 135.30/19.84 | | REDUCE: (41), (66) imply:
% 135.30/19.84 | | (73) ~ (all_10_0 = e1)
% 135.30/19.84 | |
% 135.30/19.84 | | REDUCE: (59), (66) imply:
% 135.30/19.84 | | (74) ~ (all_10_0 = e0)
% 135.30/19.84 | |
% 135.30/19.84 | | BETA: splitting (21) gives:
% 135.30/19.84 | |
% 135.30/19.84 | | Case 1:
% 135.30/19.84 | | |
% 135.30/19.84 | | | (75) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2)
% 135.30/19.84 | | | = e2)
% 135.30/19.84 | | |
% 135.30/19.84 | | | BETA: splitting (75) gives:
% 135.30/19.84 | | |
% 135.30/19.84 | | | Case 1:
% 135.30/19.84 | | | |
% 135.30/19.84 | | | | (76) all_57_12 = e2 & op(e0, e3) = e2
% 135.30/19.84 | | | |
% 135.30/19.84 | | | | ALPHA: (76) implies:
% 135.30/19.84 | | | | (77) all_57_12 = e2
% 135.30/19.84 | | | |
% 135.30/19.84 | | | | REF_CLOSE: (11), (16), (23), (27), (28), (31), (64), (67), (70), (72),
% 135.30/19.84 | | | | (73), (74), (77) are inconsistent by sub-proof #23.
% 135.30/19.84 | | | |
% 135.30/19.84 | | | Case 2:
% 135.30/19.84 | | | |
% 135.30/19.84 | | | | (78) all_57_13 = e2 & op(e0, e2) = e2
% 135.30/19.84 | | | |
% 135.30/19.84 | | | | ALPHA: (78) implies:
% 135.30/19.84 | | | | (79) all_57_13 = e2
% 135.30/19.84 | | | |
% 135.30/19.84 | | | | BETA: splitting (50) gives:
% 135.30/19.84 | | | |
% 135.30/19.84 | | | | Case 1:
% 135.30/19.84 | | | | |
% 135.30/19.84 | | | | | (80) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2,
% 135.30/19.84 | | | | | e3) = e2)
% 135.30/19.84 | | | | |
% 135.30/19.84 | | | | | BETA: splitting (80) gives:
% 135.30/19.84 | | | | |
% 135.30/19.84 | | | | | Case 1:
% 135.30/19.84 | | | | | |
% 135.30/19.84 | | | | | | (81) all_57_0 = e2 & op(e3, e3) = e2
% 135.30/19.84 | | | | | |
% 135.30/19.84 | | | | | | ALPHA: (81) implies:
% 135.30/19.84 | | | | | | (82) op(e3, e3) = e2
% 135.30/19.84 | | | | | |
% 135.30/19.84 | | | | | | REF_CLOSE: (6), (16), (54), (82) are inconsistent by sub-proof #495.
% 135.30/19.84 | | | | | |
% 135.30/19.84 | | | | | Case 2:
% 135.30/19.84 | | | | | |
% 135.30/19.84 | | | | | | (83) all_57_2 = e2 & op(e2, e3) = e2
% 135.30/19.84 | | | | | |
% 135.30/19.84 | | | | | | ALPHA: (83) implies:
% 135.30/19.84 | | | | | | (84) all_57_2 = e2
% 135.30/19.84 | | | | | | (85) op(e2, e3) = e2
% 135.30/19.84 | | | | | |
% 135.30/19.84 | | | | | | BETA: splitting (15) gives:
% 135.30/19.84 | | | | | |
% 135.30/19.84 | | | | | | Case 1:
% 135.30/19.84 | | | | | | |
% 135.30/19.84 | | | | | | | (86) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 &
% 135.30/19.84 | | | | | | | op(e2, e3) = e1)
% 135.30/19.84 | | | | | | |
% 135.30/19.84 | | | | | | | REF_CLOSE: (16), (17), (54), (56), (85), (86) are inconsistent by
% 135.30/19.84 | | | | | | | sub-proof #69.
% 135.30/19.84 | | | | | | |
% 135.30/19.84 | | | | | | Case 2:
% 135.30/19.84 | | | | | | |
% 135.30/19.84 | | | | | | | (87) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 &
% 135.30/19.84 | | | | | | | op(e0, e3) = e1)
% 135.30/19.84 | | | | | | |
% 135.30/19.84 | | | | | | | BETA: splitting (87) gives:
% 135.30/19.84 | | | | | | |
% 135.30/19.84 | | | | | | | Case 1:
% 135.30/19.84 | | | | | | | |
% 135.30/19.84 | | | | | | | | (88) all_57_6 = e1 & op(e1, e3) = e1
% 135.30/19.84 | | | | | | | |
% 135.30/19.84 | | | | | | | | ALPHA: (88) implies:
% 135.30/19.84 | | | | | | | | (89) all_57_6 = e1
% 135.30/19.84 | | | | | | | |
% 135.30/19.84 | | | | | | | | BETA: splitting (46) gives:
% 135.30/19.84 | | | | | | | |
% 135.30/19.84 | | | | | | | | Case 1:
% 135.30/19.84 | | | | | | | | |
% 135.30/19.84 | | | | | | | | | (90) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 &
% 135.30/19.84 | | | | | | | | | op(e1, e2) = e3)
% 135.30/19.84 | | | | | | | | |
% 135.30/19.84 | | | | | | | | | BETA: splitting (90) gives:
% 135.30/19.84 | | | | | | | | |
% 135.30/19.84 | | | | | | | | | Case 1:
% 135.30/19.84 | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | (91) all_57_6 = e3 & op(e1, e3) = e3
% 135.30/19.84 | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | REF_CLOSE: (55), (89), (91) are inconsistent by sub-proof
% 135.30/19.84 | | | | | | | | | | #61.
% 135.30/19.84 | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | Case 2:
% 135.30/19.84 | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | (92) all_57_7 = e3 & op(e1, e2) = e3
% 135.30/19.84 | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | ALPHA: (92) implies:
% 135.30/19.84 | | | | | | | | | | (93) all_57_7 = e3
% 135.30/19.84 | | | | | | | | | | (94) op(e1, e2) = e3
% 135.30/19.84 | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | BETA: splitting (4) gives:
% 135.30/19.84 | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | Case 1:
% 135.30/19.84 | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | (95) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 135.30/19.84 | | | | | | | | | | | & op(e2, e2) = e0)
% 135.30/19.84 | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | BETA: splitting (95) gives:
% 135.30/19.84 | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | Case 1:
% 135.30/19.84 | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | (96) all_57_1 = e0 & op(e3, e2) = e0
% 135.30/19.84 | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | REF_CLOSE: (2), (16), (47), (96) are inconsistent by
% 135.30/19.84 | | | | | | | | | | | | sub-proof #693.
% 135.30/19.84 | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | Case 2:
% 135.30/19.84 | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | (97) all_57_3 = e0 & op(e2, e2) = e0
% 135.30/19.84 | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | ALPHA: (97) implies:
% 135.30/19.84 | | | | | | | | | | | | (98) op(e2, e2) = e0
% 135.30/19.84 | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | BETA: splitting (24) gives:
% 135.30/19.84 | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | Case 1:
% 135.30/19.84 | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | (99) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 135.30/19.84 | | | | | | | | | | | | | & op(e2, e3) = e3)
% 135.30/19.84 | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | BETA: splitting (99) gives:
% 135.30/19.84 | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | Case 1:
% 135.30/19.84 | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | (100) all_57_0 = e3 & op(e3, e3) = e3
% 135.30/19.84 | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | ALPHA: (100) implies:
% 135.30/19.84 | | | | | | | | | | | | | | (101) op(e3, e3) = e3
% 135.30/19.84 | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | REF_CLOSE: (16), (19), (54), (101) are inconsistent by
% 135.30/19.84 | | | | | | | | | | | | | | sub-proof #773.
% 135.30/19.84 | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | Case 2:
% 135.30/19.84 | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | (102) all_57_2 = e3 & op(e2, e3) = e3
% 135.30/19.84 | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | REF_CLOSE: (22), (84), (102) are inconsistent by sub-proof
% 135.30/19.84 | | | | | | | | | | | | | | #590.
% 135.30/19.84 | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | End of split
% 135.30/19.84 | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | Case 2:
% 135.30/19.84 | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | (103) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 135.30/19.84 | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 135.30/19.84 | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | BETA: splitting (103) gives:
% 135.30/19.84 | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | Case 1:
% 135.30/19.84 | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | (104) all_57_6 = e3 & op(e1, e3) = e3
% 135.30/19.84 | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | ALPHA: (104) implies:
% 135.30/19.84 | | | | | | | | | | | | | | (105) all_57_6 = e3
% 135.30/19.84 | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | REF_CLOSE: (55), (89), (105) are inconsistent by sub-proof
% 135.30/19.84 | | | | | | | | | | | | | | #575.
% 135.30/19.84 | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | Case 2:
% 135.30/19.84 | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | (106) all_57_12 = e3 & op(e0, e3) = e3
% 135.30/19.84 | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | ALPHA: (106) implies:
% 135.30/19.84 | | | | | | | | | | | | | | (107) all_57_12 = e3
% 135.30/19.84 | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | BETA: splitting (51) gives:
% 135.30/19.84 | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | Case 1:
% 135.30/19.84 | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | (108) all_57_15 = e0 & op(e0, e0) = e0
% 135.30/19.84 | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | ALPHA: (108) implies:
% 135.30/19.84 | | | | | | | | | | | | | | | (109) op(e0, e0) = e0
% 135.30/19.84 | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | REF_CLOSE: (16), (23), (56), (109) are inconsistent by
% 135.30/19.84 | | | | | | | | | | | | | | | sub-proof #220.
% 135.30/19.84 | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | Case 2:
% 135.30/19.84 | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | (110) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 135.30/19.84 | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 135.30/19.84 | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 135.30/19.84 | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 135.30/19.84 | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 135.30/19.84 | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | ALPHA: (110) implies:
% 135.30/19.84 | | | | | | | | | | | | | | | (111) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 135.30/19.84 | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 135.30/19.84 | | | | | | | | | | | | | | | e1) = e0)
% 135.30/19.84 | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | BETA: splitting (57) gives:
% 135.30/19.84 | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | Case 1:
% 135.30/19.84 | | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | | (112) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 135.30/19.84 | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 135.30/19.84 | | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (56), (85), (98), (112) are
% 135.30/19.84 | | | | | | | | | | | | | | | | inconsistent by sub-proof #93.
% 135.30/19.84 | | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | Case 2:
% 135.30/19.84 | | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | | (113) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 135.30/19.84 | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 135.30/19.84 | | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 135.30/19.84 | | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.84 | | | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | | | (114) all_57_5 = e1 & op(e2, e1) = e1
% 135.30/19.84 | | | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | | | ALPHA: (114) implies:
% 135.30/19.84 | | | | | | | | | | | | | | | | | (115) all_57_5 = e1
% 135.30/19.84 | | | | | | | | | | | | | | | | | (116) op(e2, e1) = e1
% 135.30/19.84 | | | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | | | BETA: splitting (26) gives:
% 135.30/19.84 | | | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.84 | | | | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | | | | (117) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 135.30/19.84 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 135.30/19.84 | | | | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | | | | BETA: splitting (117) gives:
% 135.30/19.84 | | | | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.84 | | | | | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | | | | | (118) all_57_2 = e3 & op(e2, e3) = e3
% 135.30/19.84 | | | | | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | | | | | ALPHA: (118) implies:
% 135.30/19.84 | | | | | | | | | | | | | | | | | | | (119) all_57_2 = e3
% 135.30/19.84 | | | | | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (84), (119) imply:
% 135.30/19.84 | | | | | | | | | | | | | | | | | | | (120) e3 = e2
% 135.30/19.84 | | | | | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | | | | | SIMP: (120) implies:
% 135.30/19.84 | | | | | | | | | | | | | | | | | | | (121) e3 = e2
% 135.30/19.84 | | | | | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (121) imply:
% 135.30/19.84 | | | | | | | | | | | | | | | | | | | (122) all_57_12 = e2
% 135.30/19.84 | | | | | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (16), (23), (27), (28), (31), (64), (67),
% 135.30/19.84 | | | | | | | | | | | | | | | | | | | (70), (72), (73), (74), (122) are inconsistent by
% 135.30/19.84 | | | | | | | | | | | | | | | | | | | sub-proof #23.
% 135.30/19.84 | | | | | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.84 | | | | | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | | | | | (123) all_57_3 = e3 & op(e2, e2) = e3
% 135.30/19.84 | | | | | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | | | | | ALPHA: (123) implies:
% 135.30/19.84 | | | | | | | | | | | | | | | | | | | (124) op(e2, e2) = e3
% 135.30/19.84 | | | | | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (19), (98), (124) are inconsistent by
% 135.30/19.84 | | | | | | | | | | | | | | | | | | | sub-proof #641.
% 135.30/19.84 | | | | | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.84 | | | | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.84 | | | | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | | | | (125) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 135.30/19.84 | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 135.30/19.84 | | | | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | | | | BETA: splitting (125) gives:
% 135.30/19.84 | | | | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.84 | | | | | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | | | | | (126) all_57_5 = e3 & op(e2, e1) = e3
% 135.30/19.84 | | | | | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | | | | | ALPHA: (126) implies:
% 135.30/19.84 | | | | | | | | | | | | | | | | | | | (127) all_57_5 = e3
% 135.30/19.84 | | | | | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (115), (127) imply:
% 135.30/19.84 | | | | | | | | | | | | | | | | | | | (128) e3 = e1
% 135.30/19.84 | | | | | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | | | | | SIMP: (128) implies:
% 135.30/19.84 | | | | | | | | | | | | | | | | | | | (129) e3 = e1
% 135.30/19.84 | | | | | | | | | | | | | | | | | | |
% 135.30/19.84 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (129) imply:
% 135.30/19.84 | | | | | | | | | | | | | | | | | | | (130) all_57_12 = e1
% 135.30/19.84 | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (16), (19), (22), (23), (55), (56),
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | (79), (111), (130) are inconsistent by sub-proof
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | #4.
% 135.30/19.85 | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | (131) all_57_10 = e3 & op(e2, e0) = e3
% 135.30/19.85 | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | ALPHA: (131) implies:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | (132) op(e2, e0) = e3
% 135.30/19.85 | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | BETA: splitting (31) gives:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | (133) all_54_12 = e3
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (67), (133) imply:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | (134) all_10_0 = e3
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | SIMP: (134) implies:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | (135) all_10_0 = e3
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | REDUCE: (68), (135) imply:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | (136) ~ (all_52_2 = e3)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | BETA: splitting (39) gives:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | (137) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (137) gives:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | (138) all_57_1 = e1 & op(e3, e2) = e1
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (138) implies:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | (139) op(e3, e2) = e1
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | (140) all_54_8 = e3
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (58), (136), (140) are inconsistent by sub-proof
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | #121.
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | (141) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (40) gives:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | (142) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (142) gives:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | (143) all_57_9 = e2 & op(e3, e0) = e2
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (143) implies:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | (144) all_57_9 = e2
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | (145) op(e3, e0) = e2
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (141) gives:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (146) all_54_8 = e2
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (58), (146) are inconsistent by sub-proof
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | #430.
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (147) all_54_8 = e1 | all_54_8 = e0
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (147) gives:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (148) all_54_8 = e1
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (148) imply:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (149) all_52_2 = e1
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (149) implies:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (150) all_52_2 = e1
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (37), (150) imply:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (151) ~ (all_52_6 = e1)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (151) implies:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (152) ~ (all_52_6 = e1)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (36) gives:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (153) all_54_9 = e3
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (32), (153) imply:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (154) all_52_6 = e3
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (154) implies:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (155) all_52_6 = e3
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20), (155) imply:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (156) ~ (all_52_4 = e3)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (34) gives:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (157) gives:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (158) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (158) gives:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (159) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (159) implies:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (160) op(e3, e3) = e2
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (16), (19), (42), (56), (84), (89), (107),
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (160) are inconsistent by sub-proof #491.
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (161) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (161) implies:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (162) op(e3, e3) = e1
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10), (16), (19), (22), (47), (55), (56),
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (60), (139), (144), (156), (162) are inconsistent
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #611.
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (163) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (19), (22), (49), (98), (145), (163) are
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #13.
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (164) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (164) gives:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (165) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (22), (29), (62), (165) are inconsistent by
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #42.
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (166) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (166) gives:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (167) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (167) implies:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168) op(e2, e0) = e2
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (16), (22), (132), (168) are inconsistent by
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #546.
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (169) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29))))
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (170) implies:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (171) ~ (all_56_19 = e1)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (172) op(e2, e1) = all_56_19
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (116), (171), (172) are inconsistent by
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #106.
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (173) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29)))
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (173) implies:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (174) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (175) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27))
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (175) gives:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (176) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (176) implies:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (177) op(e0, e3) = e0
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (48), (59), (177) are inconsistent by
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #219.
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (178) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (178) implies:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179) ~ (all_56_19 = e1)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (180) op(e2, e1) = all_56_19
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (116), (179), (180) are inconsistent by
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #106.
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (181) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (52), (61), (62), (181) are inconsistent by
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #40.
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (182) ~ (all_54_9 = e3)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (32), (182) imply:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (183) ~ (all_52_6 = e3)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (35), (94), (183) are inconsistent by
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #654.
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (184) all_54_8 = e0
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (58), (184) are inconsistent by sub-proof
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | #475.
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | (185) all_57_10 = e2 & op(e2, e0) = e2
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (185) implies:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | (186) op(e2, e0) = e2
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (16), (22), (132), (186) are inconsistent by
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #546.
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | (187) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | (188) all_57_11 = e2 & op(e1, e0) = e2
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (25), (61), (188) are inconsistent by
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #514.
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | (189) all_57_15 = e2 & op(e0, e0) = e2
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (189) implies:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | (190) all_57_15 = e2
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17), (19), (38), (51), (55), (56), (79),
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | (107), (190) are inconsistent by sub-proof #11.
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | (191) all_57_3 = e1 & op(e2, e2) = e1
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (191) implies:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | (192) op(e2, e2) = e1
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (56), (98), (192) are inconsistent by
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | sub-proof #675.
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | (193) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | (194) all_57_7 = e1 & op(e1, e2) = e1
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (194) implies:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | (195) all_57_7 = e1
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (93), (195) imply:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | (196) e3 = e1
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | SIMP: (196) implies:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | (197) e3 = e1
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (197) imply:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | (198) all_57_12 = e1
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (16), (19), (22), (23), (55), (56),
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | (79), (111), (198) are inconsistent by sub-proof
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | #4.
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | (199) all_57_13 = e1 & op(e0, e2) = e1
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (28), (43), (199) are inconsistent by
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | sub-proof #178.
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | (200) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (64), (67), (73), (74), (200) are inconsistent by
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | | sub-proof #24.
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.85 | | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | | End of split
% 135.30/19.85 | | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | End of split
% 135.30/19.85 | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | Case 2:
% 135.30/19.85 | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | (201) all_57_10 = e1 & op(e2, e0) = e1
% 135.30/19.85 | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | ALPHA: (201) implies:
% 135.30/19.85 | | | | | | | | | | | | | | | | | (202) op(e2, e0) = e1
% 135.30/19.85 | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (13), (16), (202) are inconsistent by
% 135.30/19.85 | | | | | | | | | | | | | | | | | sub-proof #180.
% 135.30/19.85 | | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | | End of split
% 135.30/19.85 | | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | | End of split
% 135.30/19.85 | | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | | End of split
% 135.30/19.85 | | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | | End of split
% 135.30/19.85 | | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | | End of split
% 135.30/19.85 | | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | End of split
% 135.30/19.85 | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | Case 2:
% 135.30/19.85 | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | (203) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 135.30/19.85 | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 135.30/19.85 | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | | REF_CLOSE: (6), (16), (30), (35), (79), (203) are
% 135.30/19.85 | | | | | | | | | | | inconsistent by sub-proof #170.
% 135.30/19.85 | | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | | End of split
% 135.30/19.85 | | | | | | | | | |
% 135.30/19.85 | | | | | | | | | End of split
% 135.30/19.85 | | | | | | | | |
% 135.30/19.85 | | | | | | | | Case 2:
% 135.30/19.85 | | | | | | | | |
% 135.30/19.85 | | | | | | | | | (204) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 &
% 135.30/19.85 | | | | | | | | | op(e1, e0) = e3)
% 135.30/19.85 | | | | | | | | |
% 135.30/19.85 | | | | | | | | | REF_CLOSE: (16), (19), (22), (29), (53), (204) are
% 135.30/19.85 | | | | | | | | | inconsistent by sub-proof #3.
% 135.30/19.85 | | | | | | | | |
% 135.30/19.85 | | | | | | | | End of split
% 135.30/19.85 | | | | | | | |
% 135.30/19.86 | | | | | | | Case 2:
% 135.30/19.86 | | | | | | | |
% 135.30/19.86 | | | | | | | | (205) all_57_12 = e1 & op(e0, e3) = e1
% 135.30/19.86 | | | | | | | |
% 135.30/19.86 | | | | | | | | ALPHA: (205) implies:
% 135.30/19.86 | | | | | | | | (206) all_57_12 = e1
% 135.30/19.86 | | | | | | | |
% 135.30/19.86 | | | | | | | | BETA: splitting (51) gives:
% 135.30/19.86 | | | | | | | |
% 135.30/19.86 | | | | | | | | Case 1:
% 135.30/19.86 | | | | | | | | |
% 135.30/19.86 | | | | | | | | | (207) all_57_15 = e0 & op(e0, e0) = e0
% 135.30/19.86 | | | | | | | | |
% 135.30/19.86 | | | | | | | | | ALPHA: (207) implies:
% 135.30/19.86 | | | | | | | | | (208) op(e0, e0) = e0
% 135.30/19.86 | | | | | | | | |
% 135.30/19.86 | | | | | | | | | REF_CLOSE: (16), (23), (56), (208) are inconsistent by
% 135.30/19.86 | | | | | | | | | sub-proof #220.
% 135.30/19.86 | | | | | | | | |
% 135.30/19.86 | | | | | | | | Case 2:
% 135.30/19.86 | | | | | | | | |
% 135.30/19.86 | | | | | | | | | (209) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0
% 135.30/19.86 | | | | | | | | | & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 135.30/19.86 | | | | | | | | | = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) |
% 135.30/19.86 | | | | | | | | | (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 135.30/19.86 | | | | | | | | | e0 & op(e0, e1) = e0))
% 135.30/19.86 | | | | | | | | |
% 135.30/19.86 | | | | | | | | | ALPHA: (209) implies:
% 135.30/19.86 | | | | | | | | | (210) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0
% 135.30/19.86 | | | | | | | | | & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 135.30/19.86 | | | | | | | | | e0)
% 135.30/19.86 | | | | | | | | |
% 135.30/19.86 | | | | | | | | | REF_CLOSE: (6), (11), (16), (19), (22), (23), (55), (56),
% 135.30/19.86 | | | | | | | | | (79), (206), (210) are inconsistent by sub-proof
% 135.30/19.86 | | | | | | | | | #4.
% 135.30/19.86 | | | | | | | | |
% 135.30/19.86 | | | | | | | | End of split
% 135.30/19.86 | | | | | | | |
% 135.30/19.86 | | | | | | | End of split
% 135.30/19.86 | | | | | | |
% 135.30/19.86 | | | | | | End of split
% 135.30/19.86 | | | | | |
% 135.30/19.86 | | | | | End of split
% 135.30/19.86 | | | | |
% 135.30/19.86 | | | | Case 2:
% 135.30/19.86 | | | | |
% 135.30/19.86 | | | | | (211) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0,
% 135.30/19.86 | | | | | e3) = e2)
% 135.30/19.86 | | | | |
% 135.30/19.86 | | | | | BETA: splitting (211) gives:
% 135.30/19.86 | | | | |
% 135.30/19.86 | | | | | Case 1:
% 135.30/19.86 | | | | | |
% 135.30/19.86 | | | | | | (212) all_57_6 = e2 & op(e1, e3) = e2
% 135.30/19.86 | | | | | |
% 135.30/19.86 | | | | | | REF_CLOSE: (7), (16), (44), (212) are inconsistent by sub-proof
% 135.30/19.86 | | | | | | #341.
% 135.30/19.86 | | | | | |
% 135.30/19.86 | | | | | Case 2:
% 135.30/19.86 | | | | | |
% 135.30/19.86 | | | | | | (213) all_57_12 = e2 & op(e0, e3) = e2
% 135.30/19.86 | | | | | |
% 135.30/19.86 | | | | | | ALPHA: (213) implies:
% 135.30/19.86 | | | | | | (214) all_57_12 = e2
% 135.30/19.86 | | | | | |
% 135.30/19.86 | | | | | | REF_CLOSE: (11), (16), (23), (27), (28), (31), (64), (67), (70),
% 135.30/19.86 | | | | | | (72), (73), (74), (214) are inconsistent by sub-proof
% 135.30/19.86 | | | | | | #23.
% 135.30/19.86 | | | | | |
% 135.30/19.86 | | | | | End of split
% 135.30/19.86 | | | | |
% 135.30/19.86 | | | | End of split
% 135.30/19.86 | | | |
% 135.30/19.86 | | | End of split
% 135.30/19.86 | | |
% 135.30/19.86 | | Case 2:
% 135.30/19.86 | | |
% 135.30/19.86 | | | (215) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0)
% 135.30/19.86 | | | = e2)
% 135.30/19.86 | | |
% 135.30/19.86 | | | REF_CLOSE: (5), (16), (17), (23), (27), (215) are inconsistent by
% 135.30/19.86 | | | sub-proof #34.
% 135.30/19.86 | | |
% 135.30/19.86 | | End of split
% 135.30/19.86 | |
% 135.30/19.86 | Case 2:
% 135.30/19.86 | |
% 135.30/19.86 | | (216) ~ (all_10_1 = e1) & op(e0, e0) = all_10_1 & $i(all_10_1)
% 135.30/19.86 | |
% 135.30/19.86 | | ALPHA: (216) implies:
% 135.30/19.86 | | (217) ~ (all_10_1 = e1)
% 135.30/19.86 | | (218) op(e0, e0) = all_10_1
% 135.30/19.86 | |
% 135.30/19.86 | | GROUND_INST: instantiating (16) with e1, all_10_1, e0, e0, simplifying with
% 135.30/19.86 | | (23), (218) gives:
% 135.30/19.86 | | (219) all_10_1 = e1
% 135.30/19.86 | |
% 135.30/19.86 | | REDUCE: (217), (219) imply:
% 135.30/19.86 | | (220) $false
% 135.30/19.86 | |
% 135.30/19.86 | | CLOSE: (220) is inconsistent.
% 135.30/19.86 | |
% 135.30/19.86 | End of split
% 135.30/19.86 |
% 135.30/19.86 End of proof
% 135.30/19.86
% 135.30/19.86 Sub-proof #3 shows that the following formulas are inconsistent:
% 135.30/19.86 ----------------------------------------------------------------
% 135.30/19.86 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.30/19.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.30/19.86 (2) ~ (e3 = e0)
% 135.30/19.86 (3) ~ (e3 = e2)
% 135.30/19.86 (4) op(e1, e1) = e2
% 135.30/19.86 (5) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 135.30/19.86 (6) all_57_11 = e0
% 135.30/19.86
% 135.30/19.86 Begin of proof
% 135.30/19.86 |
% 135.30/19.86 | BETA: splitting (5) gives:
% 135.30/19.86 |
% 135.30/19.86 | Case 1:
% 135.30/19.86 | |
% 135.30/19.86 | | (7) all_57_8 = e3 & op(e1, e1) = e3
% 135.30/19.86 | |
% 135.30/19.86 | | ALPHA: (7) implies:
% 135.30/19.86 | | (8) op(e1, e1) = e3
% 135.30/19.86 | |
% 135.30/19.86 | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #109.
% 135.30/19.86 | |
% 135.30/19.86 | Case 2:
% 135.30/19.86 | |
% 135.30/19.86 | | (9) all_57_11 = e3 & op(e1, e0) = e3
% 135.30/19.86 | |
% 135.30/19.86 | | REF_CLOSE: (2), (6), (9) are inconsistent by sub-proof #256.
% 135.30/19.86 | |
% 135.30/19.86 | End of split
% 135.30/19.86 |
% 135.30/19.86 End of proof
% 135.30/19.86
% 135.30/19.86 Sub-proof #4 shows that the following formulas are inconsistent:
% 135.30/19.86 ----------------------------------------------------------------
% 135.30/19.86 (1) ~ (e2 = e0)
% 135.30/19.86 (2) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 135.30/19.86 (all_57_14 = e0 & op(e0, e1) = e0)
% 135.30/19.86 (3) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 135.30/19.86 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 135.30/19.86 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.30/19.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.30/19.86 (5) ~ (e3 = e0)
% 135.30/19.86 (6) ~ (e3 = e2)
% 135.30/19.86 (7) op(e0, e0) = e1
% 135.30/19.86 (8) all_57_13 = e2
% 135.30/19.86 (9) ~ (e3 = e1)
% 135.30/19.86 (10) ~ (e1 = e0)
% 135.30/19.86 (11) all_57_12 = e1
% 135.30/19.86
% 135.30/19.86 Begin of proof
% 135.30/19.86 |
% 135.30/19.86 | BETA: splitting (3) gives:
% 135.30/19.86 |
% 135.30/19.86 | Case 1:
% 135.30/19.86 | |
% 135.30/19.86 | | (12) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 135.30/19.86 | | e3)
% 135.30/19.86 | |
% 135.30/19.86 | | BETA: splitting (12) gives:
% 135.30/19.86 | |
% 135.30/19.86 | | Case 1:
% 135.30/19.86 | | |
% 135.30/19.86 | | | (13) all_57_12 = e3 & op(e0, e3) = e3
% 135.30/19.86 | | |
% 135.30/19.86 | | | REF_CLOSE: (9), (11), (13) are inconsistent by sub-proof #394.
% 135.30/19.86 | | |
% 135.30/19.86 | | Case 2:
% 135.30/19.86 | | |
% 135.30/19.86 | | | (14) all_57_13 = e3 & op(e0, e2) = e3
% 135.30/19.86 | | |
% 135.30/19.86 | | | ALPHA: (14) implies:
% 135.30/19.86 | | | (15) all_57_13 = e3
% 135.30/19.86 | | |
% 135.30/19.86 | | | COMBINE_EQS: (8), (15) imply:
% 135.30/19.86 | | | (16) e3 = e2
% 135.30/19.86 | | |
% 135.30/19.86 | | | REDUCE: (6), (16) imply:
% 135.30/19.86 | | | (17) $false
% 135.30/19.86 | | |
% 135.30/19.86 | | | CLOSE: (17) is inconsistent.
% 135.30/19.86 | | |
% 135.30/19.86 | | End of split
% 135.30/19.86 | |
% 135.30/19.86 | Case 2:
% 135.30/19.86 | |
% 135.30/19.86 | | (18) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 135.30/19.86 | | e3)
% 135.30/19.86 | |
% 135.30/19.86 | | BETA: splitting (18) gives:
% 135.30/19.86 | |
% 135.30/19.86 | | Case 1:
% 135.30/19.86 | | |
% 135.30/19.86 | | | (19) all_57_14 = e3 & op(e0, e1) = e3
% 135.30/19.86 | | |
% 135.30/19.86 | | | ALPHA: (19) implies:
% 135.30/19.86 | | | (20) all_57_14 = e3
% 135.30/19.86 | | |
% 135.30/19.86 | | | REF_CLOSE: (1), (2), (5), (8), (10), (11), (20) are inconsistent by
% 135.30/19.86 | | | sub-proof #399.
% 135.30/19.86 | | |
% 135.30/19.86 | | Case 2:
% 135.30/19.86 | | |
% 135.30/19.86 | | | (21) all_57_15 = e3 & op(e0, e0) = e3
% 135.30/19.86 | | |
% 135.30/19.86 | | | ALPHA: (21) implies:
% 135.30/19.86 | | | (22) op(e0, e0) = e3
% 135.30/19.86 | | |
% 135.30/19.86 | | | REF_CLOSE: (4), (7), (9), (22) are inconsistent by sub-proof #606.
% 135.30/19.86 | | |
% 135.30/19.86 | | End of split
% 135.30/19.86 | |
% 135.30/19.86 | End of split
% 135.30/19.86 |
% 135.30/19.86 End of proof
% 135.30/19.86
% 135.30/19.86 Sub-proof #5 shows that the following formulas are inconsistent:
% 135.30/19.86 ----------------------------------------------------------------
% 135.30/19.86 (1) all_57_11 = e3 & op(e1, e0) = e3
% 135.30/19.86 (2) all_57_11 = e0
% 135.30/19.86 (3) ~ (e3 = e0)
% 135.30/19.86
% 135.30/19.86 Begin of proof
% 135.30/19.86 |
% 135.30/19.86 | ALPHA: (1) implies:
% 135.30/19.86 | (4) all_57_11 = e3
% 135.30/19.86 |
% 135.30/19.86 | COMBINE_EQS: (2), (4) imply:
% 135.30/19.86 | (5) e3 = e0
% 135.30/19.86 |
% 135.30/19.86 | SIMP: (5) implies:
% 135.30/19.86 | (6) e3 = e0
% 135.30/19.86 |
% 135.30/19.86 | REDUCE: (3), (6) imply:
% 135.30/19.86 | (7) $false
% 135.30/19.86 |
% 135.30/19.86 | CLOSE: (7) is inconsistent.
% 135.30/19.86 |
% 135.30/19.86 End of proof
% 135.30/19.86
% 135.30/19.86 Sub-proof #6 shows that the following formulas are inconsistent:
% 135.30/19.86 ----------------------------------------------------------------
% 135.30/19.86 (1) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 135.30/19.86 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.30/19.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.30/19.86 (3) op(e0, e0) = e1
% 135.30/19.86 (4) ~ (e3 = e1)
% 135.30/19.86 (5) all_57_14 = e1
% 135.30/19.86
% 135.30/19.86 Begin of proof
% 135.30/19.86 |
% 135.30/19.86 | BETA: splitting (1) gives:
% 135.30/19.86 |
% 135.30/19.86 | Case 1:
% 135.30/19.86 | |
% 135.30/19.86 | | (6) all_57_14 = e3 & op(e0, e1) = e3
% 135.30/19.86 | |
% 135.30/19.86 | | ALPHA: (6) implies:
% 135.30/19.86 | | (7) all_57_14 = e3
% 135.30/19.86 | |
% 135.30/19.86 | | COMBINE_EQS: (5), (7) imply:
% 135.30/19.86 | | (8) e3 = e1
% 135.30/19.86 | |
% 135.30/19.86 | | REDUCE: (4), (8) imply:
% 135.30/19.86 | | (9) $false
% 135.30/19.86 | |
% 135.30/19.86 | | CLOSE: (9) is inconsistent.
% 135.30/19.86 | |
% 135.30/19.86 | Case 2:
% 135.30/19.86 | |
% 135.30/19.86 | | (10) all_57_15 = e3 & op(e0, e0) = e3
% 135.30/19.86 | |
% 135.30/19.86 | | ALPHA: (10) implies:
% 135.30/19.86 | | (11) op(e0, e0) = e3
% 135.30/19.86 | |
% 135.30/19.86 | | REF_CLOSE: (2), (3), (4), (11) are inconsistent by sub-proof #606.
% 135.30/19.86 | |
% 135.30/19.86 | End of split
% 135.30/19.86 |
% 135.30/19.86 End of proof
% 135.30/19.86
% 135.30/19.86 Sub-proof #7 shows that the following formulas are inconsistent:
% 135.30/19.86 ----------------------------------------------------------------
% 135.30/19.86 (1) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 135.30/19.86 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 135.30/19.86 (2) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 135.30/19.86 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 135.30/19.86 (3) ~ (all_52_13 = e0)
% 135.30/19.86 (4) op(e2, e0) = all_52_13
% 135.30/19.86 (5) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 135.30/19.86 (6) ~ (all_52_11 = e2)
% 135.30/19.86 (7) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 135.30/19.86 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 135.30/19.86 (8) ~ (all_52_13 = e1)
% 135.30/19.86 (9) ~ (all_52_7 = e3)
% 135.30/19.86 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.30/19.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.30/19.86 (11) ~ (e3 = e0)
% 135.30/19.86 (12) ~ (all_52_1 = all_52_13)
% 135.30/19.86 (13) op(e0, e0) = e1
% 135.30/19.86 (14) all_57_8 = e2
% 135.30/19.86 (15) op(e2, e2) = e3
% 135.30/19.86 (16) ~ (all_52_3 = e3)
% 135.30/19.86 (17) ~ (all_52_1 = all_52_9)
% 135.30/19.86 (18) op(e0, e1) = all_52_11
% 135.30/19.86 (19) op(e0, e2) = all_52_7
% 135.30/19.86 (20) op(e1, e1) = e2
% 135.30/19.86 (21) ~ (all_10_2 = e0)
% 135.30/19.86 (22) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 135.30/19.86 (23) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.30/19.86 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.30/19.86 op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.30/19.86 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.30/19.86 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 135.30/19.86 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.30/19.86 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 135.30/19.86 = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.30/19.86 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.30/19.86 $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~
% 135.30/19.86 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.30/19.86 (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) =
% 135.30/19.86 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0,
% 135.30/19.86 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 135.30/19.86 $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3)
% 135.30/19.86 & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 135.30/19.86 op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17
% 135.30/19.86 & op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 135.30/19.86 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 135.30/19.86 (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 135.30/19.86 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.30/19.86 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0)
% 135.30/19.86 = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) &
% 135.30/19.86 $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 &
% 135.30/19.86 all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.30/19.86 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 135.30/19.86 = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.30/19.86 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.30/19.86 $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~
% 135.30/19.86 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.30/19.86 (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 135.30/19.86 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0,
% 135.30/19.86 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 135.30/19.86 $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3)
% 135.30/19.86 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.30/19.86 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.30/19.86 all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2
% 135.30/19.86 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.30/19.86 (op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 =
% 135.30/19.86 e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.30/19.86 & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) =
% 135.30/19.86 all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.30/19.86 op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.30/19.86 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 135.30/19.86 e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.30/19.86 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 135.30/19.86 e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.30/19.86 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.30/19.86 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.30/19.86 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.30/19.86 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.30/19.86 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 135.30/19.86 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 135.30/19.86 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 135.30/19.86 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.30/19.86 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 135.30/19.86 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.30/19.86 $i(all_56_29))))
% 135.30/19.86 (24) op(e3, e3) = all_10_2
% 135.30/19.86 (25) ~ (all_52_9 = e3)
% 135.30/19.86 (26) op(e2, e1) = all_52_9
% 135.30/19.86 (27) ( ~ (all_6_0 = e0) & op(e2, e1) = all_6_0 & $i(all_6_0)) | ( ~ (all_6_1
% 135.30/19.86 = e3) & op(e2, e2) = all_6_1 & $i(all_6_1))
% 135.30/19.86 (28) op(e0, e3) = all_52_3
% 135.30/19.86 (29) ~ (all_52_13 = e3)
% 135.30/19.86 (30) all_54_6 = all_52_9
% 135.30/19.86 (31) op(e2, e3) = all_52_1
% 135.30/19.86 (32) ~ (all_52_14 = e1)
% 135.30/19.86 (33) all_54_7 = all_52_13
% 135.30/19.86 (34) op(e3, e1) = all_52_8
% 135.30/19.86 (35) ~ (e3 = e1)
% 135.30/19.86 (36) ~ (e1 = e0)
% 135.30/19.86 (37) ~ (all_52_9 = all_52_13)
% 135.30/19.86 (38) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 135.30/19.86 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 135.30/19.86 (39) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 135.30/19.86 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 135.30/19.86 (40) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 135.30/19.86 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 135.30/19.86 (41) op(e1, e0) = all_52_14
% 135.30/19.86 (42) op(e1, e0) = e0
% 135.30/19.86
% 135.30/19.86 Begin of proof
% 135.30/19.86 |
% 135.30/19.86 | BETA: splitting (27) gives:
% 135.30/19.86 |
% 135.30/19.86 | Case 1:
% 135.30/19.86 | |
% 135.30/19.86 | | (43) ~ (all_6_0 = e0) & op(e2, e1) = all_6_0 & $i(all_6_0)
% 135.30/19.86 | |
% 135.30/19.86 | | ALPHA: (43) implies:
% 135.30/19.86 | | (44) ~ (all_6_0 = e0)
% 135.30/19.86 | | (45) op(e2, e1) = all_6_0
% 135.30/19.86 | |
% 135.30/19.86 | | BETA: splitting (5) gives:
% 135.30/19.86 | |
% 135.30/19.86 | | Case 1:
% 135.30/19.86 | | |
% 135.30/19.86 | | | (46) all_54_7 = e3
% 135.30/19.86 | | |
% 135.30/19.86 | | | COMBINE_EQS: (33), (46) imply:
% 135.30/19.86 | | | (47) all_52_13 = e3
% 135.30/19.86 | | |
% 135.30/19.86 | | | REDUCE: (29), (47) imply:
% 135.30/19.86 | | | (48) $false
% 135.30/19.86 | | |
% 135.30/19.86 | | | CLOSE: (48) is inconsistent.
% 135.30/19.86 | | |
% 135.30/19.86 | | Case 2:
% 135.30/19.86 | | |
% 135.30/19.86 | | | (49) ~ (all_54_7 = e3)
% 135.30/19.86 | | | (50) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 135.30/19.86 | | |
% 135.30/19.86 | | | BETA: splitting (50) gives:
% 135.30/19.86 | | |
% 135.30/19.86 | | | Case 1:
% 135.30/19.86 | | | |
% 135.30/19.86 | | | | (51) all_54_7 = e2
% 135.30/19.86 | | | |
% 135.30/19.86 | | | | COMBINE_EQS: (33), (51) imply:
% 135.30/19.86 | | | | (52) all_52_13 = e2
% 135.30/19.86 | | | |
% 135.30/19.86 | | | | REDUCE: (12), (52) imply:
% 135.30/19.86 | | | | (53) ~ (all_52_1 = e2)
% 135.30/19.86 | | | |
% 135.30/19.86 | | | | REDUCE: (37), (52) imply:
% 135.30/19.86 | | | | (54) ~ (all_52_9 = e2)
% 135.30/19.86 | | | |
% 135.30/19.86 | | | | REDUCE: (29), (52) imply:
% 135.30/19.86 | | | | (55) ~ (e3 = e2)
% 135.30/19.86 | | | |
% 135.30/19.86 | | | | SIMP: (55) implies:
% 135.30/19.86 | | | | (56) ~ (e3 = e2)
% 135.30/19.86 | | | |
% 135.30/19.86 | | | | REDUCE: (3), (52) imply:
% 135.30/19.86 | | | | (57) ~ (e2 = e0)
% 135.30/19.86 | | | |
% 135.30/19.86 | | | | BETA: splitting (7) gives:
% 135.30/19.86 | | | |
% 135.30/19.86 | | | | Case 1:
% 135.30/19.86 | | | | |
% 135.30/19.86 | | | | | (58) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0,
% 135.30/19.86 | | | | | e2) = e3)
% 135.30/19.86 | | | | |
% 135.30/19.86 | | | | | BETA: splitting (58) gives:
% 135.30/19.86 | | | | |
% 135.30/19.86 | | | | | Case 1:
% 135.30/19.86 | | | | | |
% 135.30/19.86 | | | | | | (59) all_57_12 = e3 & op(e0, e3) = e3
% 135.30/19.86 | | | | | |
% 135.30/19.86 | | | | | | REF_CLOSE: (10), (16), (28), (59) are inconsistent by sub-proof
% 135.30/19.86 | | | | | | #628.
% 135.30/19.86 | | | | | |
% 135.30/19.86 | | | | | Case 2:
% 135.30/19.86 | | | | | |
% 135.30/19.86 | | | | | | (60) all_57_13 = e3 & op(e0, e2) = e3
% 135.30/19.86 | | | | | |
% 135.30/19.86 | | | | | | REF_CLOSE: (9), (10), (19), (60) are inconsistent by sub-proof #556.
% 135.30/19.86 | | | | | |
% 135.30/19.86 | | | | | End of split
% 135.30/19.86 | | | | |
% 135.30/19.86 | | | | Case 2:
% 135.30/19.86 | | | | |
% 135.30/19.86 | | | | | (61) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0,
% 135.30/19.86 | | | | | e0) = e3)
% 135.30/19.86 | | | | |
% 135.30/19.86 | | | | | BETA: splitting (61) gives:
% 135.30/19.86 | | | | |
% 135.30/19.86 | | | | | Case 1:
% 135.30/19.86 | | | | | |
% 135.30/19.86 | | | | | | (62) all_57_14 = e3 & op(e0, e1) = e3
% 135.30/19.86 | | | | | |
% 135.30/19.86 | | | | | | ALPHA: (62) implies:
% 135.30/19.86 | | | | | | (63) all_57_14 = e3
% 135.30/19.86 | | | | | | (64) op(e0, e1) = e3
% 135.30/19.86 | | | | | |
% 135.30/19.86 | | | | | | BETA: splitting (23) gives:
% 135.30/19.86 | | | | | |
% 135.30/19.86 | | | | | | Case 1:
% 135.30/19.86 | | | | | | |
% 135.30/19.86 | | | | | | | (65) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~
% 135.30/19.86 | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 =
% 135.30/19.86 | | | | | | | e0) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) =
% 135.30/19.86 | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.30/19.86 | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.30/19.86 | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.30/19.86 | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~
% 135.30/19.86 | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 =
% 135.30/19.86 | | | | | | | e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) =
% 135.30/19.86 | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.30/19.86 | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.30/19.86 | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 135.30/19.86 | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~
% 135.30/19.86 | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 =
% 135.30/19.86 | | | | | | | e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) =
% 135.30/19.86 | | | | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) =
% 135.30/19.86 | | | | | | | all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.30/19.86 | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.30/19.86 | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~
% 135.30/19.86 | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 =
% 135.30/19.86 | | | | | | | e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 &
% 135.30/19.86 | | | | | | | op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e2,
% 135.30/19.86 | | | | | | | e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) &
% 135.30/19.86 | | | | | | | $i(all_56_9) & $i(all_56_17) & $i(all_56_25))
% 135.30/19.86 | | | | | | |
% 135.30/19.86 | | | | | | | BETA: splitting (65) gives:
% 135.30/19.86 | | | | | | |
% 135.30/19.86 | | | | | | | Case 1:
% 135.30/19.86 | | | | | | | |
% 135.30/19.86 | | | | | | | | (66) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~
% 135.30/19.86 | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.30/19.86 | | | | | | | | = e0) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2,
% 135.30/19.86 | | | | | | | | e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1)
% 135.30/19.86 | | | | | | | | = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.30/19.86 | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.30/19.86 | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) &
% 135.30/19.86 | | | | | | | | ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.30/19.86 | | | | | | | | (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 135.30/19.86 | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 135.30/19.86 | | | | | | | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 135.30/19.86 | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.30/19.86 | | | | | | | | $i(all_56_29))
% 135.30/19.86 | | | | | | | |
% 135.30/19.86 | | | | | | | | BETA: splitting (66) gives:
% 135.30/19.86 | | | | | | | |
% 135.30/19.86 | | | | | | | | Case 1:
% 135.30/19.86 | | | | | | | | |
% 135.30/19.86 | | | | | | | | | (67) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) &
% 135.30/19.86 | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.30/19.86 | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = e3 &
% 135.30/19.86 | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.30/19.86 | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 135.30/19.86 | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.30/19.86 | | | | | | | | | $i(all_56_27)
% 135.30/19.86 | | | | | | | | |
% 135.30/19.86 | | | | | | | | | ALPHA: (67) implies:
% 135.30/19.86 | | | | | | | | | (68) ~ (all_56_27 = e0)
% 135.30/19.86 | | | | | | | | | (69) ~ (all_56_19 = e1)
% 135.30/19.86 | | | | | | | | | (70) op(e2, e0) = all_56_27
% 135.30/19.87 | | | | | | | | | (71) op(e2, e1) = all_56_19
% 135.30/19.87 | | | | | | | | |
% 135.30/19.87 | | | | | | | | | REF_CLOSE: (4), (8), (10), (11), (15), (35), (36), (39), (40),
% 135.30/19.87 | | | | | | | | | (44), (45), (68), (69), (70), (71) are inconsistent
% 135.30/19.87 | | | | | | | | | by sub-proof #10.
% 135.30/19.87 | | | | | | | | |
% 135.30/19.87 | | | | | | | | Case 2:
% 135.30/19.87 | | | | | | | | |
% 135.30/19.87 | | | | | | | | | (72) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) &
% 135.30/19.87 | | | | | | | | | ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.30/19.87 | | | | | | | | | (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 135.30/19.87 | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 135.30/19.87 | | | | | | | | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 135.30/19.87 | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.30/19.87 | | | | | | | | | $i(all_56_29)
% 135.30/19.87 | | | | | | | | |
% 135.30/19.87 | | | | | | | | | ALPHA: (72) implies:
% 135.30/19.87 | | | | | | | | | (73) op(e1, e0) = all_56_29
% 135.30/19.87 | | | | | | | | |
% 135.30/19.87 | | | | | | | | | REF_CLOSE: (1), (2), (4), (6), (8), (10), (11), (13), (14),
% 135.30/19.87 | | | | | | | | | (15), (17), (18), (20), (21), (22), (23), (24),
% 135.30/19.87 | | | | | | | | | (25), (26), (30), (31), (32), (34), (35), (36),
% 135.30/19.87 | | | | | | | | | (38), (39), (40), (41), (42), (44), (45), (53),
% 135.30/19.87 | | | | | | | | | (54), (56), (57), (63), (64), (73) are inconsistent
% 135.30/19.87 | | | | | | | | | by sub-proof #8.
% 135.30/19.87 | | | | | | | | |
% 135.30/19.87 | | | | | | | | End of split
% 135.30/19.87 | | | | | | | |
% 135.30/19.87 | | | | | | | Case 2:
% 135.30/19.87 | | | | | | | |
% 135.30/19.87 | | | | | | | | (74) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) &
% 135.30/19.87 | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.30/19.87 | | | | | | | | (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 135.30/19.87 | | | | | | | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 135.30/19.87 | | | | | | | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 &
% 135.30/19.87 | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 135.30/19.87 | | | | | | | | $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~
% 135.30/19.87 | | | | | | | | (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 135.30/19.87 | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.30/19.87 | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.30/19.87 | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2)
% 135.30/19.87 | | | | | | | | = e3 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.30/19.87 | | | | | | | | $i(all_56_25))
% 135.30/19.87 | | | | | | | |
% 135.30/19.87 | | | | | | | | REF_CLOSE: (10), (21), (24), (31), (53), (74) are inconsistent
% 135.30/19.87 | | | | | | | | by sub-proof #533.
% 135.30/19.87 | | | | | | | |
% 135.30/19.87 | | | | | | | End of split
% 135.30/19.87 | | | | | | |
% 135.30/19.87 | | | | | | Case 2:
% 135.30/19.87 | | | | | | |
% 135.30/19.87 | | | | | | | (75) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~
% 135.30/19.87 | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 =
% 135.30/19.87 | | | | | | | e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 &
% 135.30/19.87 | | | | | | | op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e1,
% 135.30/19.87 | | | | | | | e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) &
% 135.30/19.87 | | | | | | | $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 135.30/19.87 | | | | | | | (all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 135.30/19.87 | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 =
% 135.30/19.87 | | | | | | | e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 135.30/19.87 | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.30/19.87 | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.30/19.87 | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 135.30/19.87 | | | | | | | (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 135.30/19.87 | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 =
% 135.30/19.87 | | | | | | | e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 135.30/19.87 | | | | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) =
% 135.30/19.87 | | | | | | | all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.30/19.87 | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.30/19.87 | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 135.30/19.87 | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 =
% 135.30/19.87 | | | | | | | e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.30/19.87 | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e1,
% 135.30/19.87 | | | | | | | e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 135.30/19.87 | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (op(e0,
% 135.30/19.87 | | | | | | | e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 135.30/19.87 | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 135.30/19.87 | | | | | | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 135.30/19.87 | | | | | | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 &
% 135.30/19.87 | | | | | | | op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.30/19.87 | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.30/19.87 | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 &
% 135.30/19.87 | | | | | | | all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11
% 135.30/19.87 | | | | | | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0)
% 135.30/19.87 | | | | | | | & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.30/19.87 | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 135.30/19.87 | | | | | | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.30/19.87 | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 &
% 135.30/19.87 | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15
% 135.30/19.87 | | | | | | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0)
% 135.30/19.87 | | | | | | | & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 135.30/19.87 | | | | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) =
% 135.30/19.87 | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 135.30/19.87 | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 &
% 135.30/19.87 | | | | | | | ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.30/19.87 | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3)
% 135.30/19.87 | | | | | | | = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.30/19.87 | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0
% 135.30/19.87 | | | | | | | & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.30/19.87 | | | | | | | $i(all_56_29))))
% 135.30/19.87 | | | | | | |
% 135.30/19.87 | | | | | | | BETA: splitting (75) gives:
% 135.30/19.87 | | | | | | |
% 135.30/19.87 | | | | | | | Case 1:
% 135.30/19.87 | | | | | | | |
% 135.30/19.87 | | | | | | | | (76) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) &
% 135.30/19.87 | | | | | | | | ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 135.30/19.87 | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2)
% 135.30/19.87 | | | | | | | | = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) =
% 135.30/19.87 | | | | | | | | all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 135.30/19.87 | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.30/19.87 | | | | | | | | $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~
% 135.30/19.87 | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21
% 135.30/19.87 | | | | | | | | = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 &
% 135.30/19.87 | | | | | | | | op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.30/19.87 | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 135.30/19.87 | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.30/19.87 | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 135.30/19.87 | | | | | | | |
% 135.30/19.87 | | | | | | | | BETA: splitting (76) gives:
% 135.30/19.87 | | | | | | | |
% 135.30/19.87 | | | | | | | | Case 1:
% 135.30/19.87 | | | | | | | | |
% 135.30/19.87 | | | | | | | | | (77) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) &
% 135.30/19.87 | | | | | | | | | ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 135.30/19.87 | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2)
% 135.30/19.87 | | | | | | | | | = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) =
% 135.30/19.87 | | | | | | | | | all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 135.30/19.87 | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.30/19.87 | | | | | | | | | $i(all_56_25)
% 135.30/19.87 | | | | | | | | |
% 135.30/19.87 | | | | | | | | | ALPHA: (77) implies:
% 135.30/19.87 | | | | | | | | | (78) op(e1, e1) = e3
% 135.30/19.87 | | | | | | | | |
% 135.30/19.87 | | | | | | | | | REF_CLOSE: (10), (20), (56), (78) are inconsistent by
% 135.30/19.87 | | | | | | | | | sub-proof #109.
% 135.30/19.87 | | | | | | | | |
% 135.30/19.87 | | | | | | | | Case 2:
% 135.30/19.87 | | | | | | | | |
% 135.30/19.87 | | | | | | | | | (79) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) &
% 135.30/19.87 | | | | | | | | | ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.30/19.87 | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 135.30/19.87 | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 135.30/19.87 | | | | | | | | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 135.30/19.87 | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.30/19.87 | | | | | | | | | $i(all_56_29)
% 135.30/19.87 | | | | | | | | |
% 135.30/19.87 | | | | | | | | | ALPHA: (79) implies:
% 135.30/19.87 | | | | | | | | | (80) op(e1, e0) = all_56_29
% 135.30/19.87 | | | | | | | | |
% 135.30/19.87 | | | | | | | | | REF_CLOSE: (1), (2), (4), (6), (8), (10), (11), (13), (14),
% 135.30/19.87 | | | | | | | | | (15), (17), (18), (20), (21), (22), (23), (24),
% 135.30/19.87 | | | | | | | | | (25), (26), (30), (31), (32), (34), (35), (36),
% 135.30/19.87 | | | | | | | | | (38), (39), (40), (41), (42), (44), (45), (53),
% 135.30/19.87 | | | | | | | | | (54), (56), (57), (63), (64), (80) are inconsistent
% 135.30/19.87 | | | | | | | | | by sub-proof #8.
% 135.30/19.87 | | | | | | | | |
% 135.30/19.87 | | | | | | | | End of split
% 135.30/19.87 | | | | | | | |
% 135.30/19.87 | | | | | | | Case 2:
% 135.30/19.87 | | | | | | | |
% 135.30/19.87 | | | | | | | | (81) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) &
% 135.30/19.87 | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.30/19.87 | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 135.30/19.87 | | | | | | | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 135.30/19.87 | | | | | | | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 &
% 135.30/19.87 | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 135.30/19.87 | | | | | | | | $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~
% 135.30/19.87 | | | | | | | | (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19
% 135.30/19.87 | | | | | | | | = e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3
% 135.30/19.87 | | | | | | | | & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.30/19.87 | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1)
% 135.30/19.87 | | | | | | | | = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.30/19.87 | | | | | | | | $i(all_56_27)) | (op(e0, e0) = all_56_31 &
% 135.30/19.87 | | | | | | | | $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~
% 135.30/19.87 | | | | | | | | (all_56_1 = e3) & ~ (all_56_9 = e2) & ~
% 135.30/19.87 | | | | | | | | (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3,
% 135.30/19.87 | | | | | | | | e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 135.30/19.87 | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.30/19.87 | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.30/19.87 | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 &
% 135.30/19.87 | | | | | | | | all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 135.30/19.87 | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.30/19.87 | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2,
% 135.30/19.87 | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.30/19.87 | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.30/19.87 | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.30/19.87 | | | | | | | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1
% 135.30/19.87 | | | | | | | | & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~
% 135.30/19.87 | | | | | | | | (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1,
% 135.30/19.87 | | | | | | | | e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 135.30/19.87 | | | | | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) =
% 135.30/19.87 | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 135.30/19.87 | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 135.30/19.87 | | | | | | | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.30/19.87 | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1,
% 135.30/19.87 | | | | | | | | e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1,
% 135.30/19.87 | | | | | | | | e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 135.30/19.87 | | | | | | | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.30/19.87 | | | | | | | | $i(all_56_21) & $i(all_56_29))))
% 135.30/19.87 | | | | | | | |
% 135.30/19.87 | | | | | | | | BETA: splitting (81) gives:
% 135.30/19.87 | | | | | | | |
% 135.30/19.87 | | | | | | | | Case 1:
% 135.30/19.87 | | | | | | | | |
% 135.30/19.87 | | | | | | | | | (82) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) &
% 135.30/19.87 | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.30/19.87 | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 135.30/19.87 | | | | | | | | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 135.30/19.87 | | | | | | | | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 &
% 135.30/19.87 | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 135.30/19.87 | | | | | | | | | $i(all_56_31)
% 135.30/19.87 | | | | | | | | |
% 135.30/19.87 | | | | | | | | | ALPHA: (82) implies:
% 135.30/19.87 | | | | | | | | | (83) op(e2, e2) = e0
% 135.30/19.87 | | | | | | | | |
% 135.30/19.87 | | | | | | | | | REF_CLOSE: (10), (11), (15), (83) are inconsistent by
% 135.30/19.87 | | | | | | | | | sub-proof #641.
% 135.30/19.87 | | | | | | | | |
% 135.30/19.87 | | | | | | | | Case 2:
% 135.30/19.87 | | | | | | | | |
% 135.30/19.87 | | | | | | | | | (84) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3)
% 135.30/19.87 | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.30/19.87 | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2,
% 135.30/19.87 | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 135.30/19.87 | | | | | | | | | e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) =
% 135.30/19.87 | | | | | | | | | e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.30/19.87 | | | | | | | | | $i(all_56_27)) | (op(e0, e0) = all_56_31 &
% 135.30/19.87 | | | | | | | | | $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 &
% 135.30/19.87 | | | | | | | | | ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~
% 135.30/19.87 | | | | | | | | | (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3,
% 135.30/19.87 | | | | | | | | | e3) = all_56_1 & op(e3, e2) = all_56_9 &
% 135.30/19.87 | | | | | | | | | op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25
% 135.30/19.87 | | | | | | | | | & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9)
% 135.30/19.87 | | | | | | | | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 135.30/19.87 | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 135.30/19.87 | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.30/19.87 | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.30/19.87 | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 135.30/19.87 | | | | | | | | | & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.30/19.87 | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.30/19.87 | | | | | | | | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 =
% 135.30/19.87 | | | | | | | | | e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) &
% 135.30/19.87 | | | | | | | | | ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.30/19.87 | | | | | | | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 135.30/19.87 | | | | | | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) =
% 135.30/19.87 | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 135.30/19.87 | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 =
% 135.30/19.87 | | | | | | | | | e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) &
% 135.30/19.87 | | | | | | | | | ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 135.30/19.87 | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 135.30/19.87 | | | | | | | | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29
% 135.30/19.87 | | | | | | | | | & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13)
% 135.30/19.87 | | | | | | | | | & $i(all_56_21) & $i(all_56_29))))
% 135.30/19.87 | | | | | | | | |
% 135.30/19.87 | | | | | | | | | BETA: splitting (84) gives:
% 135.30/19.87 | | | | | | | | |
% 135.30/19.87 | | | | | | | | | Case 1:
% 135.30/19.87 | | | | | | | | | |
% 135.30/19.87 | | | | | | | | | | (85) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3)
% 135.30/19.87 | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.30/19.87 | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2,
% 135.30/19.87 | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 135.30/19.87 | | | | | | | | | | e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) =
% 135.30/19.87 | | | | | | | | | | e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.30/19.87 | | | | | | | | | | $i(all_56_27)
% 135.30/19.87 | | | | | | | | | |
% 135.30/19.87 | | | | | | | | | | ALPHA: (85) implies:
% 135.30/19.87 | | | | | | | | | | (86) ~ (all_56_27 = e0)
% 135.30/19.87 | | | | | | | | | | (87) ~ (all_56_19 = e1)
% 135.30/19.87 | | | | | | | | | | (88) op(e2, e0) = all_56_27
% 135.30/19.87 | | | | | | | | | | (89) op(e2, e1) = all_56_19
% 135.30/19.87 | | | | | | | | | |
% 135.30/19.87 | | | | | | | | | | REF_CLOSE: (4), (8), (10), (11), (15), (35), (36), (39),
% 135.30/19.87 | | | | | | | | | | (40), (44), (45), (86), (87), (88), (89) are
% 135.30/19.87 | | | | | | | | | | inconsistent by sub-proof #10.
% 135.30/19.87 | | | | | | | | | |
% 135.30/19.87 | | | | | | | | | Case 2:
% 135.30/19.87 | | | | | | | | | |
% 135.30/19.87 | | | | | | | | | | (90) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7
% 135.30/19.87 | | | | | | | | | | = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 135.30/19.87 | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 135.30/19.87 | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.30/19.87 | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.30/19.87 | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 135.30/19.87 | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.30/19.87 | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 135.30/19.87 | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 135.30/19.87 | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.30/19.87 | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.30/19.87 | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 135.30/19.87 | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 135.30/19.87 | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 135.30/19.87 | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.30/19.87 | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.30/19.87 | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 135.30/19.87 | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.30/19.87 | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 135.30/19.87 | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 135.30/19.87 | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 135.30/19.87 | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.30/19.87 | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 135.30/19.87 | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.30/19.87 | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 135.30/19.87 | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.30/19.87 | | | | | | | | | | $i(all_56_21) & $i(all_56_29)))
% 135.30/19.87 | | | | | | | | | |
% 135.30/19.87 | | | | | | | | | | ALPHA: (90) implies:
% 135.30/19.87 | | | | | | | | | | (91) op(e0, e0) = all_56_31
% 135.30/19.87 | | | | | | | | | | (92) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3)
% 135.30/19.87 | | | | | | | | | | & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 135.30/19.87 | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3,
% 135.30/19.87 | | | | | | | | | | e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.30/19.87 | | | | | | | | | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1)
% 135.30/19.87 | | | | | | | | | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 135.30/19.87 | | | | | | | | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 135.30/19.87 | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 135.30/19.87 | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.30/19.87 | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.30/19.87 | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.30/19.87 | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.30/19.87 | | | | | | | | | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1
% 135.30/19.87 | | | | | | | | | | & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~
% 135.30/19.87 | | | | | | | | | | (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1,
% 135.30/19.87 | | | | | | | | | | e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 135.30/19.87 | | | | | | | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) =
% 135.30/19.87 | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 135.30/19.87 | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 135.30/19.87 | | | | | | | | | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.30/19.87 | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1,
% 135.30/19.87 | | | | | | | | | | e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1,
% 135.30/19.87 | | | | | | | | | | e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 135.30/19.87 | | | | | | | | | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.30/19.87 | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 135.30/19.87 | | | | | | | | | |
% 135.30/19.87 | | | | | | | | | | GROUND_INST: instantiating (10) with e1, all_56_31, e0, e0,
% 135.30/19.87 | | | | | | | | | | simplifying with (13), (91) gives:
% 135.30/19.87 | | | | | | | | | | (93) all_56_31 = e1
% 135.30/19.87 | | | | | | | | | |
% 135.30/19.87 | | | | | | | | | | GROUND_INST: instantiating (10) with all_52_11, e3, e1, e0,
% 135.30/19.87 | | | | | | | | | | simplifying with (18), (64) gives:
% 135.30/19.87 | | | | | | | | | | (94) all_52_11 = e3
% 135.30/19.87 | | | | | | | | | |
% 135.30/19.87 | | | | | | | | | | GROUND_INST: instantiating (10) with all_52_9, all_6_0, e1, e2,
% 135.30/19.87 | | | | | | | | | | simplifying with (26), (45) gives:
% 135.30/19.87 | | | | | | | | | | (95) all_52_9 = all_6_0
% 135.30/19.87 | | | | | | | | | |
% 135.30/19.87 | | | | | | | | | | COMBINE_EQS: (30), (95) imply:
% 135.30/19.87 | | | | | | | | | | (96) all_54_6 = all_6_0
% 135.30/19.87 | | | | | | | | | |
% 135.30/19.87 | | | | | | | | | | REDUCE: (17), (95) imply:
% 135.30/19.87 | | | | | | | | | | (97) ~ (all_52_1 = all_6_0)
% 135.30/19.87 | | | | | | | | | |
% 135.30/19.87 | | | | | | | | | | REDUCE: (25), (95) imply:
% 135.30/19.87 | | | | | | | | | | (98) ~ (all_6_0 = e3)
% 135.30/19.87 | | | | | | | | | |
% 135.30/19.87 | | | | | | | | | | REDUCE: (54), (95) imply:
% 135.30/19.87 | | | | | | | | | | (99) ~ (all_6_0 = e2)
% 135.30/19.87 | | | | | | | | | |
% 135.30/19.87 | | | | | | | | | | BETA: splitting (22) gives:
% 135.30/19.87 | | | | | | | | | |
% 135.30/19.87 | | | | | | | | | | Case 1:
% 135.30/19.87 | | | | | | | | | | |
% 135.30/19.87 | | | | | | | | | | | (100) all_54_6 = e3
% 135.30/19.87 | | | | | | | | | | |
% 135.30/19.87 | | | | | | | | | | | COMBINE_EQS: (96), (100) imply:
% 135.30/19.87 | | | | | | | | | | | (101) all_6_0 = e3
% 135.30/19.87 | | | | | | | | | | |
% 135.30/19.87 | | | | | | | | | | | REDUCE: (98), (101) imply:
% 135.30/19.87 | | | | | | | | | | | (102) $false
% 135.30/19.87 | | | | | | | | | | |
% 135.30/19.87 | | | | | | | | | | | CLOSE: (102) is inconsistent.
% 135.30/19.87 | | | | | | | | | | |
% 135.30/19.87 | | | | | | | | | | Case 2:
% 135.30/19.87 | | | | | | | | | | |
% 135.30/19.87 | | | | | | | | | | | (103) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 135.30/19.87 | | | | | | | | | | |
% 135.30/19.87 | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (8), (10), (11), (14), (15), (20),
% 135.30/19.87 | | | | | | | | | | | (25), (26), (31), (32), (34), (38), (39), (41),
% 135.30/19.87 | | | | | | | | | | | (42), (44), (56), (57), (63), (92), (93), (96),
% 135.30/19.87 | | | | | | | | | | | (97), (98), (99), (103) are inconsistent by
% 135.30/19.87 | | | | | | | | | | | sub-proof #9.
% 135.30/19.87 | | | | | | | | | | |
% 135.30/19.87 | | | | | | | | | | End of split
% 135.30/19.87 | | | | | | | | | |
% 135.30/19.87 | | | | | | | | | End of split
% 135.30/19.87 | | | | | | | | |
% 135.30/19.87 | | | | | | | | End of split
% 135.30/19.87 | | | | | | | |
% 135.30/19.87 | | | | | | | End of split
% 135.30/19.87 | | | | | | |
% 135.30/19.87 | | | | | | End of split
% 135.30/19.87 | | | | | |
% 135.30/19.87 | | | | | Case 2:
% 135.30/19.87 | | | | | |
% 135.30/19.87 | | | | | | (104) all_57_15 = e3 & op(e0, e0) = e3
% 135.30/19.87 | | | | | |
% 135.30/19.87 | | | | | | ALPHA: (104) implies:
% 135.30/19.87 | | | | | | (105) op(e0, e0) = e3
% 135.30/19.87 | | | | | |
% 135.30/19.87 | | | | | | REF_CLOSE: (10), (13), (35), (105) are inconsistent by sub-proof
% 135.30/19.87 | | | | | | #606.
% 135.30/19.87 | | | | | |
% 135.30/19.87 | | | | | End of split
% 135.30/19.87 | | | | |
% 135.30/19.87 | | | | End of split
% 135.30/19.87 | | | |
% 135.30/19.87 | | | Case 2:
% 135.30/19.87 | | | |
% 135.30/19.87 | | | | (106) all_54_7 = e1 | all_54_7 = e0
% 135.30/19.87 | | | |
% 135.30/19.87 | | | | REF_CLOSE: (3), (8), (33), (106) are inconsistent by sub-proof #313.
% 135.30/19.87 | | | |
% 135.30/19.87 | | | End of split
% 135.30/19.87 | | |
% 135.30/19.87 | | End of split
% 135.30/19.87 | |
% 135.30/19.87 | Case 2:
% 135.30/19.87 | |
% 135.30/19.87 | | (107) ~ (all_6_1 = e3) & op(e2, e2) = all_6_1 & $i(all_6_1)
% 135.30/19.87 | |
% 135.30/19.87 | | REF_CLOSE: (10), (15), (107) are inconsistent by sub-proof #74.
% 135.30/19.87 | |
% 135.30/19.87 | End of split
% 135.30/19.87 |
% 135.30/19.87 End of proof
% 135.30/19.87
% 135.30/19.87 Sub-proof #8 shows that the following formulas are inconsistent:
% 135.30/19.87 ----------------------------------------------------------------
% 135.30/19.87 (1) op(e1, e0) = all_56_29
% 135.30/19.87 (2) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 135.30/19.87 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 135.30/19.87 (3) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 135.30/19.87 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 135.30/19.87 (4) op(e2, e0) = all_52_13
% 135.30/19.87 (5) ~ (all_52_11 = e2)
% 135.30/19.87 (6) ~ (e2 = e0)
% 135.30/19.87 (7) ~ (all_52_13 = e1)
% 135.30/19.87 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.30/19.87 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.30/19.87 (9) ~ (e3 = e0)
% 135.30/19.87 (10) ~ (e3 = e2)
% 135.30/19.87 (11) op(e0, e0) = e1
% 135.30/19.87 (12) all_57_8 = e2
% 135.30/19.87 (13) op(e2, e2) = e3
% 135.30/19.87 (14) ~ (all_52_1 = all_52_9)
% 135.30/19.87 (15) op(e0, e1) = all_52_11
% 135.30/19.87 (16) op(e1, e1) = e2
% 135.30/19.87 (17) ~ (all_10_2 = e0)
% 135.30/19.87 (18) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 135.30/19.87 (19) ~ (all_52_9 = e2)
% 135.30/19.87 (20) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.30/19.87 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.30/19.87 op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.30/19.87 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.30/19.87 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 135.30/19.87 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.30/19.87 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 135.30/19.87 = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.30/19.87 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.30/19.87 $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~
% 135.30/19.87 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.30/19.87 (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) =
% 135.30/19.87 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0,
% 135.30/19.87 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 135.30/19.87 $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3)
% 135.30/19.87 & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 135.30/19.87 op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17
% 135.30/19.87 & op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 135.30/19.87 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 135.30/19.87 (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 135.30/19.87 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.30/19.87 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0)
% 135.30/19.87 = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) &
% 135.30/19.87 $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 &
% 135.30/19.87 all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.30/19.87 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 135.30/19.87 = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.30/19.87 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.30/19.87 $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~
% 135.30/19.87 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.30/19.87 (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 135.30/19.87 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0,
% 135.30/19.87 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 135.30/19.87 $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3)
% 135.30/19.87 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.30/19.87 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.30/19.87 all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2
% 135.30/19.87 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.30/19.87 (op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 =
% 135.30/19.87 e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.30/19.87 & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) =
% 135.30/19.87 all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.30/19.87 op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.30/19.87 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 135.30/19.87 e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.30/19.87 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 135.30/19.87 e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.30/19.87 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.30/19.87 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.30/19.87 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.30/19.87 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.30/19.87 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 135.30/19.87 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 135.30/19.87 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 135.30/19.87 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.30/19.87 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 135.30/19.87 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.30/19.87 $i(all_56_29))))
% 135.30/19.87 (21) op(e3, e3) = all_10_2
% 135.30/19.87 (22) ~ (all_52_9 = e3)
% 135.30/19.87 (23) op(e0, e1) = e3
% 135.30/19.87 (24) op(e2, e1) = all_52_9
% 135.30/19.87 (25) ~ (all_52_1 = e2)
% 135.30/19.87 (26) op(e2, e1) = all_6_0
% 135.30/19.87 (27) all_57_14 = e3
% 135.30/19.87 (28) all_54_6 = all_52_9
% 135.30/19.87 (29) op(e2, e3) = all_52_1
% 135.30/19.87 (30) ~ (all_52_14 = e1)
% 135.30/19.87 (31) op(e3, e1) = all_52_8
% 135.30/19.87 (32) ~ (e3 = e1)
% 135.30/19.87 (33) ~ (e1 = e0)
% 135.30/19.88 (34) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 135.30/19.88 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 135.30/19.88 (35) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 135.30/19.88 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 135.30/19.88 (36) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 135.30/19.88 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 135.30/19.88 (37) op(e1, e0) = all_52_14
% 135.30/19.88 (38) ~ (all_6_0 = e0)
% 135.30/19.88 (39) op(e1, e0) = e0
% 135.30/19.88
% 135.30/19.88 Begin of proof
% 135.30/19.88 |
% 135.30/19.88 | BETA: splitting (20) gives:
% 135.30/19.88 |
% 135.30/19.88 | Case 1:
% 135.30/19.88 | |
% 135.30/19.88 | | (40) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11
% 135.30/19.88 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) =
% 135.30/19.88 | | e2 & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 135.30/19.88 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 135.30/19.88 | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.30/19.88 | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13
% 135.30/19.88 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) =
% 135.30/19.88 | | e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.30/19.88 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 135.30/19.88 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 135.30/19.88 | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15
% 135.30/19.88 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) =
% 135.30/19.88 | | e0 & op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.30/19.88 | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 &
% 135.30/19.88 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.30/19.88 | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 135.30/19.88 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.30/19.88 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.30/19.88 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 135.30/19.88 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25))
% 135.30/19.88 | |
% 135.30/19.88 | | BETA: splitting (40) gives:
% 135.30/19.88 | |
% 135.30/19.88 | | Case 1:
% 135.30/19.88 | | |
% 135.30/19.88 | | | (41) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~
% 135.30/19.88 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.30/19.88 | | | op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = all_56_3 &
% 135.30/19.88 | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 135.30/19.88 | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.30/19.88 | | | $i(all_56_27)) | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5
% 135.30/19.88 | | | = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.30/19.88 | | | (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1,
% 135.30/19.88 | | | e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.30/19.88 | | | all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.30/19.88 | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 135.30/19.88 | | |
% 135.30/19.88 | | | BETA: splitting (41) gives:
% 135.30/19.88 | | |
% 135.30/19.88 | | | Case 1:
% 135.30/19.88 | | | |
% 135.30/19.88 | | | | (42) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~
% 135.30/19.88 | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.30/19.88 | | | | op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = all_56_3 &
% 135.30/19.88 | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 135.30/19.88 | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.30/19.88 | | | | $i(all_56_27)
% 135.30/19.88 | | | |
% 135.30/19.88 | | | | ALPHA: (42) implies:
% 135.30/19.88 | | | | (43) ~ (all_56_27 = e0)
% 135.30/19.88 | | | | (44) ~ (all_56_19 = e1)
% 135.30/19.88 | | | | (45) op(e2, e0) = all_56_27
% 135.30/19.88 | | | | (46) op(e2, e1) = all_56_19
% 135.30/19.88 | | | |
% 135.30/19.88 | | | | REF_CLOSE: (4), (7), (8), (9), (13), (26), (32), (33), (35), (36), (38),
% 135.30/19.88 | | | | (43), (44), (45), (46) are inconsistent by sub-proof #10.
% 135.30/19.88 | | | |
% 135.30/19.88 | | | Case 2:
% 135.30/19.88 | | | |
% 135.30/19.88 | | | | (47) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~
% 135.30/19.88 | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 135.30/19.88 | | | | op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 &
% 135.30/19.88 | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 135.30/19.88 | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.30/19.88 | | | | $i(all_56_29)
% 135.30/19.88 | | | |
% 135.30/19.88 | | | | ALPHA: (47) implies:
% 135.30/19.88 | | | | (48) ~ (all_56_29 = e0)
% 135.30/19.88 | | | |
% 135.30/19.88 | | | | REF_CLOSE: (1), (8), (39), (48) are inconsistent by sub-proof #45.
% 135.30/19.88 | | | |
% 135.30/19.88 | | | End of split
% 135.30/19.88 | | |
% 135.30/19.88 | | Case 2:
% 135.30/19.88 | | |
% 135.30/19.88 | | | (49) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~
% 135.30/19.88 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.30/19.88 | | | op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = all_56_7 &
% 135.30/19.88 | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 135.30/19.88 | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 135.30/19.88 | | | $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1
% 135.30/19.88 | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 135.30/19.88 | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9
% 135.30/19.88 | | | & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e2, e3) =
% 135.30/19.88 | | | e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.30/19.88 | | | $i(all_56_17) & $i(all_56_25))
% 135.30/19.88 | | |
% 135.30/19.88 | | | REF_CLOSE: (8), (17), (21), (25), (29), (49) are inconsistent by sub-proof
% 135.30/19.88 | | | #533.
% 135.30/19.88 | | |
% 135.30/19.88 | | End of split
% 135.30/19.88 | |
% 135.30/19.88 | Case 2:
% 135.30/19.88 | |
% 135.30/19.88 | | (50) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 135.30/19.88 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.30/19.88 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.30/19.88 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 135.30/19.88 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 135.30/19.88 | | (all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 135.30/19.88 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 135.30/19.88 | | op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1,
% 135.30/19.88 | | e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 135.30/19.88 | | all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.30/19.88 | | $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 135.30/19.88 | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31
% 135.30/19.88 | | = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 135.30/19.88 | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.30/19.88 | | op(e0, e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 135.30/19.88 | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2
% 135.30/19.88 | | & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 135.30/19.88 | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 135.30/19.88 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 135.30/19.88 | | op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 135.30/19.88 | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = all_56_31 &
% 135.30/19.88 | | $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 135.30/19.88 | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 135.30/19.88 | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) =
% 135.30/19.88 | | all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.30/19.88 | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17)
% 135.30/19.88 | | & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~
% 135.30/19.88 | | (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 135.30/19.88 | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 135.30/19.88 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 135.30/19.88 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 135.30/19.88 | | & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~
% 135.30/19.88 | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 135.30/19.88 | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 135.30/19.88 | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) =
% 135.30/19.88 | | all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 135.30/19.88 | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 135.30/19.88 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 135.30/19.88 | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.30/19.88 | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.30/19.88 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.30/19.88 | | $i(all_56_29))))
% 135.30/19.88 | |
% 135.30/19.88 | | BETA: splitting (50) gives:
% 135.30/19.88 | |
% 135.30/19.88 | | Case 1:
% 135.30/19.88 | | |
% 135.30/19.88 | | | (51) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~
% 135.30/19.88 | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 135.30/19.88 | | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) =
% 135.30/19.88 | | | all_56_17 & op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 135.30/19.88 | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.30/19.88 | | | $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5
% 135.30/19.88 | | | = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.30/19.88 | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1,
% 135.30/19.88 | | | e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.30/19.88 | | | all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.30/19.88 | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 135.30/19.88 | | |
% 135.30/19.88 | | | REF_CLOSE: (8), (10), (16), (39), (51) are inconsistent by sub-proof #42.
% 135.30/19.88 | | |
% 135.30/19.88 | | Case 2:
% 135.30/19.88 | | |
% 135.30/19.88 | | | (52) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 135.30/19.88 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.30/19.88 | | | op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 &
% 135.30/19.88 | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 135.30/19.88 | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 135.30/19.88 | | | $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3
% 135.30/19.88 | | | = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.30/19.88 | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 135.30/19.88 | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 135.30/19.88 | | | op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11)
% 135.30/19.88 | | | & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = all_56_31 &
% 135.30/19.88 | | | $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 135.30/19.88 | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 135.30/19.88 | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) =
% 135.30/19.88 | | | all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.30/19.88 | | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.30/19.88 | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 135.30/19.88 | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~
% 135.30/19.88 | | | (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.30/19.88 | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.30/19.88 | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) &
% 135.30/19.88 | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 135.30/19.88 | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 135.30/19.88 | | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1,
% 135.30/19.88 | | | e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 135.30/19.88 | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.30/19.88 | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 =
% 135.30/19.88 | | | e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.30/19.88 | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1,
% 135.30/19.88 | | | e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.30/19.88 | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.30/19.88 | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.30/19.88 | | | $i(all_56_29))))
% 135.30/19.88 | | |
% 135.30/19.88 | | | BETA: splitting (52) gives:
% 135.30/19.88 | | |
% 135.30/19.88 | | | Case 1:
% 135.30/19.88 | | | |
% 135.30/19.88 | | | | (53) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 135.30/19.88 | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.30/19.88 | | | | op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 &
% 135.30/19.88 | | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 135.30/19.88 | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 135.30/19.88 | | | | $i(all_56_31)
% 135.30/19.88 | | | |
% 135.30/19.88 | | | | ALPHA: (53) implies:
% 135.30/19.88 | | | | (54) op(e2, e2) = e0
% 135.30/19.88 | | | |
% 135.30/19.88 | | | | REF_CLOSE: (8), (9), (13), (54) are inconsistent by sub-proof #641.
% 135.30/19.88 | | | |
% 135.30/19.88 | | | Case 2:
% 135.30/19.88 | | | |
% 135.30/19.88 | | | | (55) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 135.30/19.88 | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.30/19.88 | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.30/19.88 | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 135.30/19.88 | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.30/19.88 | | | | $i(all_56_27)) | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.30/19.88 | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 135.30/19.88 | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 =
% 135.30/19.88 | | | | e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 &
% 135.30/19.88 | | | | op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 135.30/19.88 | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.30/19.88 | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~
% 135.30/19.88 | | | | (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.30/19.88 | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.30/19.88 | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 135.30/19.88 | | | | e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) &
% 135.30/19.88 | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.30/19.88 | | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.30/19.88 | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 =
% 135.30/19.88 | | | | e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 135.30/19.88 | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23
% 135.30/19.88 | | | | & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 135.30/19.88 | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 135.30/19.88 | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 =
% 135.30/19.88 | | | | e0) & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 135.30/19.88 | | | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & op(e0,
% 135.30/19.88 | | | | e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.30/19.88 | | | | & $i(all_56_29))))
% 135.30/19.88 | | | |
% 135.30/19.88 | | | | BETA: splitting (55) gives:
% 135.30/19.88 | | | |
% 135.30/19.88 | | | | Case 1:
% 135.30/19.88 | | | | |
% 135.30/19.88 | | | | | (56) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 135.30/19.88 | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.30/19.88 | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.30/19.88 | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 135.30/19.88 | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.30/19.88 | | | | | $i(all_56_27)
% 135.30/19.88 | | | | |
% 135.30/19.88 | | | | | ALPHA: (56) implies:
% 135.30/19.88 | | | | | (57) ~ (all_56_27 = e0)
% 135.30/19.88 | | | | | (58) ~ (all_56_19 = e1)
% 135.30/19.88 | | | | | (59) op(e2, e0) = all_56_27
% 135.30/19.88 | | | | | (60) op(e2, e1) = all_56_19
% 135.30/19.88 | | | | |
% 135.30/19.88 | | | | | REF_CLOSE: (4), (7), (8), (9), (13), (26), (32), (33), (35), (36),
% 135.30/19.88 | | | | | (38), (57), (58), (59), (60) are inconsistent by sub-proof
% 135.30/19.88 | | | | | #10.
% 135.30/19.88 | | | | |
% 135.30/19.88 | | | | Case 2:
% 135.30/19.88 | | | | |
% 135.30/19.88 | | | | | (61) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 135.30/19.88 | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) &
% 135.30/19.88 | | | | | ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.30/19.88 | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17
% 135.30/19.88 | | | | | & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1)
% 135.30/19.88 | | | | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 135.30/19.88 | | | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 135.30/19.88 | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 =
% 135.30/19.88 | | | | | e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.30/19.88 | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 135.30/19.88 | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 135.30/19.88 | | | | | & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~
% 135.30/19.88 | | | | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.30/19.88 | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 135.30/19.88 | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 135.30/19.88 | | | | | op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 135.30/19.88 | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 & ~
% 135.30/19.88 | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.30/19.88 | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 135.30/19.88 | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1,
% 135.30/19.88 | | | | | e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 135.30/19.88 | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)))
% 135.30/19.88 | | | | |
% 135.30/19.88 | | | | | ALPHA: (61) implies:
% 135.30/19.88 | | | | | (62) op(e0, e0) = all_56_31
% 135.30/19.88 | | | | | (63) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 135.30/19.88 | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0)
% 135.30/19.88 | | | | | & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 135.30/19.88 | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 135.30/19.88 | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25))
% 135.30/19.88 | | | | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 135.30/19.88 | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0)
% 135.30/19.88 | | | | | & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 135.30/19.88 | | | | | e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0
% 135.30/19.88 | | | | | & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.30/19.88 | | | | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~
% 135.30/19.88 | | | | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 135.30/19.88 | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 135.30/19.88 | | | | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1)
% 135.30/19.88 | | | | | = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 135.30/19.88 | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 135.30/19.88 | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0)
% 135.30/19.88 | | | | | & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1,
% 135.30/19.88 | | | | | e1) = all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0
% 135.30/19.88 | | | | | & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.30/19.88 | | | | | $i(all_56_29))
% 135.30/19.88 | | | | |
% 135.30/19.88 | | | | | GROUND_INST: instantiating (8) with e1, all_56_31, e0, e0, simplifying
% 135.30/19.88 | | | | | with (11), (62) gives:
% 135.30/19.88 | | | | | (64) all_56_31 = e1
% 135.30/19.88 | | | | |
% 135.30/19.88 | | | | | GROUND_INST: instantiating (8) with all_52_11, e3, e1, e0, simplifying
% 135.30/19.88 | | | | | with (15), (23) gives:
% 135.30/19.88 | | | | | (65) all_52_11 = e3
% 135.30/19.88 | | | | |
% 135.30/19.88 | | | | | GROUND_INST: instantiating (8) with e0, all_56_29, e0, e1, simplifying
% 135.30/19.88 | | | | | with (1), (39) gives:
% 135.30/19.88 | | | | | (66) all_56_29 = e0
% 135.30/19.88 | | | | |
% 135.30/19.88 | | | | | GROUND_INST: instantiating (8) with all_52_9, all_6_0, e1, e2,
% 135.30/19.88 | | | | | simplifying with (24), (26) gives:
% 135.30/19.88 | | | | | (67) all_52_9 = all_6_0
% 135.30/19.88 | | | | |
% 135.30/19.88 | | | | | COMBINE_EQS: (28), (67) imply:
% 135.30/19.88 | | | | | (68) all_54_6 = all_6_0
% 135.30/19.88 | | | | |
% 135.30/19.88 | | | | | REDUCE: (14), (67) imply:
% 135.30/19.88 | | | | | (69) ~ (all_52_1 = all_6_0)
% 135.30/19.88 | | | | |
% 135.30/19.88 | | | | | REDUCE: (22), (67) imply:
% 135.30/19.88 | | | | | (70) ~ (all_6_0 = e3)
% 135.30/19.88 | | | | |
% 135.30/19.88 | | | | | REDUCE: (19), (67) imply:
% 135.30/19.88 | | | | | (71) ~ (all_6_0 = e2)
% 135.30/19.88 | | | | |
% 135.30/19.88 | | | | | BETA: splitting (18) gives:
% 135.30/19.88 | | | | |
% 135.30/19.88 | | | | | Case 1:
% 135.30/19.88 | | | | | |
% 135.30/19.88 | | | | | | (72) all_54_6 = e3
% 135.30/19.88 | | | | | |
% 135.30/19.88 | | | | | | COMBINE_EQS: (68), (72) imply:
% 135.30/19.88 | | | | | | (73) all_6_0 = e3
% 135.30/19.88 | | | | | |
% 135.30/19.88 | | | | | | REDUCE: (70), (73) imply:
% 135.30/19.88 | | | | | | (74) $false
% 135.30/19.88 | | | | | |
% 135.30/19.88 | | | | | | CLOSE: (74) is inconsistent.
% 135.30/19.88 | | | | | |
% 135.30/19.88 | | | | | Case 2:
% 135.30/19.88 | | | | | |
% 135.30/19.88 | | | | | | (75) ~ (all_54_6 = e3)
% 135.30/19.88 | | | | | | (76) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 135.30/19.88 | | | | | |
% 135.30/19.88 | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (12), (13),
% 135.30/19.88 | | | | | | (16), (22), (24), (27), (29), (30), (31), (34), (35),
% 135.30/19.88 | | | | | | (37), (38), (39), (63), (64), (68), (69), (70), (71),
% 135.30/19.88 | | | | | | (76) are inconsistent by sub-proof #9.
% 135.30/19.88 | | | | | |
% 135.30/19.88 | | | | | End of split
% 135.30/19.88 | | | | |
% 135.30/19.88 | | | | End of split
% 135.30/19.88 | | | |
% 135.30/19.88 | | | End of split
% 135.30/19.88 | | |
% 135.30/19.88 | | End of split
% 135.30/19.88 | |
% 135.30/19.88 | End of split
% 135.30/19.88 |
% 135.30/19.88 End of proof
% 135.30/19.88
% 135.30/19.88 Sub-proof #9 shows that the following formulas are inconsistent:
% 135.30/19.88 ----------------------------------------------------------------
% 135.30/19.88 (1) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 135.30/19.88 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 135.30/19.88 (2) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 135.30/19.88 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 135.30/19.88 (3) all_54_6 = all_6_0
% 135.30/19.88 (4) ~ (all_6_0 = e3)
% 135.30/19.88 (5) op(e2, e0) = all_52_13
% 135.30/19.88 (6) ~ (e2 = e0)
% 135.30/19.88 (7) ~ (all_52_13 = e1)
% 135.30/19.88 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.30/19.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.30/19.88 (9) ~ (e3 = e0)
% 135.30/19.88 (10) ~ (all_6_0 = e2)
% 135.30/19.88 (11) ~ (e3 = e2)
% 135.30/19.88 (12) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 135.30/19.88 (13) all_57_8 = e2
% 135.30/19.88 (14) op(e2, e2) = e3
% 135.30/19.88 (15) all_56_31 = e1
% 135.30/19.88 (16) op(e1, e1) = e2
% 135.30/19.88 (17) ~ (all_52_1 = all_6_0)
% 135.30/19.88 (18) ~ (all_52_9 = e3)
% 135.30/19.88 (19) op(e2, e1) = all_52_9
% 135.30/19.88 (20) all_57_14 = e3
% 135.30/19.88 (21) op(e2, e3) = all_52_1
% 135.30/19.88 (22) ~ (all_52_14 = e1)
% 135.30/19.88 (23) op(e3, e1) = all_52_8
% 135.30/19.88 (24) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 135.30/19.88 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.30/19.88 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0)
% 135.30/19.88 = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.30/19.88 $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~
% 135.30/19.88 (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.30/19.88 (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.30/19.88 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.30/19.88 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.30/19.88 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 135.30/19.88 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 135.30/19.88 op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 135.30/19.88 op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 135.30/19.88 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13
% 135.30/19.88 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 135.30/19.88 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1,
% 135.30/19.88 e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.30/19.88 $i(all_56_21) & $i(all_56_29))
% 135.30/19.88 (25) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 135.30/19.88 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 135.30/19.88 (26) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 135.30/19.88 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 135.30/19.88 (27) op(e1, e0) = all_52_14
% 135.30/19.88 (28) ~ (all_6_0 = e0)
% 135.30/19.88 (29) op(e1, e0) = e0
% 135.30/19.88
% 135.30/19.88 Begin of proof
% 135.30/19.88 |
% 135.30/19.88 | BETA: splitting (12) gives:
% 135.30/19.88 |
% 135.30/19.88 | Case 1:
% 135.30/19.88 | |
% 135.30/19.88 | | (30) all_54_6 = e2
% 135.30/19.88 | |
% 135.30/19.88 | | COMBINE_EQS: (3), (30) imply:
% 135.30/19.88 | | (31) all_6_0 = e2
% 135.30/19.88 | |
% 135.30/19.88 | | REDUCE: (10), (31) imply:
% 135.30/19.88 | | (32) $false
% 135.30/19.88 | |
% 135.30/19.88 | | CLOSE: (32) is inconsistent.
% 135.30/19.88 | |
% 135.30/19.88 | Case 2:
% 135.30/19.88 | |
% 135.30/19.88 | | (33) ~ (all_54_6 = e2)
% 135.30/19.88 | | (34) all_54_6 = e1 | all_54_6 = e0
% 135.30/19.88 | |
% 135.30/19.88 | | BETA: splitting (34) gives:
% 135.30/19.88 | |
% 135.30/19.88 | | Case 1:
% 135.30/19.88 | | |
% 135.30/19.88 | | | (35) all_54_6 = e1
% 135.30/19.88 | | |
% 135.30/19.88 | | | COMBINE_EQS: (3), (35) imply:
% 135.30/19.88 | | | (36) all_6_0 = e1
% 135.30/19.88 | | |
% 135.30/19.88 | | | REDUCE: (17), (36) imply:
% 135.30/19.88 | | | (37) ~ (all_52_1 = e1)
% 135.30/19.88 | | |
% 135.30/19.88 | | | REDUCE: (4), (36) imply:
% 135.30/19.88 | | | (38) ~ (e3 = e1)
% 135.30/19.88 | | |
% 135.30/19.88 | | | SIMP: (38) implies:
% 135.30/19.88 | | | (39) ~ (e3 = e1)
% 135.30/19.88 | | |
% 135.30/19.88 | | | REDUCE: (10), (36) imply:
% 135.30/19.88 | | | (40) ~ (e2 = e1)
% 135.30/19.88 | | |
% 135.30/19.88 | | | SIMP: (40) implies:
% 135.30/19.88 | | | (41) ~ (e2 = e1)
% 135.30/19.88 | | |
% 135.30/19.88 | | | REDUCE: (28), (36) imply:
% 135.30/19.88 | | | (42) ~ (e1 = e0)
% 135.30/19.88 | | |
% 135.30/19.89 | | | BETA: splitting (26) gives:
% 135.30/19.89 | | |
% 135.30/19.89 | | | Case 1:
% 135.30/19.89 | | | |
% 135.30/19.89 | | | | (43) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2)
% 135.30/19.89 | | | | = e1)
% 135.30/19.89 | | | |
% 135.30/19.89 | | | | REF_CLOSE: (8), (14), (21), (37), (39), (43) are inconsistent by
% 135.30/19.89 | | | | sub-proof #77.
% 135.30/19.89 | | | |
% 135.30/19.89 | | | Case 2:
% 135.30/19.89 | | | |
% 135.30/19.89 | | | | (44) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0)
% 135.30/19.89 | | | | = e1)
% 135.30/19.89 | | | |
% 135.30/19.89 | | | | BETA: splitting (44) gives:
% 135.30/19.89 | | | |
% 135.30/19.89 | | | | Case 1:
% 135.30/19.89 | | | | |
% 135.30/19.89 | | | | | (45) all_57_5 = e1 & op(e2, e1) = e1
% 135.30/19.89 | | | | |
% 135.30/19.89 | | | | | ALPHA: (45) implies:
% 135.30/19.89 | | | | | (46) all_57_5 = e1
% 135.30/19.89 | | | | | (47) op(e2, e1) = e1
% 135.30/19.89 | | | | |
% 135.30/19.89 | | | | | BETA: splitting (24) gives:
% 135.30/19.89 | | | | |
% 135.30/19.89 | | | | | Case 1:
% 135.30/19.89 | | | | | |
% 135.30/19.89 | | | | | | (48) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 135.30/19.89 | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 =
% 135.30/19.89 | | | | | | e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 &
% 135.30/19.89 | | | | | | op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 135.30/19.89 | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.30/19.89 | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~
% 135.30/19.89 | | | | | | (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.30/19.89 | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.30/19.89 | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 135.30/19.89 | | | | | | e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) &
% 135.30/19.89 | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27))
% 135.30/19.89 | | | | | |
% 135.30/19.89 | | | | | | BETA: splitting (48) gives:
% 135.30/19.89 | | | | | |
% 135.30/19.89 | | | | | | Case 1:
% 135.30/19.89 | | | | | | |
% 135.30/19.89 | | | | | | | (49) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 135.30/19.89 | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 =
% 135.30/19.89 | | | | | | | e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 &
% 135.30/19.89 | | | | | | | op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 135.30/19.89 | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.30/19.89 | | | | | | | $i(all_56_25)
% 135.30/19.89 | | | | | | |
% 135.30/19.89 | | | | | | | ALPHA: (49) implies:
% 135.30/19.89 | | | | | | | (50) all_56_31 = e3
% 135.30/19.89 | | | | | | |
% 135.30/19.89 | | | | | | | COMBINE_EQS: (15), (50) imply:
% 135.30/19.89 | | | | | | | (51) e3 = e1
% 135.30/19.89 | | | | | | |
% 135.30/19.89 | | | | | | | COMBINE_EQS: (20), (51) imply:
% 135.30/19.89 | | | | | | | (52) all_57_14 = e1
% 135.30/19.89 | | | | | | |
% 135.48/19.89 | | | | | | | REF_CLOSE: (1), (2), (6), (8), (9), (11), (13), (16), (18), (19),
% 135.48/19.89 | | | | | | | (23), (25), (39), (41), (42), (46), (52) are
% 135.48/19.89 | | | | | | | inconsistent by sub-proof #76.
% 135.48/19.89 | | | | | | |
% 135.48/19.89 | | | | | | Case 2:
% 135.48/19.89 | | | | | | |
% 135.48/19.89 | | | | | | | (53) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 135.48/19.89 | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 =
% 135.48/19.89 | | | | | | | e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.48/19.89 | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 135.48/19.89 | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 135.48/19.89 | | | | | | | & $i(all_56_27)
% 135.48/19.89 | | | | | | |
% 135.48/19.89 | | | | | | | ALPHA: (53) implies:
% 135.48/19.89 | | | | | | | (54) ~ (all_56_19 = e1)
% 135.48/19.89 | | | | | | | (55) op(e2, e1) = all_56_19
% 135.48/19.89 | | | | | | |
% 135.48/19.89 | | | | | | | REF_CLOSE: (8), (47), (54), (55) are inconsistent by sub-proof
% 135.48/19.89 | | | | | | | #106.
% 135.48/19.89 | | | | | | |
% 135.48/19.89 | | | | | | End of split
% 135.48/19.89 | | | | | |
% 135.48/19.89 | | | | | Case 2:
% 135.48/19.89 | | | | | |
% 135.48/19.89 | | | | | | (56) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.48/19.89 | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 =
% 135.48/19.89 | | | | | | e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 135.48/19.89 | | | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23
% 135.48/19.89 | | | | | | & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 135.48/19.89 | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 135.48/19.89 | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 =
% 135.48/19.89 | | | | | | e0) & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 135.48/19.89 | | | | | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & op(e0,
% 135.48/19.89 | | | | | | e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.48/19.89 | | | | | | & $i(all_56_29))
% 135.48/19.89 | | | | | |
% 135.48/19.89 | | | | | | REF_CLOSE: (8), (22), (27), (29), (56) are inconsistent by sub-proof
% 135.48/19.89 | | | | | | #40.
% 135.48/19.89 | | | | | |
% 135.48/19.89 | | | | | End of split
% 135.48/19.89 | | | | |
% 135.48/19.89 | | | | Case 2:
% 135.48/19.89 | | | | |
% 135.48/19.89 | | | | | (57) all_57_10 = e1 & op(e2, e0) = e1
% 135.48/19.89 | | | | |
% 135.48/19.89 | | | | | ALPHA: (57) implies:
% 135.48/19.89 | | | | | (58) op(e2, e0) = e1
% 135.48/19.89 | | | | |
% 135.48/19.89 | | | | | REF_CLOSE: (5), (7), (8), (58) are inconsistent by sub-proof #180.
% 135.48/19.89 | | | | |
% 135.48/19.89 | | | | End of split
% 135.48/19.89 | | | |
% 135.48/19.89 | | | End of split
% 135.48/19.89 | | |
% 135.48/19.89 | | Case 2:
% 135.48/19.89 | | |
% 135.48/19.89 | | | (59) all_54_6 = e0
% 135.48/19.89 | | |
% 135.48/19.89 | | | COMBINE_EQS: (3), (59) imply:
% 135.48/19.89 | | | (60) all_6_0 = e0
% 135.48/19.89 | | |
% 135.48/19.89 | | | REDUCE: (28), (60) imply:
% 135.48/19.89 | | | (61) $false
% 135.48/19.89 | | |
% 135.48/19.89 | | | CLOSE: (61) is inconsistent.
% 135.48/19.89 | | |
% 135.48/19.89 | | End of split
% 135.48/19.89 | |
% 135.48/19.89 | End of split
% 135.48/19.89 |
% 135.48/19.89 End of proof
% 135.48/19.89
% 135.48/19.89 Sub-proof #10 shows that the following formulas are inconsistent:
% 135.48/19.89 ----------------------------------------------------------------
% 135.48/19.89 (1) op(e2, e0) = all_52_13
% 135.48/19.89 (2) ~ (all_52_13 = e1)
% 135.48/19.89 (3) op(e2, e1) = all_56_19
% 135.48/19.89 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.89 (5) ~ (e3 = e0)
% 135.48/19.89 (6) ~ (all_56_19 = e1)
% 135.48/19.89 (7) op(e2, e2) = e3
% 135.48/19.89 (8) op(e2, e1) = all_6_0
% 135.48/19.89 (9) ~ (all_56_27 = e0)
% 135.48/19.89 (10) ~ (e3 = e1)
% 135.48/19.89 (11) ~ (e1 = e0)
% 135.48/19.89 (12) op(e2, e0) = all_56_27
% 135.48/19.89 (13) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 135.48/19.89 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 135.48/19.89 (14) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 135.48/19.89 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 135.48/19.89 (15) ~ (all_6_0 = e0)
% 135.48/19.89
% 135.48/19.89 Begin of proof
% 135.48/19.89 |
% 135.48/19.89 | BETA: splitting (13) gives:
% 135.48/19.89 |
% 135.48/19.89 | Case 1:
% 135.48/19.89 | |
% 135.48/19.89 | | (16) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 135.48/19.89 | | e1)
% 135.48/19.89 | |
% 135.48/19.89 | | BETA: splitting (16) gives:
% 135.48/19.89 | |
% 135.48/19.89 | | Case 1:
% 135.48/19.89 | | |
% 135.48/19.89 | | | (17) all_57_2 = e1 & op(e2, e3) = e1
% 135.48/19.89 | | |
% 135.48/19.89 | | | ALPHA: (17) implies:
% 135.48/19.89 | | | (18) all_57_2 = e1
% 135.48/19.89 | | |
% 135.48/19.89 | | | BETA: splitting (14) gives:
% 135.48/19.89 | | |
% 135.48/19.89 | | | Case 1:
% 135.48/19.89 | | | |
% 135.48/19.89 | | | | (19) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2)
% 135.48/19.89 | | | | = e0)
% 135.48/19.89 | | | |
% 135.48/19.89 | | | | BETA: splitting (19) gives:
% 135.48/19.89 | | | |
% 135.48/19.89 | | | | Case 1:
% 135.48/19.89 | | | | |
% 135.48/19.89 | | | | | (20) all_57_2 = e0 & op(e2, e3) = e0
% 135.48/19.89 | | | | |
% 135.48/19.89 | | | | | REF_CLOSE: (11), (18), (20) are inconsistent by sub-proof #272.
% 135.48/19.89 | | | | |
% 135.48/19.89 | | | | Case 2:
% 135.48/19.89 | | | | |
% 135.48/19.89 | | | | | (21) all_57_3 = e0 & op(e2, e2) = e0
% 135.48/19.89 | | | | |
% 135.48/19.89 | | | | | ALPHA: (21) implies:
% 135.48/19.89 | | | | | (22) op(e2, e2) = e0
% 135.48/19.89 | | | | |
% 135.48/19.89 | | | | | REF_CLOSE: (4), (5), (7), (22) are inconsistent by sub-proof #641.
% 135.48/19.89 | | | | |
% 135.48/19.89 | | | | End of split
% 135.48/19.89 | | | |
% 135.48/19.89 | | | Case 2:
% 135.48/19.89 | | | |
% 135.48/19.89 | | | | (23) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0)
% 135.48/19.89 | | | | = e0)
% 135.48/19.89 | | | |
% 135.48/19.89 | | | | BETA: splitting (23) gives:
% 135.48/19.89 | | | |
% 135.48/19.89 | | | | Case 1:
% 135.48/19.89 | | | | |
% 135.48/19.89 | | | | | (24) all_57_5 = e0 & op(e2, e1) = e0
% 135.48/19.89 | | | | |
% 135.48/19.89 | | | | | ALPHA: (24) implies:
% 135.48/19.89 | | | | | (25) op(e2, e1) = e0
% 135.48/19.89 | | | | |
% 135.48/19.89 | | | | | GROUND_INST: instantiating (4) with e0, all_6_0, e1, e2, simplifying
% 135.48/19.89 | | | | | with (8), (25) gives:
% 135.48/19.89 | | | | | (26) all_6_0 = e0
% 135.48/19.89 | | | | |
% 135.48/19.89 | | | | | REDUCE: (15), (26) imply:
% 135.48/19.89 | | | | | (27) $false
% 135.48/19.89 | | | | |
% 135.48/19.89 | | | | | CLOSE: (27) is inconsistent.
% 135.48/19.89 | | | | |
% 135.48/19.89 | | | | Case 2:
% 135.48/19.89 | | | | |
% 135.48/19.89 | | | | | (28) all_57_10 = e0 & op(e2, e0) = e0
% 135.48/19.89 | | | | |
% 135.48/19.89 | | | | | ALPHA: (28) implies:
% 135.48/19.89 | | | | | (29) op(e2, e0) = e0
% 135.48/19.89 | | | | |
% 135.48/19.89 | | | | | REF_CLOSE: (4), (9), (12), (29) are inconsistent by sub-proof #275.
% 135.48/19.89 | | | | |
% 135.48/19.89 | | | | End of split
% 135.48/19.89 | | | |
% 135.48/19.89 | | | End of split
% 135.48/19.89 | | |
% 135.48/19.89 | | Case 2:
% 135.48/19.89 | | |
% 135.48/19.89 | | | (30) all_57_3 = e1 & op(e2, e2) = e1
% 135.48/19.89 | | |
% 135.48/19.89 | | | ALPHA: (30) implies:
% 135.48/19.89 | | | (31) op(e2, e2) = e1
% 135.48/19.89 | | |
% 135.48/19.89 | | | REF_CLOSE: (4), (7), (10), (31) are inconsistent by sub-proof #325.
% 135.48/19.89 | | |
% 135.48/19.89 | | End of split
% 135.48/19.89 | |
% 135.48/19.89 | Case 2:
% 135.48/19.89 | |
% 135.48/19.89 | | (32) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 135.48/19.89 | | e1)
% 135.48/19.89 | |
% 135.48/19.89 | | BETA: splitting (32) gives:
% 135.48/19.89 | |
% 135.48/19.89 | | Case 1:
% 135.48/19.89 | | |
% 135.48/19.89 | | | (33) all_57_5 = e1 & op(e2, e1) = e1
% 135.48/19.89 | | |
% 135.48/19.89 | | | ALPHA: (33) implies:
% 135.48/19.89 | | | (34) op(e2, e1) = e1
% 135.48/19.89 | | |
% 135.48/19.89 | | | REF_CLOSE: (3), (4), (6), (34) are inconsistent by sub-proof #106.
% 135.48/19.89 | | |
% 135.48/19.89 | | Case 2:
% 135.48/19.89 | | |
% 135.48/19.89 | | | (35) all_57_10 = e1 & op(e2, e0) = e1
% 135.48/19.89 | | |
% 135.48/19.89 | | | ALPHA: (35) implies:
% 135.48/19.89 | | | (36) op(e2, e0) = e1
% 135.48/19.89 | | |
% 135.48/19.89 | | | REF_CLOSE: (1), (2), (4), (36) are inconsistent by sub-proof #180.
% 135.48/19.89 | | |
% 135.48/19.89 | | End of split
% 135.48/19.89 | |
% 135.48/19.89 | End of split
% 135.48/19.89 |
% 135.48/19.89 End of proof
% 135.48/19.89
% 135.48/19.89 Sub-proof #11 shows that the following formulas are inconsistent:
% 135.48/19.89 ----------------------------------------------------------------
% 135.48/19.89 (1) ~ (e2 = e0)
% 135.48/19.89 (2) ~ (e2 = e1)
% 135.48/19.89 (3) ~ (e3 = e0)
% 135.48/19.89 (4) all_57_15 = e2
% 135.48/19.89 (5) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 135.48/19.89 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 135.48/19.89 (6) all_57_13 = e2
% 135.48/19.89 (7) all_57_12 = e3
% 135.48/19.89 (8) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 135.48/19.89 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 135.48/19.89 e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 135.48/19.89 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 135.48/19.89 (9) ~ (e3 = e1)
% 135.48/19.89 (10) ~ (e1 = e0)
% 135.48/19.89
% 135.48/19.89 Begin of proof
% 135.48/19.89 |
% 135.48/19.89 | BETA: splitting (8) gives:
% 135.48/19.89 |
% 135.48/19.89 | Case 1:
% 135.48/19.89 | |
% 135.48/19.89 | | (11) all_57_15 = e0 & op(e0, e0) = e0
% 135.48/19.89 | |
% 135.48/19.89 | | REF_CLOSE: (1), (4), (11) are inconsistent by sub-proof #437.
% 135.48/19.89 | |
% 135.48/19.89 | Case 2:
% 135.48/19.89 | |
% 135.48/19.89 | | (12) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 135.48/19.89 | | e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 135.48/19.89 | | op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 135.48/19.89 | | (all_57_14 = e0 & op(e0, e1) = e0))
% 135.48/19.89 | |
% 135.48/19.89 | | ALPHA: (12) implies:
% 135.48/19.89 | | (13) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 135.48/19.89 | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 135.48/19.89 | |
% 135.48/19.89 | | BETA: splitting (13) gives:
% 135.48/19.89 | |
% 135.48/19.89 | | Case 1:
% 135.48/19.89 | | |
% 135.48/19.89 | | | (14) all_57_12 = e0 & op(e0, e3) = e0
% 135.48/19.89 | | |
% 135.48/19.89 | | | ALPHA: (14) implies:
% 135.48/19.89 | | | (15) all_57_12 = e0
% 135.48/19.89 | | |
% 135.48/19.89 | | | REF_CLOSE: (3), (7), (15) are inconsistent by sub-proof #492.
% 135.48/19.89 | | |
% 135.48/19.89 | | Case 2:
% 135.48/19.89 | | |
% 135.48/19.89 | | | (16) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1)
% 135.48/19.89 | | | = e0)
% 135.48/19.89 | | |
% 135.48/19.89 | | | BETA: splitting (16) gives:
% 135.48/19.89 | | |
% 135.48/19.89 | | | Case 1:
% 135.48/19.89 | | | |
% 135.48/19.89 | | | | (17) all_57_13 = e0 & op(e0, e2) = e0
% 135.48/19.89 | | | |
% 135.48/19.89 | | | | REF_CLOSE: (1), (6), (17) are inconsistent by sub-proof #411.
% 135.48/19.89 | | | |
% 135.48/19.89 | | | Case 2:
% 135.48/19.89 | | | |
% 135.48/19.89 | | | | (18) all_57_14 = e0 & op(e0, e1) = e0
% 135.48/19.89 | | | |
% 135.48/19.89 | | | | ALPHA: (18) implies:
% 135.48/19.89 | | | | (19) all_57_14 = e0
% 135.48/19.89 | | | |
% 135.48/19.89 | | | | BETA: splitting (5) gives:
% 135.48/19.89 | | | |
% 135.48/19.89 | | | | Case 1:
% 135.48/19.89 | | | | |
% 135.48/19.89 | | | | | (20) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0,
% 135.48/19.89 | | | | | e2) = e1)
% 135.48/19.89 | | | | |
% 135.48/19.89 | | | | | REF_CLOSE: (2), (6), (7), (9), (20) are inconsistent by sub-proof
% 135.48/19.89 | | | | | #245.
% 135.48/19.89 | | | | |
% 135.48/19.89 | | | | Case 2:
% 135.48/19.89 | | | | |
% 135.48/19.89 | | | | | (21) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0,
% 135.48/19.89 | | | | | e0) = e1)
% 135.48/19.89 | | | | |
% 135.48/19.89 | | | | | BETA: splitting (21) gives:
% 135.48/19.89 | | | | |
% 135.48/19.89 | | | | | Case 1:
% 135.48/19.89 | | | | | |
% 135.48/19.89 | | | | | | (22) all_57_14 = e1 & op(e0, e1) = e1
% 135.48/19.89 | | | | | |
% 135.48/19.89 | | | | | | REF_CLOSE: (10), (19), (22) are inconsistent by sub-proof #231.
% 135.48/19.89 | | | | | |
% 135.48/19.89 | | | | | Case 2:
% 135.48/19.89 | | | | | |
% 135.48/19.89 | | | | | | (23) all_57_15 = e1 & op(e0, e0) = e1
% 135.48/19.89 | | | | | |
% 135.48/19.89 | | | | | | REF_CLOSE: (2), (4), (23) are inconsistent by sub-proof #435.
% 135.48/19.89 | | | | | |
% 135.48/19.89 | | | | | End of split
% 135.48/19.89 | | | | |
% 135.48/19.89 | | | | End of split
% 135.48/19.89 | | | |
% 135.48/19.89 | | | End of split
% 135.48/19.89 | | |
% 135.48/19.89 | | End of split
% 135.48/19.89 | |
% 135.48/19.89 | End of split
% 135.48/19.89 |
% 135.48/19.89 End of proof
% 135.48/19.89
% 135.48/19.89 Sub-proof #12 shows that the following formulas are inconsistent:
% 135.48/19.89 ----------------------------------------------------------------
% 135.48/19.89 (1) op(e2, e2) = all_8_2
% 135.48/19.89 (2) op(e2, e1) = e1
% 135.48/19.89 (3) ~ (all_8_2 = e1)
% 135.48/19.89 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.89 (5) op(e0, e0) = e1
% 135.48/19.89 (6) op(e0, e2) = all_52_7
% 135.48/19.89 (7) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 135.48/19.89 (8) all_54_5 = all_8_2
% 135.48/19.89 (9) ~ (all_52_14 = e1)
% 135.48/19.89 (10) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.48/19.89 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.48/19.89 all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 135.48/19.89 e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 135.48/19.89 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 135.48/19.89 all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~
% 135.48/19.89 (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 135.48/19.89 (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 &
% 135.48/19.89 op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0
% 135.48/19.89 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 135.48/19.89 (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 135.48/19.89 (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.48/19.89 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.48/19.89 all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.48/19.89 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.48/19.89 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.48/19.89 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.48/19.89 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.48/19.89 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 135.48/19.89 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 135.48/19.89 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 135.48/19.89 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.48/19.89 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 135.48/19.89 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.48/19.89 $i(all_56_29))))
% 135.48/19.89 (11) ~ (e3 = e1)
% 135.48/19.89 (12) ~ (all_52_7 = all_8_2)
% 135.48/19.89 (13) ~ (all_8_2 = e3)
% 135.48/19.89 (14) op(e1, e0) = all_52_14
% 135.48/19.89 (15) op(e1, e0) = e0
% 135.48/19.89
% 135.48/19.89 Begin of proof
% 135.48/19.89 |
% 135.48/19.89 | BETA: splitting (10) gives:
% 135.48/19.89 |
% 135.48/19.89 | Case 1:
% 135.48/19.89 | |
% 135.48/19.89 | | (16) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11
% 135.48/19.89 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.48/19.89 | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 135.48/19.89 | | e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3)
% 135.48/19.89 | | & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)
% 135.48/19.89 | |
% 135.48/19.89 | | ALPHA: (16) implies:
% 135.48/19.89 | | (17) ~ (all_56_19 = e1)
% 135.48/19.89 | | (18) op(e2, e1) = all_56_19
% 135.48/19.89 | |
% 135.48/19.89 | | REF_CLOSE: (2), (4), (17), (18) are inconsistent by sub-proof #106.
% 135.48/19.89 | |
% 135.48/19.89 | Case 2:
% 135.48/19.89 | |
% 135.48/19.89 | | (19) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31
% 135.48/19.89 | | = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 135.48/19.89 | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2)
% 135.48/19.89 | | = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.48/19.89 | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.48/19.89 | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3
% 135.48/19.89 | | = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.48/19.89 | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 135.48/19.89 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 135.48/19.89 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.48/19.89 | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7
% 135.48/19.89 | | = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.48/19.89 | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 135.48/19.89 | | e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) =
% 135.48/19.89 | | all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 135.48/19.89 | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 135.48/19.89 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 135.48/19.89 | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.48/19.89 | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.48/19.89 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)))
% 135.48/19.89 | |
% 135.48/19.89 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), (14),
% 135.48/19.89 | | (15), (19) are inconsistent by sub-proof #39.
% 135.48/19.89 | |
% 135.48/19.89 | End of split
% 135.48/19.89 |
% 135.48/19.89 End of proof
% 135.48/19.89
% 135.48/19.89 Sub-proof #13 shows that the following formulas are inconsistent:
% 135.48/19.89 ----------------------------------------------------------------
% 135.48/19.89 (1) op(e2, e2) = e0
% 135.48/19.89 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.89 (3) ~ (e3 = e0)
% 135.48/19.89 (4) ~ (e3 = e2)
% 135.48/19.89 (5) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 135.48/19.89 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.48/19.89 op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 135.48/19.89 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.48/19.89 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 &
% 135.48/19.89 all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~
% 135.48/19.89 (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3,
% 135.48/19.89 e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.48/19.89 op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.48/19.89 $i(all_56_17) & $i(all_56_25))
% 135.48/19.89 (6) op(e3, e0) = all_52_12
% 135.48/19.89 (7) op(e3, e0) = e2
% 135.48/19.89
% 135.48/19.89 Begin of proof
% 135.48/19.89 |
% 135.48/19.89 | BETA: splitting (5) gives:
% 135.48/19.89 |
% 135.48/19.89 | Case 1:
% 135.48/19.89 | |
% 135.48/19.89 | | (8) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 135.48/19.89 | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.48/19.89 | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 135.48/19.89 | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.48/19.89 | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)
% 135.48/19.89 | |
% 135.48/19.89 | | ALPHA: (8) implies:
% 135.48/19.89 | | (9) op(e3, e0) = e3
% 135.48/19.89 | |
% 135.48/19.89 | | REF_CLOSE: (2), (4), (6), (7), (9) are inconsistent by sub-proof #111.
% 135.48/19.89 | |
% 135.48/19.89 | Case 2:
% 135.48/19.89 | |
% 135.48/19.89 | | (10) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 135.48/19.89 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.48/19.89 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.48/19.89 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1)
% 135.48/19.89 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)
% 135.48/19.89 | |
% 135.48/19.89 | | ALPHA: (10) implies:
% 135.48/19.89 | | (11) op(e2, e2) = e3
% 135.48/19.89 | |
% 135.48/19.89 | | REF_CLOSE: (1), (2), (3), (11) are inconsistent by sub-proof #641.
% 135.48/19.89 | |
% 135.48/19.89 | End of split
% 135.48/19.89 |
% 135.48/19.89 End of proof
% 135.48/19.89
% 135.48/19.89 Sub-proof #14 shows that the following formulas are inconsistent:
% 135.48/19.89 ----------------------------------------------------------------
% 135.48/19.89 (1) ~ (e2 = e0)
% 135.48/19.89 (2) op(e3, e3) = e1
% 135.48/19.89 (3) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 135.48/19.89 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 135.48/19.89 (4) op(e3, e1) = e1
% 135.48/19.89 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.89 (6) ~ (e2 = e1)
% 135.48/19.89 (7) ~ (e3 = e0)
% 135.48/19.89 (8) ~ (e3 = e2)
% 135.48/19.89 (9) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 135.48/19.89 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 135.48/19.89 (10) ~ (all_52_8 = e2)
% 135.48/19.89 (11) all_57_4 = e1
% 135.48/19.89 (12) op(e3, e0) = all_52_12
% 135.48/19.89 (13) op(e3, e1) = all_52_8
% 135.48/19.89 (14) ~ (e3 = e1)
% 135.48/19.89 (15) ~ (e1 = e0)
% 135.48/19.89 (16) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 135.48/19.89 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 135.48/19.89
% 135.48/19.89 Begin of proof
% 135.48/19.89 |
% 135.48/19.89 | BETA: splitting (16) gives:
% 135.48/19.89 |
% 135.48/19.89 | Case 1:
% 135.48/19.89 | |
% 135.48/19.89 | | (17) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 135.48/19.89 | | e3)
% 135.48/19.89 | |
% 135.48/19.89 | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (11), (14), (15), (16),
% 135.48/19.89 | | (17) are inconsistent by sub-proof #164.
% 135.48/19.89 | |
% 135.48/19.89 | Case 2:
% 135.48/19.89 | |
% 135.48/19.89 | | (18) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 135.48/19.89 | | e3)
% 135.48/19.89 | |
% 135.48/19.89 | | BETA: splitting (18) gives:
% 135.48/19.89 | |
% 135.48/19.89 | | Case 1:
% 135.48/19.89 | | |
% 135.48/19.89 | | | (19) all_57_4 = e3 & op(e3, e1) = e3
% 135.48/19.89 | | |
% 135.48/19.89 | | | REF_CLOSE: (11), (14), (19) are inconsistent by sub-proof #438.
% 135.48/19.89 | | |
% 135.48/19.89 | | Case 2:
% 135.48/19.89 | | |
% 135.48/19.89 | | | (20) all_57_9 = e3 & op(e3, e0) = e3
% 135.48/19.89 | | |
% 135.48/19.89 | | | ALPHA: (20) implies:
% 135.48/19.89 | | | (21) op(e3, e0) = e3
% 135.48/19.89 | | |
% 135.48/19.89 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 135.48/19.89 | | | (13), (14), (15), (16), (21) are inconsistent by sub-proof #18.
% 135.48/19.89 | | |
% 135.48/19.89 | | End of split
% 135.48/19.89 | |
% 135.48/19.89 | End of split
% 135.48/19.89 |
% 135.48/19.90 End of proof
% 135.48/19.90
% 135.48/19.90 Sub-proof #15 shows that the following formulas are inconsistent:
% 135.48/19.90 ----------------------------------------------------------------
% 135.48/19.90 (1) op(e3, e1) = e1
% 135.48/19.90 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.90 (3) ~ (e2 = e1)
% 135.48/19.90 (4) op(e0, e0) = e1
% 135.48/19.90 (5) op(e0, e1) = all_52_11
% 135.48/19.90 (6) ~ (all_52_14 = e1)
% 135.48/19.90 (7) ~ (all_52_11 = e0)
% 135.48/19.90 (8) op(e1, e0) = all_52_14
% 135.48/19.90 (9) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3
% 135.48/19.90 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 135.48/19.90 (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 &
% 135.48/19.90 op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 135.48/19.90 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 135.48/19.90 (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.48/19.90 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.48/19.90 all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 135.48/19.90 e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.48/19.90 $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 &
% 135.48/19.90 ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.48/19.90 (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 135.48/19.90 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.48/19.90 $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 &
% 135.48/19.90 all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.48/19.90 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 135.48/19.90 op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 135.48/19.90 all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.48/19.90 $i(all_56_21) & $i(all_56_29)))
% 135.48/19.90
% 135.48/19.90 Begin of proof
% 135.48/19.90 |
% 135.48/19.90 | ALPHA: (9) implies:
% 135.48/19.90 | (10) op(e0, e0) = all_56_31
% 135.48/19.90 | (11) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 135.48/19.90 | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.48/19.90 | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.48/19.90 | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.48/19.90 | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 &
% 135.48/19.90 | ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.48/19.90 | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.48/19.90 | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.48/19.90 | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.48/19.90 | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15
% 135.48/19.90 | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) =
% 135.48/19.90 | e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.48/19.90 | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 135.48/19.90 | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 135.48/19.90 | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 =
% 135.48/19.90 | e0) & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1)
% 135.48/19.90 | = all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.48/19.90 | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 135.48/19.90 |
% 135.48/19.90 | BETA: splitting (11) gives:
% 135.48/19.90 |
% 135.48/19.90 | Case 1:
% 135.48/19.90 | |
% 135.48/19.90 | | (12) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 135.48/19.90 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.48/19.90 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.48/19.90 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9)
% 135.48/19.90 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 135.48/19.90 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.48/19.90 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 135.48/19.90 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 135.48/19.90 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.48/19.90 | | $i(all_56_27))
% 135.48/19.90 | |
% 135.48/19.90 | | REF_CLOSE: (1), (2), (3), (4), (10), (12) are inconsistent by sub-proof #21.
% 135.48/19.90 | |
% 135.48/19.90 | Case 2:
% 135.48/19.90 | |
% 135.48/19.90 | | (13) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.48/19.90 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.48/19.90 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.48/19.90 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 135.48/19.90 | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 135.48/19.90 | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 135.48/19.90 | | ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.48/19.90 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 135.48/19.90 | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.48/19.90 | | $i(all_56_29))
% 135.48/19.90 | |
% 135.48/19.90 | | BETA: splitting (13) gives:
% 135.48/19.90 | |
% 135.48/19.90 | | Case 1:
% 135.48/19.90 | | |
% 135.48/19.90 | | | (14) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.48/19.90 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.48/19.90 | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.48/19.90 | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 135.48/19.90 | | | $i(all_56_15) & $i(all_56_23)
% 135.48/19.90 | | |
% 135.48/19.90 | | | ALPHA: (14) implies:
% 135.48/19.90 | | | (15) op(e1, e0) = e1
% 135.48/19.90 | | |
% 135.48/19.90 | | | REF_CLOSE: (2), (6), (8), (15) are inconsistent by sub-proof #327.
% 135.48/19.90 | | |
% 135.48/19.90 | | Case 2:
% 135.48/19.90 | | |
% 135.48/19.90 | | | (16) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 135.48/19.90 | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 135.48/19.90 | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.48/19.90 | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.48/19.90 | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 135.48/19.90 | | |
% 135.48/19.90 | | | ALPHA: (16) implies:
% 135.48/19.90 | | | (17) op(e0, e1) = e0
% 135.48/19.90 | | |
% 135.48/19.90 | | | GROUND_INST: instantiating (2) with all_52_11, e0, e1, e0, simplifying
% 135.48/19.90 | | | with (5), (17) gives:
% 135.48/19.90 | | | (18) all_52_11 = e0
% 135.48/19.90 | | |
% 135.48/19.90 | | | REDUCE: (7), (18) imply:
% 135.48/19.90 | | | (19) $false
% 135.48/19.90 | | |
% 135.48/19.90 | | | CLOSE: (19) is inconsistent.
% 135.48/19.90 | | |
% 135.48/19.90 | | End of split
% 135.48/19.90 | |
% 135.48/19.90 | End of split
% 135.48/19.90 |
% 135.48/19.90 End of proof
% 135.48/19.90
% 135.48/19.90 Sub-proof #16 shows that the following formulas are inconsistent:
% 135.48/19.90 ----------------------------------------------------------------
% 135.48/19.90 (1) ~ (all_10_1 = e1) & op(e0, e0) = all_10_1 & $i(all_10_1)
% 135.48/19.90 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.90 (3) op(e0, e0) = e1
% 135.48/19.90
% 135.48/19.90 Begin of proof
% 135.48/19.90 |
% 135.48/19.90 | ALPHA: (1) implies:
% 135.48/19.90 | (4) ~ (all_10_1 = e1)
% 135.48/19.90 | (5) op(e0, e0) = all_10_1
% 135.48/19.90 |
% 135.48/19.90 | GROUND_INST: instantiating (2) with e1, all_10_1, e0, e0, simplifying with
% 135.48/19.90 | (3), (5) gives:
% 135.48/19.90 | (6) all_10_1 = e1
% 135.48/19.90 |
% 135.48/19.90 | REDUCE: (4), (6) imply:
% 135.48/19.90 | (7) $false
% 135.48/19.90 |
% 135.48/19.90 | CLOSE: (7) is inconsistent.
% 135.48/19.90 |
% 135.48/19.90 End of proof
% 135.48/19.90
% 135.48/19.90 Sub-proof #17 shows that the following formulas are inconsistent:
% 135.48/19.90 ----------------------------------------------------------------
% 135.48/19.90 (1) op(e3, e1) = e1
% 135.48/19.90 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.90 (3) op(e0, e0) = e1
% 135.48/19.90 (4) ~ (all_52_8 = e2)
% 135.48/19.90 (5) ~ (all_52_14 = e1)
% 135.48/19.90 (6) op(e3, e1) = all_52_8
% 135.48/19.90 (7) op(e1, e0) = all_52_14
% 135.48/19.90 (8) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3
% 135.48/19.90 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 135.48/19.90 (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 &
% 135.48/19.90 op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 135.48/19.90 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 135.48/19.90 (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.48/19.90 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.48/19.90 all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 135.48/19.90 e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.48/19.90 $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 &
% 135.48/19.90 ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.48/19.90 (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 135.48/19.90 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.48/19.90 $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 &
% 135.48/19.90 all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.48/19.90 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 135.48/19.90 op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 135.48/19.90 all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.48/19.90 $i(all_56_21) & $i(all_56_29)))
% 135.48/19.90 (9) op(e1, e0) = e0
% 135.48/19.90
% 135.48/19.90 Begin of proof
% 135.48/19.90 |
% 135.48/19.90 | ALPHA: (8) implies:
% 135.48/19.90 | (10) op(e0, e0) = all_56_31
% 135.48/19.90 | (11) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 135.48/19.90 | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.48/19.90 | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.48/19.90 | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.48/19.90 | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 &
% 135.48/19.90 | ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.48/19.90 | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.48/19.90 | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.48/19.90 | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.48/19.90 | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15
% 135.48/19.90 | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) =
% 135.48/19.90 | e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.48/19.90 | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 135.48/19.90 | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 135.48/19.90 | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 =
% 135.48/19.90 | e0) & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1)
% 135.48/19.90 | = all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.48/19.90 | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 135.48/19.90 |
% 135.48/19.90 | GROUND_INST: instantiating (2) with e1, all_56_31, e0, e0, simplifying with
% 135.48/19.90 | (3), (10) gives:
% 135.48/19.90 | (12) all_56_31 = e1
% 135.48/19.90 |
% 135.48/19.90 | GROUND_INST: instantiating (2) with all_52_8, e1, e1, e3, simplifying with
% 135.48/19.90 | (1), (6) gives:
% 135.48/19.90 | (13) all_52_8 = e1
% 135.48/19.90 |
% 135.48/19.90 | REDUCE: (4), (13) imply:
% 135.48/19.90 | (14) ~ (e2 = e1)
% 135.48/19.90 |
% 135.48/19.90 | SIMP: (14) implies:
% 135.48/19.90 | (15) ~ (e2 = e1)
% 135.48/19.90 |
% 135.48/19.90 | BETA: splitting (11) gives:
% 135.48/19.90 |
% 135.48/19.90 | Case 1:
% 135.48/19.90 | |
% 135.48/19.90 | | (16) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 135.48/19.90 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.48/19.90 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.48/19.90 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9)
% 135.48/19.90 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 135.48/19.90 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.48/19.90 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 135.48/19.90 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 135.48/19.90 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.48/19.90 | | $i(all_56_27))
% 135.48/19.90 | |
% 135.48/19.90 | | BETA: splitting (16) gives:
% 135.48/19.90 | |
% 135.48/19.90 | | Case 1:
% 135.48/19.90 | | |
% 135.48/19.90 | | | (17) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 135.48/19.90 | | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.48/19.90 | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.48/19.90 | | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9)
% 135.48/19.90 | | | & $i(all_56_17) & $i(all_56_25)
% 135.48/19.90 | | |
% 135.48/19.90 | | | ALPHA: (17) implies:
% 135.48/19.90 | | | (18) ~ (all_56_17 = e1)
% 135.48/19.90 | | | (19) op(e3, e1) = all_56_17
% 135.48/19.90 | | |
% 135.48/19.90 | | | REF_CLOSE: (1), (2), (18), (19) are inconsistent by sub-proof #349.
% 135.48/19.90 | | |
% 135.48/19.90 | | Case 2:
% 135.48/19.90 | | |
% 135.48/19.90 | | | (20) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 135.48/19.90 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.48/19.90 | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.48/19.90 | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.48/19.90 | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)
% 135.48/19.90 | | |
% 135.48/19.90 | | | REF_CLOSE: (12), (15), (20) are inconsistent by sub-proof #33.
% 135.48/19.90 | | |
% 135.48/19.90 | | End of split
% 135.48/19.90 | |
% 135.48/19.90 | Case 2:
% 135.48/19.90 | |
% 135.48/19.90 | | (21) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.48/19.90 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.48/19.90 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.48/19.90 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 135.48/19.90 | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 135.48/19.90 | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 135.48/19.90 | | ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.48/19.90 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 135.48/19.90 | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.48/19.90 | | $i(all_56_29))
% 135.48/19.90 | |
% 135.48/19.90 | | REF_CLOSE: (2), (5), (7), (9), (21) are inconsistent by sub-proof #40.
% 135.48/19.90 | |
% 135.48/19.90 | End of split
% 135.48/19.90 |
% 135.48/19.90 End of proof
% 135.48/19.90
% 135.48/19.90 Sub-proof #18 shows that the following formulas are inconsistent:
% 135.48/19.90 ----------------------------------------------------------------
% 135.48/19.90 (1) ~ (e2 = e0)
% 135.48/19.90 (2) op(e3, e3) = e1
% 135.48/19.90 (3) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 135.48/19.90 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 135.48/19.90 (4) op(e3, e1) = e1
% 135.48/19.90 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.90 (6) ~ (e2 = e1)
% 135.48/19.90 (7) ~ (e3 = e0)
% 135.48/19.90 (8) ~ (e3 = e2)
% 135.48/19.90 (9) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 135.48/19.90 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 135.48/19.90 (10) ~ (all_52_8 = e2)
% 135.48/19.90 (11) op(e3, e0) = e3
% 135.48/19.90 (12) all_57_4 = e1
% 135.48/19.90 (13) op(e3, e0) = all_52_12
% 135.48/19.90 (14) op(e3, e1) = all_52_8
% 135.48/19.90 (15) ~ (e3 = e1)
% 135.48/19.90 (16) ~ (e1 = e0)
% 135.48/19.90 (17) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 135.48/19.90 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 135.48/19.90
% 135.48/19.90 Begin of proof
% 135.48/19.90 |
% 135.48/19.90 | BETA: splitting (3) gives:
% 135.48/19.90 |
% 135.48/19.90 | Case 1:
% 135.48/19.90 | |
% 135.48/19.90 | | (18) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 135.48/19.90 | | e0)
% 135.48/19.90 | |
% 135.48/19.90 | | BETA: splitting (18) gives:
% 135.48/19.90 | |
% 135.48/19.90 | | Case 1:
% 135.48/19.90 | | |
% 135.48/19.90 | | | (19) all_57_0 = e0 & op(e3, e3) = e0
% 135.48/19.90 | | |
% 135.48/19.90 | | | ALPHA: (19) implies:
% 135.48/19.90 | | | (20) op(e3, e3) = e0
% 135.48/19.90 | | |
% 135.48/19.90 | | | REF_CLOSE: (2), (5), (16), (20) are inconsistent by sub-proof #717.
% 135.48/19.90 | | |
% 135.48/19.90 | | Case 2:
% 135.48/19.90 | | |
% 135.48/19.90 | | | (21) all_57_1 = e0 & op(e3, e2) = e0
% 135.48/19.90 | | |
% 135.48/19.90 | | | ALPHA: (21) implies:
% 135.48/19.90 | | | (22) all_57_1 = e0
% 135.48/19.90 | | |
% 135.48/19.90 | | | BETA: splitting (9) gives:
% 135.48/19.90 | | |
% 135.48/19.90 | | | Case 1:
% 135.48/19.90 | | | |
% 135.48/19.90 | | | | (23) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2)
% 135.48/19.90 | | | | = e2)
% 135.48/19.90 | | | |
% 135.48/19.90 | | | | REF_CLOSE: (1), (2), (5), (6), (22), (23) are inconsistent by sub-proof
% 135.48/19.90 | | | | #148.
% 135.48/19.90 | | | |
% 135.48/19.90 | | | Case 2:
% 135.48/19.90 | | | |
% 135.48/19.90 | | | | (24) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0)
% 135.48/19.90 | | | | = e2)
% 135.48/19.90 | | | |
% 135.48/19.90 | | | | REF_CLOSE: (5), (8), (10), (11), (13), (14), (24) are inconsistent by
% 135.48/19.90 | | | | sub-proof #19.
% 135.48/19.90 | | | |
% 135.48/19.90 | | | End of split
% 135.48/19.90 | | |
% 135.48/19.90 | | End of split
% 135.48/19.90 | |
% 135.48/19.90 | Case 2:
% 135.48/19.90 | |
% 135.48/19.90 | | (25) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 135.48/19.90 | | e0)
% 135.48/19.90 | |
% 135.48/19.90 | | BETA: splitting (25) gives:
% 135.48/19.90 | |
% 135.48/19.90 | | Case 1:
% 135.48/19.90 | | |
% 135.48/19.90 | | | (26) all_57_4 = e0 & op(e3, e1) = e0
% 135.48/19.90 | | |
% 135.48/19.90 | | | ALPHA: (26) implies:
% 135.48/19.90 | | | (27) op(e3, e1) = e0
% 135.48/19.90 | | |
% 135.48/19.90 | | | REF_CLOSE: (4), (5), (16), (27) are inconsistent by sub-proof #343.
% 135.48/19.90 | | |
% 135.48/19.90 | | Case 2:
% 135.48/19.90 | | |
% 135.48/19.90 | | | (28) all_57_9 = e0 & op(e3, e0) = e0
% 135.48/19.90 | | |
% 135.48/19.90 | | | ALPHA: (28) implies:
% 135.48/19.90 | | | (29) all_57_9 = e0
% 135.48/19.90 | | |
% 135.48/19.90 | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (12), (15), (17), (29) are
% 135.48/19.90 | | | inconsistent by sub-proof #668.
% 135.48/19.90 | | |
% 135.48/19.90 | | End of split
% 135.48/19.90 | |
% 135.48/19.90 | End of split
% 135.48/19.90 |
% 135.48/19.90 End of proof
% 135.48/19.90
% 135.48/19.90 Sub-proof #19 shows that the following formulas are inconsistent:
% 135.48/19.90 ----------------------------------------------------------------
% 135.48/19.90 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.90 (2) ~ (e3 = e2)
% 135.48/19.90 (3) ~ (all_52_8 = e2)
% 135.48/19.90 (4) op(e3, e0) = e3
% 135.48/19.90 (5) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 135.48/19.90 (6) op(e3, e0) = all_52_12
% 135.48/19.90 (7) op(e3, e1) = all_52_8
% 135.48/19.90
% 135.48/19.90 Begin of proof
% 135.48/19.90 |
% 135.48/19.90 | BETA: splitting (5) gives:
% 135.48/19.90 |
% 135.48/19.90 | Case 1:
% 135.48/19.90 | |
% 135.48/19.90 | | (8) all_57_4 = e2 & op(e3, e1) = e2
% 135.48/19.90 | |
% 135.48/19.90 | | REF_CLOSE: (1), (3), (7), (8) are inconsistent by sub-proof #442.
% 135.48/19.90 | |
% 135.48/19.90 | Case 2:
% 135.48/19.90 | |
% 135.48/19.90 | | (9) all_57_9 = e2 & op(e3, e0) = e2
% 135.48/19.90 | |
% 135.48/19.90 | | ALPHA: (9) implies:
% 135.48/19.90 | | (10) op(e3, e0) = e2
% 135.48/19.90 | |
% 135.48/19.90 | | REF_CLOSE: (1), (2), (4), (6), (10) are inconsistent by sub-proof #111.
% 135.48/19.90 | |
% 135.48/19.90 | End of split
% 135.48/19.90 |
% 135.48/19.90 End of proof
% 135.48/19.90
% 135.48/19.90 Sub-proof #20 shows that the following formulas are inconsistent:
% 135.48/19.90 ----------------------------------------------------------------
% 135.48/19.90 (1) op(e3, e1) = e1
% 135.48/19.90 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.90 (3) ~ (e2 = e1)
% 135.48/19.90 (4) op(e0, e0) = e1
% 135.48/19.90 (5) ~ (all_52_14 = e1)
% 135.48/19.90 (6) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2)
% 135.48/19.90 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.48/19.90 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25
% 135.48/19.90 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.48/19.90 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3)
% 135.48/19.90 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.48/19.90 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 135.48/19.90 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) &
% 135.48/19.90 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 &
% 135.48/19.90 all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~
% 135.48/19.90 (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) =
% 135.48/19.90 e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) =
% 135.48/19.90 all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23
% 135.48/19.90 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.48/19.90 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1,
% 135.48/19.90 e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 135.48/19.90 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.48/19.90 $i(all_56_29))
% 135.48/19.90 (7) op(e1, e0) = all_52_14
% 135.48/19.90 (8) op(e0, e0) = all_56_31
% 135.48/19.90 (9) op(e1, e0) = e0
% 135.48/19.90
% 135.48/19.90 Begin of proof
% 135.48/19.90 |
% 135.48/19.90 | BETA: splitting (6) gives:
% 135.48/19.90 |
% 135.48/19.90 | Case 1:
% 135.48/19.90 | |
% 135.48/19.90 | | (10) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 135.48/19.90 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.48/19.90 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.48/19.90 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9)
% 135.48/19.90 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 135.48/19.90 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.48/19.90 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 135.48/19.90 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 135.48/19.90 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.48/19.90 | | $i(all_56_27))
% 135.48/19.90 | |
% 135.48/19.90 | | REF_CLOSE: (1), (2), (3), (4), (8), (10) are inconsistent by sub-proof #21.
% 135.48/19.90 | |
% 135.48/19.90 | Case 2:
% 135.48/19.90 | |
% 135.48/19.90 | | (11) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.48/19.90 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.48/19.90 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.48/19.90 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 135.48/19.90 | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 135.48/19.90 | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 135.48/19.90 | | ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.48/19.90 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 135.48/19.90 | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.48/19.90 | | $i(all_56_29))
% 135.48/19.90 | |
% 135.48/19.90 | | REF_CLOSE: (2), (5), (7), (9), (11) are inconsistent by sub-proof #40.
% 135.48/19.90 | |
% 135.48/19.90 | End of split
% 135.48/19.90 |
% 135.48/19.90 End of proof
% 135.48/19.90
% 135.48/19.90 Sub-proof #21 shows that the following formulas are inconsistent:
% 135.48/19.90 ----------------------------------------------------------------
% 135.48/19.90 (1) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2)
% 135.48/19.90 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.48/19.90 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25
% 135.48/19.90 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.48/19.90 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3)
% 135.48/19.90 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.48/19.90 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 135.48/19.90 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) &
% 135.48/19.90 $i(all_56_11) & $i(all_56_19) & $i(all_56_27))
% 135.48/19.90 (2) op(e3, e1) = e1
% 135.48/19.90 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.90 (4) ~ (e2 = e1)
% 135.48/19.90 (5) op(e0, e0) = e1
% 135.48/19.90 (6) op(e0, e0) = all_56_31
% 135.48/19.90
% 135.48/19.90 Begin of proof
% 135.48/19.90 |
% 135.48/19.90 | BETA: splitting (1) gives:
% 135.48/19.90 |
% 135.48/19.90 | Case 1:
% 135.48/19.90 | |
% 135.48/19.90 | | (7) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 135.48/19.90 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.48/19.90 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.48/19.90 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.48/19.90 | | $i(all_56_17) & $i(all_56_25)
% 135.48/19.90 | |
% 135.48/19.90 | | ALPHA: (7) implies:
% 135.48/19.90 | | (8) ~ (all_56_17 = e1)
% 135.48/19.90 | | (9) op(e3, e1) = all_56_17
% 135.48/19.90 | |
% 135.48/19.90 | | REF_CLOSE: (2), (3), (8), (9) are inconsistent by sub-proof #349.
% 135.48/19.90 | |
% 135.48/19.90 | Case 2:
% 135.48/19.90 | |
% 135.48/19.90 | | (10) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11
% 135.48/19.90 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.48/19.90 | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 135.48/19.90 | | e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.48/19.90 | | $i(all_56_19) & $i(all_56_27)
% 135.48/19.90 | |
% 135.48/19.90 | | ALPHA: (10) implies:
% 135.48/19.90 | | (11) all_56_31 = e2
% 135.48/19.90 | |
% 135.48/19.90 | | REDUCE: (6), (11) imply:
% 135.48/19.91 | | (12) op(e0, e0) = e2
% 135.48/19.91 | |
% 135.48/19.91 | | REF_CLOSE: (3), (4), (5), (12) are inconsistent by sub-proof #636.
% 135.48/19.91 | |
% 135.48/19.91 | End of split
% 135.48/19.91 |
% 135.48/19.91 End of proof
% 135.48/19.91
% 135.48/19.91 Sub-proof #22 shows that the following formulas are inconsistent:
% 135.48/19.91 ----------------------------------------------------------------
% 135.48/19.91 (1) all_57_2 = e1
% 135.48/19.91 (2) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2)
% 135.48/19.91 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3,
% 135.48/19.91 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 135.48/19.91 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.48/19.91 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 135.48/19.91 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.48/19.91 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) =
% 135.48/19.91 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.48/19.91 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.48/19.91 $i(all_56_21) & $i(all_56_29))
% 135.48/19.91 (3) ~ (e2 = e0)
% 135.48/19.91 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.91 (5) ~ (e2 = e1)
% 135.48/19.91 (6) ~ (e3 = e0)
% 135.48/19.91 (7) ~ (all_52_1 = e0)
% 135.48/19.91 (8) ~ (e3 = e2)
% 135.48/19.91 (9) ~ (all_52_2 = e0)
% 135.48/19.91 (10) all_57_12 = e3
% 135.48/19.91 (11) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 135.48/19.91 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 135.48/19.91 (12) op(e1, e3) = all_52_2
% 135.48/19.91 (13) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 135.48/19.91 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 135.48/19.91 (14) op(e2, e3) = all_52_1
% 135.48/19.91 (15) ~ (e1 = e0)
% 135.48/19.91 (16) op(e2, e3) = e1
% 135.48/19.91
% 135.48/19.91 Begin of proof
% 135.48/19.91 |
% 135.48/19.91 | BETA: splitting (2) gives:
% 135.48/19.91 |
% 135.48/19.91 | Case 1:
% 135.48/19.91 | |
% 135.48/19.91 | | (17) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.48/19.91 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2
% 135.48/19.91 | | & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.48/19.91 | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.48/19.91 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)
% 135.48/19.91 | |
% 135.48/19.91 | | ALPHA: (17) implies:
% 135.48/19.91 | | (18) op(e3, e3) = e2
% 135.48/19.91 | |
% 135.48/19.91 | | REF_CLOSE: (3), (4), (6), (7), (9), (10), (11), (12), (14), (18) are
% 135.48/19.91 | | inconsistent by sub-proof #25.
% 135.48/19.91 | |
% 135.48/19.91 | Case 2:
% 135.48/19.91 | |
% 135.48/19.91 | | (19) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13
% 135.48/19.91 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) =
% 135.48/19.91 | | e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.48/19.91 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 135.48/19.91 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 135.48/19.91 | |
% 135.48/19.91 | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (10), (11), (13), (15), (16), (19)
% 135.48/19.91 | | are inconsistent by sub-proof #195.
% 135.48/19.91 | |
% 135.48/19.91 | End of split
% 135.48/19.91 |
% 135.48/19.91 End of proof
% 135.48/19.91
% 135.48/19.91 Sub-proof #23 shows that the following formulas are inconsistent:
% 135.48/19.91 ----------------------------------------------------------------
% 135.48/19.91 (1) ~ (all_10_0 = e1)
% 135.48/19.91 (2) ~ (all_52_11 = all_10_0)
% 135.48/19.91 (3) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 135.48/19.91 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 135.48/19.91 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.91 (5) op(e0, e0) = e1
% 135.48/19.91 (6) op(e0, e1) = all_52_11
% 135.48/19.91 (7) op(e0, e2) = all_52_7
% 135.48/19.91 (8) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 135.48/19.91 (9) ~ (all_10_0 = e2)
% 135.48/19.91 (10) ~ (all_52_7 = all_10_0)
% 135.48/19.91 (11) ~ (all_10_0 = e0)
% 135.48/19.91 (12) all_54_12 = all_10_0
% 135.48/19.91 (13) all_57_12 = e2
% 135.48/19.91
% 135.48/19.91 Begin of proof
% 135.48/19.91 |
% 135.48/19.91 | BETA: splitting (8) gives:
% 135.48/19.91 |
% 135.48/19.91 | Case 1:
% 135.48/19.91 | |
% 135.48/19.91 | | (14) all_54_12 = e3
% 135.48/19.91 | |
% 135.48/19.91 | | COMBINE_EQS: (12), (14) imply:
% 135.48/19.91 | | (15) all_10_0 = e3
% 135.48/19.91 | |
% 135.48/19.91 | | SIMP: (15) implies:
% 135.48/19.91 | | (16) all_10_0 = e3
% 135.48/19.91 | |
% 135.48/19.91 | | REDUCE: (10), (16) imply:
% 135.48/19.91 | | (17) ~ (all_52_7 = e3)
% 135.48/19.91 | |
% 135.48/19.91 | | REDUCE: (2), (16) imply:
% 135.48/19.91 | | (18) ~ (all_52_11 = e3)
% 135.48/19.91 | |
% 135.48/19.91 | | REDUCE: (9), (16) imply:
% 135.48/19.91 | | (19) ~ (e3 = e2)
% 135.48/19.91 | |
% 135.48/19.91 | | REDUCE: (1), (16) imply:
% 135.48/19.91 | | (20) ~ (e3 = e1)
% 135.48/19.91 | |
% 135.48/19.91 | | REF_CLOSE: (3), (4), (5), (6), (7), (13), (17), (18), (19), (20) are
% 135.48/19.91 | | inconsistent by sub-proof #29.
% 135.48/19.91 | |
% 135.48/19.91 | Case 2:
% 135.48/19.91 | |
% 135.48/19.91 | | (21) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 135.48/19.91 | |
% 135.48/19.91 | | REF_CLOSE: (1), (9), (11), (12), (21) are inconsistent by sub-proof #24.
% 135.48/19.91 | |
% 135.48/19.91 | End of split
% 135.48/19.91 |
% 135.48/19.91 End of proof
% 135.48/19.91
% 135.48/19.91 Sub-proof #24 shows that the following formulas are inconsistent:
% 135.48/19.91 ----------------------------------------------------------------
% 135.48/19.91 (1) ~ (all_10_0 = e1)
% 135.48/19.91 (2) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 135.48/19.91 (3) ~ (all_10_0 = e2)
% 135.48/19.91 (4) ~ (all_10_0 = e0)
% 135.48/19.91 (5) all_54_12 = all_10_0
% 135.48/19.91
% 135.48/19.91 Begin of proof
% 135.48/19.91 |
% 135.48/19.91 | BETA: splitting (2) gives:
% 135.48/19.91 |
% 135.48/19.91 | Case 1:
% 135.48/19.91 | |
% 135.48/19.91 | | (6) all_54_12 = e2
% 135.48/19.91 | |
% 135.48/19.91 | | COMBINE_EQS: (5), (6) imply:
% 135.48/19.91 | | (7) all_10_0 = e2
% 135.48/19.91 | |
% 135.48/19.91 | | SIMP: (7) implies:
% 135.48/19.91 | | (8) all_10_0 = e2
% 135.48/19.91 | |
% 135.48/19.91 | | REDUCE: (3), (8) imply:
% 135.48/19.91 | | (9) $false
% 135.48/19.91 | |
% 135.48/19.91 | | CLOSE: (9) is inconsistent.
% 135.48/19.91 | |
% 135.48/19.91 | Case 2:
% 135.48/19.91 | |
% 135.48/19.91 | | (10) all_54_12 = e1 | all_54_12 = e0
% 135.48/19.91 | |
% 135.48/19.91 | | BETA: splitting (10) gives:
% 135.48/19.91 | |
% 135.48/19.91 | | Case 1:
% 135.48/19.91 | | |
% 135.48/19.91 | | | (11) all_54_12 = e1
% 135.48/19.91 | | |
% 135.48/19.91 | | | COMBINE_EQS: (5), (11) imply:
% 135.48/19.91 | | | (12) all_10_0 = e1
% 135.48/19.91 | | |
% 135.48/19.91 | | | SIMP: (12) implies:
% 135.48/19.91 | | | (13) all_10_0 = e1
% 135.48/19.91 | | |
% 135.48/19.91 | | | REDUCE: (1), (13) imply:
% 135.48/19.91 | | | (14) $false
% 135.48/19.91 | | |
% 135.48/19.91 | | | CLOSE: (14) is inconsistent.
% 135.48/19.91 | | |
% 135.48/19.91 | | Case 2:
% 135.48/19.91 | | |
% 135.48/19.91 | | | (15) all_54_12 = e0
% 135.48/19.91 | | |
% 135.48/19.91 | | | COMBINE_EQS: (5), (15) imply:
% 135.48/19.91 | | | (16) all_10_0 = e0
% 135.48/19.91 | | |
% 135.48/19.91 | | | SIMP: (16) implies:
% 135.48/19.91 | | | (17) all_10_0 = e0
% 135.48/19.91 | | |
% 135.48/19.91 | | | REDUCE: (4), (17) imply:
% 135.48/19.91 | | | (18) $false
% 135.48/19.91 | | |
% 135.48/19.91 | | | CLOSE: (18) is inconsistent.
% 135.48/19.91 | | |
% 135.48/19.91 | | End of split
% 135.48/19.91 | |
% 135.48/19.91 | End of split
% 135.48/19.91 |
% 135.48/19.91 End of proof
% 135.48/19.91
% 135.48/19.91 Sub-proof #25 shows that the following formulas are inconsistent:
% 135.48/19.91 ----------------------------------------------------------------
% 135.48/19.91 (1) op(e3, e3) = e2
% 135.48/19.91 (2) ~ (e2 = e0)
% 135.48/19.91 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.91 (4) ~ (e3 = e0)
% 135.48/19.91 (5) ~ (all_52_1 = e0)
% 135.48/19.91 (6) ~ (all_52_2 = e0)
% 135.48/19.91 (7) all_57_12 = e3
% 135.48/19.91 (8) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 135.48/19.91 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 135.48/19.91 (9) op(e1, e3) = all_52_2
% 135.48/19.91 (10) op(e2, e3) = all_52_1
% 135.48/19.91
% 135.48/19.91 Begin of proof
% 135.48/19.91 |
% 135.48/19.91 | BETA: splitting (8) gives:
% 135.48/19.91 |
% 135.48/19.91 | Case 1:
% 135.48/19.91 | |
% 135.48/19.91 | | (11) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 135.48/19.91 | | e0)
% 135.48/19.91 | |
% 135.48/19.91 | | REF_CLOSE: (1), (2), (3), (5), (10), (11) are inconsistent by sub-proof #89.
% 135.48/19.91 | |
% 135.48/19.91 | Case 2:
% 135.48/19.91 | |
% 135.48/19.91 | | (12) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 135.48/19.91 | | e0)
% 135.48/19.91 | |
% 135.48/19.91 | | REF_CLOSE: (3), (4), (6), (7), (9), (12) are inconsistent by sub-proof #27.
% 135.48/19.91 | |
% 135.48/19.91 | End of split
% 135.48/19.91 |
% 135.48/19.91 End of proof
% 135.48/19.91
% 135.48/19.91 Sub-proof #26 shows that the following formulas are inconsistent:
% 135.48/19.91 ----------------------------------------------------------------
% 135.48/19.91 (1) ~ (e2 = e0)
% 135.48/19.91 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.91 (3) ~ (e3 = e0)
% 135.48/19.91 (4) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 135.48/19.91 (5) all_57_9 = e3
% 135.48/19.91 (6) ~ (e3 = e2)
% 135.48/19.91 (7) op(e1, e1) = e3
% 135.48/19.91 (8) all_57_15 = e1
% 135.48/19.91 (9) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 135.48/19.91 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 135.48/19.91 e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 135.48/19.91 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 135.48/19.91 (10) ~ (e1 = e0)
% 135.48/19.91 (11) all_57_10 = e2
% 135.48/19.91
% 135.48/19.91 Begin of proof
% 135.48/19.91 |
% 135.48/19.91 | BETA: splitting (4) gives:
% 135.48/19.91 |
% 135.48/19.91 | Case 1:
% 135.48/19.91 | |
% 135.48/19.91 | | (12) all_57_8 = e2 & op(e1, e1) = e2
% 135.48/19.91 | |
% 135.48/19.91 | | ALPHA: (12) implies:
% 135.48/19.91 | | (13) op(e1, e1) = e2
% 135.48/19.91 | |
% 135.48/19.91 | | REF_CLOSE: (2), (6), (7), (13) are inconsistent by sub-proof #109.
% 135.48/19.91 | |
% 135.48/19.91 | Case 2:
% 135.48/19.91 | |
% 135.48/19.91 | | (14) all_57_11 = e2 & op(e1, e0) = e2
% 135.48/19.91 | |
% 135.48/19.91 | | ALPHA: (14) implies:
% 135.48/19.91 | | (15) all_57_11 = e2
% 135.48/19.91 | |
% 135.48/19.91 | | BETA: splitting (9) gives:
% 135.48/19.91 | |
% 135.48/19.91 | | Case 1:
% 135.48/19.91 | | |
% 135.48/19.91 | | | (16) all_57_15 = e0 & op(e0, e0) = e0
% 135.48/19.91 | | |
% 135.48/19.91 | | | REF_CLOSE: (8), (10), (16) are inconsistent by sub-proof #412.
% 135.48/19.91 | | |
% 135.48/19.91 | | Case 2:
% 135.48/19.91 | | |
% 135.48/19.91 | | | (17) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0)
% 135.48/19.91 | | | = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0
% 135.48/19.91 | | | & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 135.48/19.91 | | | (all_57_14 = e0 & op(e0, e1) = e0))
% 135.48/19.91 | | |
% 135.48/19.91 | | | ALPHA: (17) implies:
% 135.48/19.91 | | | (18) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 135.48/19.91 | | | e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 135.48/19.91 | | |
% 135.48/19.91 | | | BETA: splitting (18) gives:
% 135.48/19.91 | | |
% 135.48/19.91 | | | Case 1:
% 135.48/19.91 | | | |
% 135.48/19.91 | | | | (19) all_57_9 = e0 & op(e3, e0) = e0
% 135.48/19.91 | | | |
% 135.48/19.91 | | | | ALPHA: (19) implies:
% 135.48/19.91 | | | | (20) all_57_9 = e0
% 135.48/19.91 | | | |
% 135.48/19.91 | | | | REF_CLOSE: (3), (5), (20) are inconsistent by sub-proof #670.
% 135.48/19.91 | | | |
% 135.48/19.91 | | | Case 2:
% 135.48/19.91 | | | |
% 135.48/19.91 | | | | (21) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 135.48/19.91 | | | | e0) = e0)
% 135.48/19.91 | | | |
% 135.48/19.91 | | | | BETA: splitting (21) gives:
% 135.48/19.91 | | | |
% 135.48/19.91 | | | | Case 1:
% 135.48/19.91 | | | | |
% 135.48/19.91 | | | | | (22) all_57_10 = e0 & op(e2, e0) = e0
% 135.48/19.91 | | | | |
% 135.48/19.91 | | | | | REF_CLOSE: (1), (11), (22) are inconsistent by sub-proof #363.
% 135.48/19.91 | | | | |
% 135.48/19.91 | | | | Case 2:
% 135.48/19.91 | | | | |
% 135.48/19.91 | | | | | (23) all_57_11 = e0 & op(e1, e0) = e0
% 135.48/19.91 | | | | |
% 135.48/19.91 | | | | | ALPHA: (23) implies:
% 135.48/19.91 | | | | | (24) all_57_11 = e0
% 135.48/19.91 | | | | |
% 135.48/19.91 | | | | | REF_CLOSE: (1), (15), (24) are inconsistent by sub-proof #638.
% 135.48/19.91 | | | | |
% 135.48/19.91 | | | | End of split
% 135.48/19.91 | | | |
% 135.48/19.91 | | | End of split
% 135.48/19.91 | | |
% 135.48/19.91 | | End of split
% 135.48/19.91 | |
% 135.48/19.91 | End of split
% 135.48/19.91 |
% 135.48/19.91 End of proof
% 135.48/19.91
% 135.48/19.91 Sub-proof #27 shows that the following formulas are inconsistent:
% 135.48/19.91 ----------------------------------------------------------------
% 135.48/19.91 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.91 (2) ~ (e3 = e0)
% 135.48/19.91 (3) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 135.48/19.91 (4) ~ (all_52_2 = e0)
% 135.48/19.91 (5) all_57_12 = e3
% 135.48/19.91 (6) op(e1, e3) = all_52_2
% 135.48/19.91
% 135.48/19.91 Begin of proof
% 135.48/19.91 |
% 135.48/19.91 | BETA: splitting (3) gives:
% 135.48/19.91 |
% 135.48/19.91 | Case 1:
% 135.48/19.91 | |
% 135.48/19.91 | | (7) all_57_6 = e0 & op(e1, e3) = e0
% 135.48/19.91 | |
% 135.48/19.91 | | REF_CLOSE: (1), (4), (6), (7) are inconsistent by sub-proof #73.
% 135.48/19.91 | |
% 135.48/19.91 | Case 2:
% 135.48/19.91 | |
% 135.48/19.91 | | (8) all_57_12 = e0 & op(e0, e3) = e0
% 135.48/19.91 | |
% 135.48/19.91 | | ALPHA: (8) implies:
% 135.48/19.91 | | (9) all_57_12 = e0
% 135.48/19.91 | |
% 135.48/19.91 | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #492.
% 135.48/19.91 | |
% 135.48/19.91 | End of split
% 135.48/19.91 |
% 135.48/19.91 End of proof
% 135.48/19.91
% 135.48/19.91 Sub-proof #28 shows that the following formulas are inconsistent:
% 135.48/19.91 ----------------------------------------------------------------
% 135.48/19.91 (1) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2)
% 135.48/19.91 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.48/19.91 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25
% 135.48/19.91 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.48/19.91 $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~
% 135.48/19.91 (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.48/19.91 (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 135.48/19.91 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.48/19.91 = all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.48/19.91 $i(all_56_29))
% 135.48/19.91 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.91 (3) ~ (e2 = e1)
% 135.48/19.91 (4) op(e1, e3) = e2
% 135.48/19.91 (5) op(e1, e3) = all_52_2
% 135.48/19.91 (6) op(e1, e0) = e0
% 135.48/19.91
% 135.48/19.91 Begin of proof
% 135.48/19.91 |
% 135.48/19.91 | BETA: splitting (1) gives:
% 135.48/19.91 |
% 135.48/19.91 | Case 1:
% 135.48/19.91 | |
% 135.48/19.91 | | (7) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 135.48/19.91 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.48/19.91 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.48/19.91 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1)
% 135.48/19.91 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)
% 135.48/19.91 | |
% 135.48/19.91 | | ALPHA: (7) implies:
% 135.48/19.91 | | (8) op(e1, e3) = e1
% 135.48/19.91 | |
% 135.48/19.91 | | REF_CLOSE: (2), (3), (4), (5), (8) are inconsistent by sub-proof #517.
% 135.48/19.91 | |
% 135.48/19.91 | Case 2:
% 135.48/19.91 | |
% 135.48/19.91 | | (9) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13
% 135.48/19.91 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1
% 135.48/19.91 | | & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 135.48/19.91 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.48/19.91 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 135.48/19.91 | |
% 135.48/19.91 | | ALPHA: (9) implies:
% 135.48/19.91 | | (10) ~ (all_56_29 = e0)
% 135.48/19.91 | | (11) op(e1, e0) = all_56_29
% 135.48/19.91 | |
% 135.48/19.91 | | REF_CLOSE: (2), (6), (10), (11) are inconsistent by sub-proof #45.
% 135.48/19.91 | |
% 135.48/19.91 | End of split
% 135.48/19.91 |
% 135.48/19.91 End of proof
% 135.48/19.91
% 135.48/19.91 Sub-proof #29 shows that the following formulas are inconsistent:
% 135.48/19.91 ----------------------------------------------------------------
% 135.48/19.91 (1) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 135.48/19.91 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 135.48/19.91 (2) ~ (all_52_7 = e3)
% 135.48/19.91 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.91 (4) ~ (e3 = e2)
% 135.48/19.91 (5) op(e0, e0) = e1
% 135.48/19.91 (6) op(e0, e1) = all_52_11
% 135.48/19.91 (7) op(e0, e2) = all_52_7
% 135.48/19.91 (8) ~ (all_52_11 = e3)
% 135.48/19.91 (9) ~ (e3 = e1)
% 135.48/19.91 (10) all_57_12 = e2
% 135.48/19.91
% 135.48/19.91 Begin of proof
% 135.48/19.91 |
% 135.48/19.91 | BETA: splitting (1) gives:
% 135.48/19.91 |
% 135.48/19.91 | Case 1:
% 135.48/19.91 | |
% 135.48/19.91 | | (11) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 135.48/19.91 | | e3)
% 135.48/19.91 | |
% 135.48/19.91 | | BETA: splitting (11) gives:
% 135.48/19.91 | |
% 135.48/19.91 | | Case 1:
% 135.48/19.91 | | |
% 135.48/19.91 | | | (12) all_57_12 = e3 & op(e0, e3) = e3
% 135.48/19.91 | | |
% 135.48/19.91 | | | ALPHA: (12) implies:
% 135.48/19.91 | | | (13) all_57_12 = e3
% 135.48/19.91 | | |
% 135.48/19.91 | | | REF_CLOSE: (4), (10), (13) are inconsistent by sub-proof #518.
% 135.48/19.91 | | |
% 135.48/19.91 | | Case 2:
% 135.48/19.91 | | |
% 135.48/19.91 | | | (14) all_57_13 = e3 & op(e0, e2) = e3
% 135.48/19.91 | | |
% 135.48/19.91 | | | REF_CLOSE: (2), (3), (7), (14) are inconsistent by sub-proof #556.
% 135.48/19.91 | | |
% 135.48/19.91 | | End of split
% 135.48/19.91 | |
% 135.48/19.91 | Case 2:
% 135.48/19.91 | |
% 135.48/19.91 | | (15) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 135.48/19.91 | | e3)
% 135.48/19.91 | |
% 135.48/19.91 | | REF_CLOSE: (3), (5), (6), (8), (9), (15) are inconsistent by sub-proof #37.
% 135.48/19.91 | |
% 135.48/19.91 | End of split
% 135.48/19.91 |
% 135.48/19.91 End of proof
% 135.48/19.91
% 135.48/19.91 Sub-proof #30 shows that the following formulas are inconsistent:
% 135.48/19.91 ----------------------------------------------------------------
% 135.48/19.91 (1) op(e1, e1) = all_6_2
% 135.48/19.91 (2) ~ (all_6_2 = e3)
% 135.48/19.91 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.91 (4) ~ (e2 = e1)
% 135.48/19.91 (5) op(e0, e0) = e1
% 135.48/19.91 (6) ~ (all_52_11 = all_6_2)
% 135.48/19.91 (7) op(e0, e1) = all_52_11
% 135.48/19.91 (8) all_54_10 = all_6_2
% 135.48/19.91 (9) ~ (all_6_2 = e2)
% 135.48/19.91 (10) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 135.48/19.91 (11) ~ (all_52_14 = e1)
% 135.48/19.91 (12) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.48/19.91 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.48/19.91 all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 135.48/19.91 e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 135.48/19.91 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 135.48/19.91 all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~
% 135.48/19.91 (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 135.48/19.91 (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 &
% 135.48/19.91 op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0
% 135.48/19.91 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 135.48/19.91 (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 135.48/19.91 (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.48/19.91 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.48/19.91 all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.48/19.91 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.48/19.91 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.48/19.91 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.48/19.91 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.48/19.91 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 135.48/19.91 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 135.48/19.91 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 135.48/19.91 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.48/19.91 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 135.48/19.91 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.48/19.91 $i(all_56_29))))
% 135.48/19.91 (13) ~ (e3 = e1)
% 135.48/19.91 (14) op(e1, e0) = all_52_14
% 135.48/19.91
% 135.48/19.91 Begin of proof
% 135.48/19.91 |
% 135.48/19.91 | BETA: splitting (12) gives:
% 135.48/19.91 |
% 135.48/19.91 | Case 1:
% 135.48/19.91 | |
% 135.48/19.91 | | (15) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11
% 135.48/19.91 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.48/19.91 | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 135.48/19.91 | | e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3)
% 135.48/19.91 | | & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)
% 135.48/19.91 | |
% 135.48/19.91 | | ALPHA: (15) implies:
% 135.48/19.91 | | (16) op(e1, e1) = e2
% 135.48/19.91 | |
% 135.48/19.91 | | REF_CLOSE: (1), (3), (9), (16) are inconsistent by sub-proof #767.
% 135.48/19.91 | |
% 135.48/19.91 | Case 2:
% 135.48/19.91 | |
% 135.48/19.91 | | (17) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31
% 135.48/19.91 | | = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 135.48/19.91 | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2)
% 135.48/19.91 | | = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.48/19.91 | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.48/19.91 | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3
% 135.48/19.91 | | = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.48/19.91 | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 135.48/19.91 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 135.48/19.91 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.48/19.91 | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7
% 135.48/19.91 | | = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.48/19.91 | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 135.48/19.91 | | e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) =
% 135.48/19.91 | | all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 135.48/19.91 | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 135.48/19.91 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 135.48/19.91 | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.48/19.91 | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.48/19.91 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)))
% 135.48/19.91 | |
% 135.48/19.91 | | ALPHA: (17) implies:
% 135.48/19.91 | | (18) op(e0, e0) = all_56_31
% 135.48/19.91 | | (19) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 135.48/19.91 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.48/19.91 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.48/19.91 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9)
% 135.48/19.91 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 135.48/19.91 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.48/19.91 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 135.48/19.91 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 135.48/19.91 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.48/19.91 | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 135.48/19.91 | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31
% 135.48/19.91 | | = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 135.48/19.91 | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.48/19.91 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 &
% 135.48/19.91 | | all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.48/19.91 | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 135.48/19.91 | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 135.48/19.91 | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.48/19.91 | | $i(all_56_21) & $i(all_56_29))
% 135.48/19.91 | |
% 135.48/19.91 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 135.48/19.91 | | (14), (18), (19) are inconsistent by sub-proof #31.
% 135.48/19.91 | |
% 135.48/19.91 | End of split
% 135.48/19.91 |
% 135.48/19.91 End of proof
% 135.48/19.91
% 135.48/19.91 Sub-proof #31 shows that the following formulas are inconsistent:
% 135.48/19.91 ----------------------------------------------------------------
% 135.48/19.92 (1) op(e1, e1) = all_6_2
% 135.48/19.92 (2) ~ (all_6_2 = e3)
% 135.48/19.92 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.92 (4) ~ (e2 = e1)
% 135.48/19.92 (5) op(e0, e0) = e1
% 135.48/19.92 (6) ~ (all_52_11 = all_6_2)
% 135.48/19.92 (7) op(e0, e1) = all_52_11
% 135.48/19.92 (8) all_54_10 = all_6_2
% 135.48/19.92 (9) ~ (all_6_2 = e2)
% 135.48/19.92 (10) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 135.48/19.92 (11) ~ (all_52_14 = e1)
% 135.48/19.92 (12) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 135.48/19.92 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.48/19.92 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0)
% 135.48/19.92 = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.48/19.92 $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~
% 135.48/19.92 (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.48/19.92 (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.48/19.92 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.48/19.92 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.48/19.92 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 135.48/19.92 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 135.48/19.92 op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 135.48/19.92 op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 135.48/19.92 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13
% 135.48/19.92 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 135.48/19.92 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1,
% 135.48/19.92 e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.48/19.92 $i(all_56_21) & $i(all_56_29))
% 135.48/19.92 (13) ~ (e3 = e1)
% 135.48/19.92 (14) op(e1, e0) = all_52_14
% 135.48/19.92 (15) op(e0, e0) = all_56_31
% 135.48/19.92
% 135.48/19.92 Begin of proof
% 135.48/19.92 |
% 135.48/19.92 | GROUND_INST: instantiating (3) with e1, all_56_31, e0, e0, simplifying with
% 135.48/19.92 | (5), (15) gives:
% 135.48/19.92 | (16) all_56_31 = e1
% 135.48/19.92 |
% 135.48/19.92 | BETA: splitting (12) gives:
% 135.48/19.92 |
% 135.48/19.92 | Case 1:
% 135.48/19.92 | |
% 135.48/19.92 | | (17) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 135.48/19.92 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.48/19.92 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.48/19.92 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9)
% 135.48/19.92 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 135.48/19.92 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.48/19.92 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 135.48/19.92 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 135.48/19.92 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.48/19.92 | | $i(all_56_27))
% 135.48/19.92 | |
% 135.48/19.92 | | REF_CLOSE: (4), (13), (16), (17) are inconsistent by sub-proof #32.
% 135.48/19.92 | |
% 135.48/19.92 | Case 2:
% 135.48/19.92 | |
% 135.48/19.92 | | (18) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.48/19.92 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.48/19.92 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.48/19.92 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 135.48/19.92 | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 135.48/19.92 | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 135.48/19.92 | | ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.48/19.92 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 135.48/19.92 | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.48/19.92 | | $i(all_56_29))
% 135.48/19.92 | |
% 135.48/19.92 | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (11), (14), (18) are
% 135.48/19.92 | | inconsistent by sub-proof #59.
% 135.48/19.92 | |
% 135.48/19.92 | End of split
% 135.48/19.92 |
% 135.48/19.92 End of proof
% 135.48/19.92
% 135.48/19.92 Sub-proof #32 shows that the following formulas are inconsistent:
% 135.48/19.92 ----------------------------------------------------------------
% 135.48/19.92 (1) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2)
% 135.48/19.92 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.48/19.92 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25
% 135.48/19.92 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.48/19.92 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3)
% 135.48/19.92 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.48/19.92 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 135.48/19.92 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) &
% 135.48/19.92 $i(all_56_11) & $i(all_56_19) & $i(all_56_27))
% 135.48/19.92 (2) all_56_31 = e1
% 135.48/19.92 (3) ~ (e3 = e1)
% 135.48/19.92 (4) ~ (e2 = e1)
% 135.48/19.92
% 135.48/19.92 Begin of proof
% 135.48/19.92 |
% 135.48/19.92 | BETA: splitting (1) gives:
% 135.48/19.92 |
% 135.48/19.92 | Case 1:
% 135.48/19.92 | |
% 135.48/19.92 | | (5) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 135.48/19.92 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.48/19.92 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.48/19.92 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.48/19.92 | | $i(all_56_17) & $i(all_56_25)
% 135.48/19.92 | |
% 135.48/19.92 | | ALPHA: (5) implies:
% 135.48/19.92 | | (6) all_56_31 = e3
% 135.48/19.92 | |
% 135.48/19.92 | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #253.
% 135.48/19.92 | |
% 135.48/19.92 | Case 2:
% 135.48/19.92 | |
% 135.48/19.92 | | (7) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11
% 135.48/19.92 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.48/19.92 | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 135.48/19.92 | | e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.48/19.92 | | $i(all_56_19) & $i(all_56_27)
% 135.48/19.92 | |
% 135.48/19.92 | | REF_CLOSE: (2), (4), (7) are inconsistent by sub-proof #33.
% 135.48/19.92 | |
% 135.48/19.92 | End of split
% 135.48/19.92 |
% 135.48/19.92 End of proof
% 135.48/19.92
% 135.48/19.92 Sub-proof #33 shows that the following formulas are inconsistent:
% 135.48/19.92 ----------------------------------------------------------------
% 135.48/19.92 (1) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.48/19.92 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3
% 135.48/19.92 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 135.48/19.92 all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.48/19.92 $i(all_56_19) & $i(all_56_27)
% 135.48/19.92 (2) all_56_31 = e1
% 135.48/19.92 (3) ~ (e2 = e1)
% 135.48/19.92
% 135.48/19.92 Begin of proof
% 135.48/19.92 |
% 135.48/19.92 | ALPHA: (1) implies:
% 135.48/19.92 | (4) all_56_31 = e2
% 135.48/19.92 |
% 135.48/19.92 | COMBINE_EQS: (2), (4) imply:
% 135.48/19.92 | (5) e2 = e1
% 135.48/19.92 |
% 135.48/19.92 | SIMP: (5) implies:
% 135.48/19.92 | (6) e2 = e1
% 135.48/19.92 |
% 135.48/19.92 | REDUCE: (3), (6) imply:
% 135.48/19.92 | (7) $false
% 135.48/19.92 |
% 135.48/19.92 | CLOSE: (7) is inconsistent.
% 135.48/19.92 |
% 135.48/19.92 End of proof
% 135.48/19.92
% 135.48/19.92 Sub-proof #34 shows that the following formulas are inconsistent:
% 135.48/19.92 ----------------------------------------------------------------
% 135.48/19.92 (1) ~ (all_52_11 = e2)
% 135.48/19.92 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.92 (3) ~ (e2 = e1)
% 135.48/19.92 (4) op(e0, e0) = e1
% 135.48/19.92 (5) op(e0, e1) = all_52_11
% 135.48/19.92 (6) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 135.48/19.92
% 135.48/19.92 Begin of proof
% 135.48/19.92 |
% 135.48/19.92 | BETA: splitting (6) gives:
% 135.48/19.92 |
% 135.48/19.92 | Case 1:
% 135.48/19.92 | |
% 135.48/19.92 | | (7) all_57_14 = e2 & op(e0, e1) = e2
% 135.48/19.92 | |
% 135.48/19.92 | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #512.
% 135.48/19.92 | |
% 135.48/19.92 | Case 2:
% 135.48/19.92 | |
% 135.48/19.92 | | (8) all_57_15 = e2 & op(e0, e0) = e2
% 135.48/19.92 | |
% 135.48/19.92 | | ALPHA: (8) implies:
% 135.48/19.92 | | (9) op(e0, e0) = e2
% 135.48/19.92 | |
% 135.48/19.92 | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #636.
% 135.48/19.92 | |
% 135.48/19.92 | End of split
% 135.48/19.92 |
% 135.48/19.92 End of proof
% 135.48/19.92
% 135.48/19.92 Sub-proof #35 shows that the following formulas are inconsistent:
% 135.48/19.92 ----------------------------------------------------------------
% 135.48/19.92 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.92 (2) op(e1, e0) = all_12_0
% 135.48/19.92 (3) op(e1, e0) = e2
% 135.48/19.92 (4) ~ (all_12_0 = e2)
% 135.48/19.92
% 135.48/19.92 Begin of proof
% 135.48/19.92 |
% 135.48/19.92 | GROUND_INST: instantiating (1) with e2, all_12_0, e0, e1, simplifying with
% 135.48/19.92 | (2), (3) gives:
% 135.48/19.92 | (5) all_12_0 = e2
% 135.48/19.92 |
% 135.48/19.92 | REDUCE: (4), (5) imply:
% 135.48/19.92 | (6) $false
% 135.48/19.92 |
% 135.48/19.92 | CLOSE: (6) is inconsistent.
% 135.48/19.92 |
% 135.48/19.92 End of proof
% 135.48/19.92
% 135.48/19.92 Sub-proof #36 shows that the following formulas are inconsistent:
% 135.48/19.92 ----------------------------------------------------------------
% 135.48/19.92 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.92 (2) op(e1, e1) = all_12_1
% 135.48/19.92 (3) op(e1, e1) = e3
% 135.48/19.92 (4) ~ (all_12_1 = e3)
% 135.48/19.92
% 135.48/19.92 Begin of proof
% 135.48/19.92 |
% 135.48/19.92 | GROUND_INST: instantiating (1) with e3, all_12_1, e1, e1, simplifying with
% 135.48/19.92 | (2), (3) gives:
% 135.48/19.92 | (5) all_12_1 = e3
% 135.48/19.92 |
% 135.48/19.92 | REDUCE: (4), (5) imply:
% 135.48/19.92 | (6) $false
% 135.48/19.92 |
% 135.48/19.92 | CLOSE: (6) is inconsistent.
% 135.48/19.92 |
% 135.48/19.92 End of proof
% 135.48/19.92
% 135.48/19.92 Sub-proof #37 shows that the following formulas are inconsistent:
% 135.48/19.92 ----------------------------------------------------------------
% 135.48/19.92 (1) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 135.48/19.92 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.92 (3) op(e0, e0) = e1
% 135.48/19.92 (4) op(e0, e1) = all_52_11
% 135.48/19.92 (5) ~ (all_52_11 = e3)
% 135.48/19.92 (6) ~ (e3 = e1)
% 135.48/19.92
% 135.48/19.92 Begin of proof
% 135.48/19.92 |
% 135.48/19.92 | BETA: splitting (1) gives:
% 135.48/19.92 |
% 135.48/19.92 | Case 1:
% 135.48/19.92 | |
% 135.48/19.92 | | (7) all_57_14 = e3 & op(e0, e1) = e3
% 135.48/19.92 | |
% 135.48/19.92 | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #652.
% 135.48/19.92 | |
% 135.48/19.92 | Case 2:
% 135.48/19.92 | |
% 135.48/19.92 | | (8) all_57_15 = e3 & op(e0, e0) = e3
% 135.48/19.92 | |
% 135.48/19.92 | | ALPHA: (8) implies:
% 135.48/19.92 | | (9) op(e0, e0) = e3
% 135.48/19.92 | |
% 135.48/19.92 | | REF_CLOSE: (2), (3), (6), (9) are inconsistent by sub-proof #606.
% 135.48/19.92 | |
% 135.48/19.92 | End of split
% 135.48/19.92 |
% 135.48/19.92 End of proof
% 135.48/19.92
% 135.48/19.92 Sub-proof #38 shows that the following formulas are inconsistent:
% 135.48/19.92 ----------------------------------------------------------------
% 135.48/19.92 (1) op(e2, e2) = all_8_2
% 135.48/19.92 (2) op(e2, e0) = all_52_13
% 135.48/19.92 (3) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 135.48/19.92 (4) ~ (all_8_2 = e1)
% 135.48/19.92 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.92 (6) ~ (e3 = e2)
% 135.48/19.92 (7) op(e0, e0) = e1
% 135.48/19.92 (8) op(e0, e2) = all_52_7
% 135.48/19.92 (9) op(e1, e1) = e2
% 135.48/19.92 (10) ~ (all_10_2 = e0)
% 135.48/19.92 (11) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.48/19.92 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.48/19.92 op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.48/19.92 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.48/19.92 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 135.48/19.92 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.48/19.92 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 135.48/19.92 = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.48/19.92 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.48/19.92 $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~
% 135.48/19.92 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.48/19.92 (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) =
% 135.48/19.92 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0,
% 135.48/19.92 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 135.48/19.92 $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3)
% 135.48/19.92 & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 135.48/19.92 op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17
% 135.48/19.92 & op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 135.48/19.92 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 135.48/19.92 (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 135.48/19.92 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.48/19.92 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0)
% 135.48/19.92 = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) &
% 135.48/19.92 $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 &
% 135.48/19.92 all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.48/19.92 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 135.48/19.92 = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.48/19.92 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.48/19.92 $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~
% 135.48/19.92 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.48/19.92 (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 135.48/19.92 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0,
% 135.48/19.92 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 135.48/19.92 $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3)
% 135.48/19.92 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.48/19.92 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.48/19.92 all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2
% 135.48/19.92 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.48/19.92 (op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 =
% 135.48/19.92 e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.48/19.92 & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) =
% 135.48/19.92 all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.48/19.92 op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.48/19.92 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 135.48/19.92 e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.48/19.92 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 135.48/19.92 e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.48/19.92 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.48/19.92 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.48/19.92 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.48/19.92 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.48/19.92 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 135.48/19.92 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 135.48/19.92 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 135.48/19.92 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.48/19.92 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 135.48/19.92 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.48/19.92 $i(all_56_29))))
% 135.48/19.92 (12) op(e3, e3) = all_10_2
% 135.48/19.92 (13) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 135.48/19.92 (14) all_54_5 = all_8_2
% 135.48/19.92 (15) ~ (all_8_2 = e0)
% 135.48/19.92 (16) ~ (all_52_13 = all_8_2)
% 135.48/19.92 (17) ~ (all_10_2 = e2)
% 135.48/19.92 (18) ~ (all_52_14 = e1)
% 135.48/19.92 (19) ~ (e3 = e1)
% 135.48/19.92 (20) ~ (all_52_7 = all_8_2)
% 135.48/19.92 (21) ~ (all_8_2 = e3)
% 135.48/19.92 (22) op(e1, e0) = all_52_14
% 135.48/19.92 (23) op(e1, e0) = e0
% 135.48/19.92
% 135.48/19.92 Begin of proof
% 135.48/19.92 |
% 135.48/19.92 | BETA: splitting (11) gives:
% 135.48/19.92 |
% 135.48/19.92 | Case 1:
% 135.48/19.92 | |
% 135.48/19.92 | | (24) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11
% 135.48/19.92 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) =
% 135.48/19.92 | | e2 & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 135.48/19.92 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 135.48/19.92 | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.48/19.92 | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13
% 135.48/19.92 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) =
% 135.48/19.92 | | e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.48/19.92 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 135.48/19.92 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 135.48/19.92 | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15
% 135.48/19.92 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) =
% 135.48/19.92 | | e0 & op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.48/19.92 | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 &
% 135.48/19.92 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.48/19.92 | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 135.48/19.92 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.48/19.92 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.48/19.92 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 135.48/19.92 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25))
% 135.48/19.92 | |
% 135.48/19.92 | | REF_CLOSE: (1), (5), (10), (12), (17), (21), (23), (24) are inconsistent by
% 135.48/19.92 | | sub-proof #43.
% 135.48/19.92 | |
% 135.48/19.92 | Case 2:
% 135.48/19.92 | |
% 135.48/19.92 | | (25) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 135.48/19.92 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.48/19.92 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.48/19.92 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 135.48/19.92 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 135.48/19.92 | | (all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 135.48/19.92 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 135.48/19.92 | | op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1,
% 135.48/19.92 | | e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 135.48/19.92 | | all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.48/19.92 | | $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 135.48/19.92 | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31
% 135.48/19.92 | | = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 135.48/19.92 | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.48/19.92 | | op(e0, e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 135.48/19.92 | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2
% 135.48/19.92 | | & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 135.48/19.92 | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 135.48/19.92 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 135.48/19.92 | | op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 135.48/19.92 | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = all_56_31 &
% 135.48/19.92 | | $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 135.48/19.92 | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 135.48/19.92 | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) =
% 135.48/19.92 | | all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.48/19.92 | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17)
% 135.48/19.92 | | & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~
% 135.48/19.92 | | (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 135.48/19.92 | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 135.48/19.92 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 135.48/19.92 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 135.48/19.92 | | & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~
% 135.48/19.92 | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 135.48/19.92 | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 135.48/19.92 | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) =
% 135.48/19.92 | | all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 135.48/19.92 | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 135.48/19.92 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 135.48/19.92 | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.48/19.92 | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.48/19.92 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.48/19.92 | | $i(all_56_29))))
% 135.48/19.92 | |
% 135.48/19.92 | | BETA: splitting (25) gives:
% 135.48/19.92 | |
% 135.48/19.92 | | Case 1:
% 135.48/19.92 | | |
% 135.48/19.92 | | | (26) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~
% 135.48/19.92 | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 135.48/19.92 | | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) =
% 135.48/19.92 | | | all_56_17 & op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 135.48/19.92 | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.48/19.92 | | | $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5
% 135.48/19.92 | | | = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.48/19.92 | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1,
% 135.48/19.92 | | | e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.48/19.92 | | | all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.48/19.92 | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 135.48/19.92 | | |
% 135.48/19.92 | | | REF_CLOSE: (5), (6), (9), (23), (26) are inconsistent by sub-proof #42.
% 135.48/19.92 | | |
% 135.48/19.92 | | Case 2:
% 135.48/19.92 | | |
% 135.48/19.92 | | | (27) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 135.48/19.92 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.48/19.92 | | | op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 &
% 135.48/19.92 | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 135.48/19.92 | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 135.48/19.92 | | | $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3
% 135.48/19.92 | | | = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.48/19.92 | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 135.48/19.92 | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 135.48/19.92 | | | op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11)
% 135.48/19.92 | | | & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = all_56_31 &
% 135.48/19.92 | | | $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 135.48/19.92 | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 135.48/19.92 | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) =
% 135.48/19.92 | | | all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.48/19.92 | | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.48/19.92 | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 135.48/19.92 | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~
% 135.48/19.92 | | | (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.48/19.92 | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.48/19.92 | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) &
% 135.48/19.92 | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 135.48/19.92 | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 135.48/19.92 | | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1,
% 135.48/19.92 | | | e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 135.48/19.92 | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.48/19.92 | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 =
% 135.48/19.92 | | | e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.48/19.92 | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1,
% 135.48/19.92 | | | e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.48/19.92 | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.48/19.92 | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.48/19.92 | | | $i(all_56_29))))
% 135.48/19.92 | | |
% 135.48/19.92 | | | BETA: splitting (27) gives:
% 135.48/19.92 | | |
% 135.48/19.92 | | | Case 1:
% 135.48/19.92 | | | |
% 135.48/19.92 | | | | (28) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 135.48/19.92 | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.48/19.92 | | | | op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 &
% 135.48/19.92 | | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 135.48/19.92 | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 135.48/19.92 | | | | $i(all_56_31)
% 135.48/19.92 | | | |
% 135.48/19.92 | | | | ALPHA: (28) implies:
% 135.48/19.92 | | | | (29) op(e2, e0) = e2
% 135.48/19.92 | | | |
% 135.48/19.92 | | | | REF_CLOSE: (2), (3), (4), (5), (14), (15), (16), (29) are inconsistent
% 135.48/19.92 | | | | by sub-proof #60.
% 135.48/19.92 | | | |
% 135.48/19.92 | | | Case 2:
% 135.48/19.92 | | | |
% 135.48/19.92 | | | | (30) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 135.48/19.92 | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.48/19.92 | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.48/19.92 | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 135.48/19.92 | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.48/19.92 | | | | $i(all_56_27)) | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.48/19.92 | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 135.48/19.92 | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 =
% 135.48/19.92 | | | | e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 &
% 135.48/19.92 | | | | op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 135.48/19.92 | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.48/19.92 | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~
% 135.48/19.92 | | | | (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.48/19.92 | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.48/19.92 | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 135.48/19.92 | | | | e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) &
% 135.48/19.92 | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.48/19.92 | | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.48/19.92 | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 =
% 135.48/19.92 | | | | e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 135.48/19.92 | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23
% 135.48/19.92 | | | | & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 135.48/19.92 | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 135.48/19.92 | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 =
% 135.48/19.92 | | | | e0) & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 135.48/19.92 | | | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & op(e0,
% 135.48/19.92 | | | | e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.48/19.92 | | | | & $i(all_56_29))))
% 135.48/19.92 | | | |
% 135.48/19.92 | | | | BETA: splitting (30) gives:
% 135.48/19.92 | | | |
% 135.48/19.92 | | | | Case 1:
% 135.48/19.92 | | | | |
% 135.48/19.92 | | | | | (31) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 135.48/19.92 | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.48/19.92 | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.48/19.92 | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 135.48/19.92 | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.48/19.92 | | | | | $i(all_56_27)
% 135.48/19.92 | | | | |
% 135.48/19.92 | | | | | ALPHA: (31) implies:
% 135.48/19.92 | | | | | (32) ~ (all_56_11 = e2)
% 135.48/19.92 | | | | | (33) op(e2, e2) = all_56_11
% 135.48/19.92 | | | | |
% 135.48/19.92 | | | | | BETA: splitting (3) gives:
% 135.48/19.92 | | | | |
% 135.48/19.92 | | | | | Case 1:
% 135.48/19.92 | | | | | |
% 135.48/19.92 | | | | | | (34) all_54_5 = e2
% 135.48/19.92 | | | | | |
% 135.48/19.92 | | | | | | COMBINE_EQS: (14), (34) imply:
% 135.48/19.92 | | | | | | (35) all_8_2 = e2
% 135.48/19.93 | | | | | |
% 135.48/19.93 | | | | | | SIMP: (35) implies:
% 135.48/19.93 | | | | | | (36) all_8_2 = e2
% 135.48/19.93 | | | | | |
% 135.48/19.93 | | | | | | REDUCE: (1), (36) imply:
% 135.48/19.93 | | | | | | (37) op(e2, e2) = e2
% 135.48/19.93 | | | | | |
% 135.48/19.93 | | | | | | REF_CLOSE: (5), (32), (33), (37) are inconsistent by sub-proof #531.
% 135.48/19.93 | | | | | |
% 135.48/19.93 | | | | | Case 2:
% 135.48/19.93 | | | | | |
% 135.48/19.93 | | | | | | (38) all_54_5 = e1 | all_54_5 = e0
% 135.48/19.93 | | | | | |
% 135.48/19.93 | | | | | | REF_CLOSE: (4), (14), (15), (38) are inconsistent by sub-proof #624.
% 135.48/19.93 | | | | | |
% 135.48/19.93 | | | | | End of split
% 135.48/19.93 | | | | |
% 135.48/19.93 | | | | Case 2:
% 135.48/19.93 | | | | |
% 135.48/19.93 | | | | | (39) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 135.48/19.93 | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) &
% 135.48/19.93 | | | | | ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.48/19.93 | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17
% 135.48/19.93 | | | | | & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1)
% 135.48/19.93 | | | | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 135.48/19.93 | | | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 135.48/19.93 | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 =
% 135.48/19.93 | | | | | e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.48/19.93 | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 135.48/19.93 | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 135.48/19.93 | | | | | & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~
% 135.48/19.93 | | | | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.48/19.93 | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 135.48/19.93 | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 135.48/19.93 | | | | | op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 135.48/19.93 | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 & ~
% 135.48/19.93 | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.48/19.93 | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 135.48/19.93 | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1,
% 135.48/19.93 | | | | | e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 135.48/19.93 | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)))
% 135.48/19.93 | | | | |
% 135.48/19.93 | | | | | REF_CLOSE: (1), (4), (5), (7), (8), (13), (14), (18), (19), (20),
% 135.48/19.93 | | | | | (21), (22), (23), (39) are inconsistent by sub-proof #39.
% 135.48/19.93 | | | | |
% 135.48/19.93 | | | | End of split
% 135.48/19.93 | | | |
% 135.48/19.93 | | | End of split
% 135.48/19.93 | | |
% 135.48/19.93 | | End of split
% 135.48/19.93 | |
% 135.48/19.93 | End of split
% 135.48/19.93 |
% 135.48/19.93 End of proof
% 135.48/19.93
% 135.48/19.93 Sub-proof #39 shows that the following formulas are inconsistent:
% 135.48/19.93 ----------------------------------------------------------------
% 135.48/19.93 (1) op(e2, e2) = all_8_2
% 135.48/19.93 (2) ~ (all_8_2 = e1)
% 135.48/19.93 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.93 (4) op(e0, e0) = e1
% 135.48/19.93 (5) op(e0, e2) = all_52_7
% 135.48/19.93 (6) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 135.48/19.93 (7) all_54_5 = all_8_2
% 135.48/19.93 (8) ~ (all_52_14 = e1)
% 135.48/19.93 (9) ~ (e3 = e1)
% 135.48/19.93 (10) ~ (all_52_7 = all_8_2)
% 135.48/19.93 (11) ~ (all_8_2 = e3)
% 135.48/19.93 (12) op(e1, e0) = all_52_14
% 135.48/19.93 (13) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 =
% 135.48/19.93 e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 135.48/19.93 ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9
% 135.48/19.93 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0
% 135.48/19.93 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 135.48/19.93 (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11
% 135.48/19.93 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.48/19.93 all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 135.48/19.93 e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.48/19.93 $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 &
% 135.48/19.93 ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.48/19.93 (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 135.48/19.93 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.48/19.93 $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 &
% 135.48/19.93 all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.48/19.93 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 135.48/19.93 op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 135.48/19.93 all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.48/19.93 $i(all_56_21) & $i(all_56_29)))
% 135.48/19.93 (14) op(e1, e0) = e0
% 135.48/19.93
% 135.48/19.93 Begin of proof
% 135.48/19.93 |
% 135.48/19.93 | ALPHA: (13) implies:
% 135.48/19.93 | (15) op(e0, e0) = all_56_31
% 135.48/19.93 | (16) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 135.48/19.93 | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.48/19.93 | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.48/19.93 | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.48/19.93 | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 &
% 135.48/19.93 | ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.48/19.93 | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.48/19.93 | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.48/19.93 | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.48/19.93 | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15
% 135.48/19.93 | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) =
% 135.48/19.93 | e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.48/19.93 | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 135.48/19.93 | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 135.48/19.93 | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 =
% 135.48/19.93 | e0) & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1)
% 135.48/19.93 | = all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.48/19.93 | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 135.48/19.93 |
% 135.48/19.93 | BETA: splitting (16) gives:
% 135.48/19.93 |
% 135.48/19.93 | Case 1:
% 135.48/19.93 | |
% 135.48/19.93 | | (17) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 135.48/19.93 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.48/19.93 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.48/19.93 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9)
% 135.48/19.93 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 135.48/19.93 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.48/19.93 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 135.48/19.93 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 135.48/19.93 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.48/19.93 | | $i(all_56_27))
% 135.48/19.93 | |
% 135.48/19.93 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (15), (17)
% 135.48/19.93 | | are inconsistent by sub-proof #41.
% 135.48/19.93 | |
% 135.48/19.93 | Case 2:
% 135.48/19.93 | |
% 135.48/19.93 | | (18) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.48/19.93 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.48/19.93 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.48/19.93 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 135.48/19.93 | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 135.48/19.93 | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 135.48/19.93 | | ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.48/19.93 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 135.48/19.93 | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.48/19.93 | | $i(all_56_29))
% 135.48/19.93 | |
% 135.48/19.93 | | REF_CLOSE: (3), (8), (12), (14), (18) are inconsistent by sub-proof #40.
% 135.48/19.93 | |
% 135.48/19.93 | End of split
% 135.48/19.93 |
% 135.48/19.93 End of proof
% 135.48/19.93
% 135.48/19.93 Sub-proof #40 shows that the following formulas are inconsistent:
% 135.48/19.93 ----------------------------------------------------------------
% 135.48/19.93 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.93 (2) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 135.48/19.93 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 135.48/19.93 op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 135.48/19.93 op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 135.48/19.93 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.48/19.93 e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 135.48/19.93 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.48/19.93 = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.48/19.93 $i(all_56_21) & $i(all_56_29))
% 135.48/19.93 (3) ~ (all_52_14 = e1)
% 135.48/19.93 (4) op(e1, e0) = all_52_14
% 135.48/19.93 (5) op(e1, e0) = e0
% 135.48/19.93
% 135.48/19.93 Begin of proof
% 135.48/19.93 |
% 135.48/19.93 | BETA: splitting (2) gives:
% 135.48/19.93 |
% 135.48/19.93 | Case 1:
% 135.48/19.93 | |
% 135.48/19.93 | | (6) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15
% 135.48/19.93 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0
% 135.48/19.93 | | & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 135.48/19.93 | | op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)
% 135.48/19.93 | |
% 135.48/19.93 | | ALPHA: (6) implies:
% 135.48/19.93 | | (7) op(e1, e0) = e1
% 135.48/19.93 | |
% 135.48/19.93 | | REF_CLOSE: (1), (3), (4), (7) are inconsistent by sub-proof #327.
% 135.48/19.93 | |
% 135.48/19.93 | Case 2:
% 135.48/19.93 | |
% 135.48/19.93 | | (8) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13
% 135.48/19.93 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 135.48/19.93 | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1,
% 135.48/19.93 | | e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.48/19.93 | | $i(all_56_21) & $i(all_56_29)
% 135.48/19.93 | |
% 135.48/19.93 | | ALPHA: (8) implies:
% 135.48/19.93 | | (9) ~ (all_56_29 = e0)
% 135.48/19.93 | | (10) op(e1, e0) = all_56_29
% 135.48/19.93 | |
% 135.48/19.93 | | REF_CLOSE: (1), (5), (9), (10) are inconsistent by sub-proof #45.
% 135.48/19.93 | |
% 135.48/19.93 | End of split
% 135.48/19.93 |
% 135.48/19.93 End of proof
% 135.48/19.93
% 135.48/19.93 Sub-proof #41 shows that the following formulas are inconsistent:
% 135.48/19.93 ----------------------------------------------------------------
% 135.48/19.93 (1) op(e2, e2) = all_8_2
% 135.48/19.93 (2) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2)
% 135.48/19.93 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.48/19.93 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25
% 135.48/19.93 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.48/19.93 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3)
% 135.48/19.93 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.48/19.93 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 135.48/19.93 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) &
% 135.48/19.93 $i(all_56_11) & $i(all_56_19) & $i(all_56_27))
% 135.48/19.93 (3) ~ (all_8_2 = e1)
% 135.48/19.93 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.93 (5) op(e0, e0) = e1
% 135.48/19.93 (6) op(e0, e2) = all_52_7
% 135.48/19.93 (7) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 135.48/19.93 (8) all_54_5 = all_8_2
% 135.48/19.93 (9) ~ (e3 = e1)
% 135.48/19.93 (10) ~ (all_52_7 = all_8_2)
% 135.48/19.93 (11) ~ (all_8_2 = e3)
% 135.48/19.93 (12) op(e0, e0) = all_56_31
% 135.48/19.93
% 135.48/19.93 Begin of proof
% 135.48/19.93 |
% 135.48/19.93 | BETA: splitting (2) gives:
% 135.48/19.93 |
% 135.48/19.93 | Case 1:
% 135.48/19.93 | |
% 135.48/19.93 | | (13) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 135.48/19.93 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.48/19.93 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.48/19.93 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.48/19.93 | | $i(all_56_17) & $i(all_56_25)
% 135.48/19.93 | |
% 135.48/19.93 | | ALPHA: (13) implies:
% 135.48/19.93 | | (14) all_56_31 = e3
% 135.48/19.93 | |
% 135.48/19.93 | | REDUCE: (12), (14) imply:
% 135.48/19.93 | | (15) op(e0, e0) = e3
% 135.48/19.93 | |
% 135.48/19.93 | | REF_CLOSE: (4), (5), (9), (15) are inconsistent by sub-proof #606.
% 135.48/19.93 | |
% 135.48/19.93 | Case 2:
% 135.48/19.93 | |
% 135.48/19.93 | | (16) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11
% 135.48/19.93 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.48/19.93 | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 135.48/19.93 | | e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.48/19.93 | | $i(all_56_19) & $i(all_56_27)
% 135.48/19.93 | |
% 135.48/19.93 | | ALPHA: (16) implies:
% 135.48/19.93 | | (17) ~ (all_56_11 = e2)
% 135.48/19.93 | | (18) op(e0, e2) = e0
% 135.48/19.93 | | (19) op(e2, e2) = all_56_11
% 135.48/19.93 | |
% 135.48/19.93 | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (10), (11), (17), (18), (19) are
% 135.48/19.93 | | inconsistent by sub-proof #227.
% 135.48/19.93 | |
% 135.48/19.93 | End of split
% 135.48/19.93 |
% 135.48/19.93 End of proof
% 135.48/19.93
% 135.48/19.93 Sub-proof #42 shows that the following formulas are inconsistent:
% 135.48/19.93 ----------------------------------------------------------------
% 135.48/19.93 (1) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2)
% 135.48/19.93 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.48/19.93 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25
% 135.48/19.93 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.48/19.93 $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~
% 135.48/19.93 (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.48/19.93 (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 135.48/19.93 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.48/19.93 = all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.48/19.93 $i(all_56_29))
% 135.48/19.93 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.93 (3) ~ (e3 = e2)
% 135.48/19.93 (4) op(e1, e1) = e2
% 135.48/19.93 (5) op(e1, e0) = e0
% 135.48/19.93
% 135.48/19.93 Begin of proof
% 135.48/19.93 |
% 135.48/19.93 | BETA: splitting (1) gives:
% 135.48/19.93 |
% 135.48/19.93 | Case 1:
% 135.48/19.93 | |
% 135.48/19.93 | | (6) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 135.48/19.93 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.48/19.93 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.48/19.93 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1)
% 135.48/19.93 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)
% 135.48/19.93 | |
% 135.48/19.93 | | ALPHA: (6) implies:
% 135.48/19.93 | | (7) op(e1, e1) = e3
% 135.48/19.93 | |
% 135.48/19.93 | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #109.
% 135.48/19.93 | |
% 135.48/19.93 | Case 2:
% 135.48/19.93 | |
% 135.48/19.93 | | (8) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13
% 135.48/19.93 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1
% 135.48/19.93 | | & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 135.48/19.93 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.48/19.93 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 135.48/19.93 | |
% 135.48/19.93 | | ALPHA: (8) implies:
% 135.48/19.93 | | (9) ~ (all_56_29 = e0)
% 135.48/19.93 | | (10) op(e1, e0) = all_56_29
% 135.48/19.93 | |
% 135.48/19.93 | | REF_CLOSE: (2), (5), (9), (10) are inconsistent by sub-proof #45.
% 135.48/19.93 | |
% 135.48/19.93 | End of split
% 135.48/19.93 |
% 135.48/19.93 End of proof
% 135.48/19.93
% 135.48/19.93 Sub-proof #43 shows that the following formulas are inconsistent:
% 135.48/19.93 ----------------------------------------------------------------
% 135.48/19.93 (1) op(e2, e2) = all_8_2
% 135.48/19.93 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.93 (3) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2)
% 135.48/19.93 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3,
% 135.48/19.93 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 135.48/19.93 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.48/19.93 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 135.48/19.93 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.48/19.93 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) =
% 135.48/19.93 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.48/19.93 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.48/19.93 $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~
% 135.48/19.93 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.48/19.93 (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) =
% 135.48/19.93 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 135.48/19.93 = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 135.48/19.93 $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) &
% 135.48/19.93 ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3,
% 135.48/19.93 e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.48/19.93 op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 135.48/19.93 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25))
% 135.48/19.93 (4) ~ (all_10_2 = e0)
% 135.48/19.93 (5) op(e3, e3) = all_10_2
% 135.48/19.93 (6) ~ (all_10_2 = e2)
% 135.48/19.93 (7) ~ (all_8_2 = e3)
% 135.48/19.93 (8) op(e1, e0) = e0
% 135.48/19.93
% 135.48/19.93 Begin of proof
% 135.48/19.93 |
% 135.48/19.93 | BETA: splitting (3) gives:
% 135.48/19.93 |
% 135.48/19.93 | Case 1:
% 135.48/19.93 | |
% 135.48/19.93 | | (9) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.48/19.93 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2
% 135.48/19.93 | | & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11
% 135.48/19.93 | | & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.48/19.93 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 135.48/19.93 | | all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.48/19.93 | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 135.48/19.93 | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 135.48/19.93 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.48/19.93 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 135.48/19.93 | |
% 135.48/19.93 | | REF_CLOSE: (2), (5), (6), (8), (9) are inconsistent by sub-proof #44.
% 135.48/19.93 | |
% 135.48/19.93 | Case 2:
% 135.48/19.93 | |
% 135.48/19.93 | | (10) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15
% 135.48/19.93 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) =
% 135.48/19.93 | | e0 & op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.48/19.93 | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 &
% 135.48/19.93 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.48/19.93 | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 135.48/19.93 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.48/19.93 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.48/19.93 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 135.48/19.93 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25))
% 135.48/19.93 | |
% 135.48/19.93 | | BETA: splitting (10) gives:
% 135.48/19.93 | |
% 135.48/19.93 | | Case 1:
% 135.48/19.93 | | |
% 135.48/19.93 | | | (11) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~
% 135.48/19.93 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.48/19.93 | | | op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 135.48/19.93 | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 135.48/19.93 | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 135.48/19.93 | | | $i(all_56_31)
% 135.48/19.93 | | |
% 135.48/19.93 | | | ALPHA: (11) implies:
% 135.48/19.93 | | | (12) op(e3, e3) = e0
% 135.48/19.93 | | |
% 135.48/19.93 | | | REF_CLOSE: (2), (4), (5), (12) are inconsistent by sub-proof #534.
% 135.48/19.93 | | |
% 135.48/19.93 | | Case 2:
% 135.48/19.93 | | |
% 135.48/19.93 | | | (13) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 135.48/19.93 | | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.48/19.93 | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.48/19.93 | | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 135.48/19.93 | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)
% 135.48/19.93 | | |
% 135.48/19.93 | | | ALPHA: (13) implies:
% 135.48/19.93 | | | (14) op(e2, e2) = e3
% 135.48/19.93 | | |
% 135.48/19.93 | | | REF_CLOSE: (1), (2), (7), (14) are inconsistent by sub-proof #228.
% 135.48/19.93 | | |
% 135.48/19.93 | | End of split
% 135.48/19.93 | |
% 135.48/19.93 | End of split
% 135.48/19.93 |
% 135.48/19.93 End of proof
% 135.48/19.93
% 135.48/19.93 Sub-proof #44 shows that the following formulas are inconsistent:
% 135.48/19.93 ----------------------------------------------------------------
% 135.48/19.93 (1) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2)
% 135.48/19.93 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3,
% 135.48/19.93 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 135.48/19.93 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.48/19.93 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 135.48/19.93 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.48/19.93 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) =
% 135.48/19.93 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.48/19.93 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.48/19.93 $i(all_56_21) & $i(all_56_29))
% 135.48/19.93 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.93 (3) op(e3, e3) = all_10_2
% 135.48/19.93 (4) ~ (all_10_2 = e2)
% 135.48/19.93 (5) op(e1, e0) = e0
% 135.48/19.93
% 135.48/19.93 Begin of proof
% 135.48/19.93 |
% 135.48/19.93 | BETA: splitting (1) gives:
% 135.48/19.93 |
% 135.48/19.93 | Case 1:
% 135.48/19.93 | |
% 135.48/19.93 | | (6) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.48/19.93 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.48/19.93 | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.48/19.93 | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.48/19.93 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)
% 135.48/19.93 | |
% 135.48/19.93 | | ALPHA: (6) implies:
% 135.48/19.93 | | (7) op(e3, e3) = e2
% 135.48/19.93 | |
% 135.48/19.93 | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #536.
% 135.48/19.93 | |
% 135.48/19.93 | Case 2:
% 135.48/19.93 | |
% 135.48/19.93 | | (8) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.48/19.93 | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 135.48/19.93 | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 135.48/19.93 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.48/19.93 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 135.48/19.93 | |
% 135.48/19.93 | | ALPHA: (8) implies:
% 135.48/19.93 | | (9) ~ (all_56_29 = e0)
% 135.48/19.93 | | (10) op(e1, e0) = all_56_29
% 135.48/19.93 | |
% 135.48/19.93 | | REF_CLOSE: (2), (5), (9), (10) are inconsistent by sub-proof #45.
% 135.48/19.93 | |
% 135.48/19.93 | End of split
% 135.48/19.93 |
% 135.48/19.93 End of proof
% 135.48/19.93
% 135.48/19.93 Sub-proof #45 shows that the following formulas are inconsistent:
% 135.48/19.93 ----------------------------------------------------------------
% 135.48/19.93 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.93 (2) op(e1, e0) = all_56_29
% 135.48/19.93 (3) op(e1, e0) = e0
% 135.48/19.93 (4) ~ (all_56_29 = e0)
% 135.48/19.93
% 135.48/19.93 Begin of proof
% 135.48/19.93 |
% 135.48/19.93 | GROUND_INST: instantiating (1) with e0, all_56_29, e0, e1, simplifying with
% 135.48/19.93 | (2), (3) gives:
% 135.48/19.93 | (5) all_56_29 = e0
% 135.48/19.93 |
% 135.48/19.93 | REDUCE: (4), (5) imply:
% 135.48/19.93 | (6) $false
% 135.48/19.93 |
% 135.48/19.93 | CLOSE: (6) is inconsistent.
% 135.48/19.93 |
% 135.48/19.93 End of proof
% 135.48/19.93
% 135.48/19.93 Sub-proof #46 shows that the following formulas are inconsistent:
% 135.48/19.93 ----------------------------------------------------------------
% 135.48/19.93 (1) ~ (all_52_14 = e3)
% 135.48/19.93 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.93 (3) op(e0, e0) = e1
% 135.48/19.93 (4) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 135.48/19.93 (5) ~ (e3 = e1)
% 135.48/19.93 (6) op(e1, e0) = all_52_14
% 135.48/19.93
% 135.48/19.93 Begin of proof
% 135.48/19.93 |
% 135.48/19.93 | BETA: splitting (4) gives:
% 135.48/19.93 |
% 135.48/19.93 | Case 1:
% 135.48/19.93 | |
% 135.48/19.93 | | (7) all_57_11 = e3 & op(e1, e0) = e3
% 135.48/19.93 | |
% 135.48/19.93 | | REF_CLOSE: (1), (2), (6), (7) are inconsistent by sub-proof #750.
% 135.48/19.93 | |
% 135.48/19.93 | Case 2:
% 135.48/19.93 | |
% 135.48/19.93 | | (8) all_57_15 = e3 & op(e0, e0) = e3
% 135.48/19.93 | |
% 135.48/19.93 | | ALPHA: (8) implies:
% 135.48/19.94 | | (9) op(e0, e0) = e3
% 135.48/19.94 | |
% 135.48/19.94 | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #606.
% 135.48/19.94 | |
% 135.48/19.94 | End of split
% 135.48/19.94 |
% 135.48/19.94 End of proof
% 135.48/19.94
% 135.48/19.94 Sub-proof #47 shows that the following formulas are inconsistent:
% 135.48/19.94 ----------------------------------------------------------------
% 135.48/19.94 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.94 (2) ~ (e2 = e1)
% 135.48/19.94 (3) op(e1, e3) = e2
% 135.48/19.94 (4) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 135.48/19.94 (5) ~ (all_52_3 = e1)
% 135.48/19.94 (6) op(e1, e3) = all_52_2
% 135.48/19.94 (7) op(e0, e3) = all_52_3
% 135.48/19.94
% 135.48/19.94 Begin of proof
% 135.48/19.94 |
% 135.48/19.94 | BETA: splitting (4) gives:
% 135.48/19.94 |
% 135.48/19.94 | Case 1:
% 135.48/19.94 | |
% 135.48/19.94 | | (8) all_57_6 = e1 & op(e1, e3) = e1
% 135.48/19.94 | |
% 135.48/19.94 | | ALPHA: (8) implies:
% 135.48/19.94 | | (9) op(e1, e3) = e1
% 135.48/19.94 | |
% 135.48/19.94 | | REF_CLOSE: (1), (2), (3), (6), (9) are inconsistent by sub-proof #517.
% 135.48/19.94 | |
% 135.48/19.94 | Case 2:
% 135.48/19.94 | |
% 135.48/19.94 | | (10) all_57_12 = e1 & op(e0, e3) = e1
% 135.48/19.94 | |
% 135.48/19.94 | | REF_CLOSE: (1), (5), (7), (10) are inconsistent by sub-proof #48.
% 135.48/19.94 | |
% 135.48/19.94 | End of split
% 135.48/19.94 |
% 135.48/19.94 End of proof
% 135.48/19.94
% 135.48/19.94 Sub-proof #48 shows that the following formulas are inconsistent:
% 135.48/19.94 ----------------------------------------------------------------
% 135.48/19.94 (1) all_57_12 = e1 & op(e0, e3) = e1
% 135.48/19.94 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.94 (3) op(e0, e3) = all_52_3
% 135.48/19.94 (4) ~ (all_52_3 = e1)
% 135.48/19.94
% 135.48/19.94 Begin of proof
% 135.48/19.94 |
% 135.48/19.94 | ALPHA: (1) implies:
% 135.48/19.94 | (5) op(e0, e3) = e1
% 135.48/19.94 |
% 135.48/19.94 | GROUND_INST: instantiating (2) with all_52_3, e1, e3, e0, simplifying with
% 135.48/19.94 | (3), (5) gives:
% 135.48/19.94 | (6) all_52_3 = e1
% 135.48/19.94 |
% 135.48/19.94 | REDUCE: (4), (6) imply:
% 135.48/19.94 | (7) $false
% 135.48/19.94 |
% 135.48/19.94 | CLOSE: (7) is inconsistent.
% 135.48/19.94 |
% 135.48/19.94 End of proof
% 135.48/19.94
% 135.48/19.94 Sub-proof #49 shows that the following formulas are inconsistent:
% 135.48/19.94 ----------------------------------------------------------------
% 135.48/19.94 (1) all_57_6 = e0
% 135.48/19.94 (2) ~ (e2 = e0)
% 135.48/19.94 (3) all_57_12 = e0
% 135.48/19.94 (4) op(e3, e3) = e1
% 135.48/19.94 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.94 (6) ~ (e2 = e1)
% 135.48/19.94 (7) ~ (e3 = e2)
% 135.48/19.94 (8) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 135.48/19.94 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 135.48/19.94 (9) all_57_2 = e3
% 135.48/19.94
% 135.48/19.94 Begin of proof
% 135.48/19.94 |
% 135.48/19.94 | BETA: splitting (8) gives:
% 135.48/19.94 |
% 135.48/19.94 | Case 1:
% 135.48/19.94 | |
% 135.48/19.94 | | (10) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) =
% 135.48/19.94 | | e2)
% 135.48/19.94 | |
% 135.48/19.94 | | BETA: splitting (10) gives:
% 135.48/19.94 | |
% 135.48/19.94 | | Case 1:
% 135.48/19.94 | | |
% 135.48/19.94 | | | (11) all_57_0 = e2 & op(e3, e3) = e2
% 135.48/19.94 | | |
% 135.48/19.94 | | | ALPHA: (11) implies:
% 135.48/19.94 | | | (12) op(e3, e3) = e2
% 135.48/19.94 | | |
% 135.48/19.94 | | | REF_CLOSE: (4), (5), (6), (12) are inconsistent by sub-proof #743.
% 135.48/19.94 | | |
% 135.48/19.94 | | Case 2:
% 135.48/19.94 | | |
% 135.48/19.94 | | | (13) all_57_2 = e2 & op(e2, e3) = e2
% 135.48/19.94 | | |
% 135.48/19.94 | | | REF_CLOSE: (7), (9), (13) are inconsistent by sub-proof #454.
% 135.48/19.94 | | |
% 135.48/19.94 | | End of split
% 135.48/19.94 | |
% 135.48/19.94 | Case 2:
% 135.48/19.94 | |
% 135.48/19.94 | | (14) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) =
% 135.48/19.94 | | e2)
% 135.48/19.94 | |
% 135.48/19.94 | | REF_CLOSE: (1), (2), (3), (14) are inconsistent by sub-proof #140.
% 135.48/19.94 | |
% 135.48/19.94 | End of split
% 135.48/19.94 |
% 135.48/19.94 End of proof
% 135.48/19.94
% 135.48/19.94 Sub-proof #50 shows that the following formulas are inconsistent:
% 135.48/19.94 ----------------------------------------------------------------
% 135.48/19.94 (1) all_54_11 = all_12_0
% 135.48/19.94 (2) all_54_11 = e1
% 135.48/19.94 (3) ~ (all_12_0 = e1)
% 135.48/19.94
% 135.48/19.94 Begin of proof
% 135.48/19.94 |
% 135.48/19.94 | COMBINE_EQS: (1), (2) imply:
% 135.48/19.94 | (4) all_12_0 = e1
% 135.48/19.94 |
% 135.48/19.94 | SIMP: (4) implies:
% 135.48/19.94 | (5) all_12_0 = e1
% 135.48/19.94 |
% 135.48/19.94 | REDUCE: (3), (5) imply:
% 135.48/19.94 | (6) $false
% 135.48/19.94 |
% 135.48/19.94 | CLOSE: (6) is inconsistent.
% 135.48/19.94 |
% 135.48/19.94 End of proof
% 135.48/19.94
% 135.48/19.94 Sub-proof #51 shows that the following formulas are inconsistent:
% 135.48/19.94 ----------------------------------------------------------------
% 135.48/19.94 (1) all_54_11 = all_12_0
% 135.48/19.94 (2) all_54_11 = e2
% 135.48/19.94 (3) ~ (all_12_0 = e2)
% 135.48/19.94
% 135.48/19.94 Begin of proof
% 135.48/19.94 |
% 135.48/19.94 | COMBINE_EQS: (1), (2) imply:
% 135.48/19.94 | (4) all_12_0 = e2
% 135.48/19.94 |
% 135.48/19.94 | SIMP: (4) implies:
% 135.48/19.94 | (5) all_12_0 = e2
% 135.48/19.94 |
% 135.48/19.94 | REDUCE: (3), (5) imply:
% 135.48/19.94 | (6) $false
% 135.48/19.94 |
% 135.48/19.94 | CLOSE: (6) is inconsistent.
% 135.48/19.94 |
% 135.48/19.94 End of proof
% 135.48/19.94
% 135.48/19.94 Sub-proof #52 shows that the following formulas are inconsistent:
% 135.48/19.94 ----------------------------------------------------------------
% 135.48/19.94 (1) all_54_11 = all_12_0
% 135.48/19.94 (2) all_54_11 = e3
% 135.48/19.94 (3) ~ (all_12_0 = e3)
% 135.48/19.94
% 135.48/19.94 Begin of proof
% 135.48/19.94 |
% 135.48/19.94 | COMBINE_EQS: (1), (2) imply:
% 135.48/19.94 | (4) all_12_0 = e3
% 135.48/19.94 |
% 135.48/19.94 | SIMP: (4) implies:
% 135.48/19.94 | (5) all_12_0 = e3
% 135.48/19.94 |
% 135.48/19.94 | REDUCE: (3), (5) imply:
% 135.48/19.94 | (6) $false
% 135.48/19.94 |
% 135.48/19.94 | CLOSE: (6) is inconsistent.
% 135.48/19.94 |
% 135.48/19.94 End of proof
% 135.48/19.94
% 135.48/19.94 Sub-proof #53 shows that the following formulas are inconsistent:
% 135.48/19.94 ----------------------------------------------------------------
% 135.48/19.94 (1) ~ (all_30_1 = e1) & op(e0, e0) = all_30_1 & $i(all_30_1)
% 135.48/19.94 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.94 (3) op(e0, e0) = e1
% 135.48/19.94
% 135.48/19.94 Begin of proof
% 135.48/19.94 |
% 135.48/19.94 | ALPHA: (1) implies:
% 135.48/19.94 | (4) ~ (all_30_1 = e1)
% 135.48/19.94 | (5) op(e0, e0) = all_30_1
% 135.48/19.94 |
% 135.48/19.94 | GROUND_INST: instantiating (2) with e1, all_30_1, e0, e0, simplifying with
% 135.48/19.94 | (3), (5) gives:
% 135.48/19.94 | (6) all_30_1 = e1
% 135.48/19.94 |
% 135.48/19.94 | REDUCE: (4), (6) imply:
% 135.48/19.94 | (7) $false
% 135.48/19.94 |
% 135.48/19.94 | CLOSE: (7) is inconsistent.
% 135.48/19.94 |
% 135.48/19.94 End of proof
% 135.48/19.94
% 135.48/19.94 Sub-proof #54 shows that the following formulas are inconsistent:
% 135.48/19.94 ----------------------------------------------------------------
% 135.48/19.94 (1) all_54_13 = all_30_0
% 135.48/19.94 (2) all_54_13 = e3
% 135.48/19.94 (3) ~ (all_30_0 = e3)
% 135.48/19.94
% 135.48/19.94 Begin of proof
% 135.48/19.94 |
% 135.48/19.94 | COMBINE_EQS: (1), (2) imply:
% 135.48/19.94 | (4) all_30_0 = e3
% 135.48/19.94 |
% 135.48/19.94 | SIMP: (4) implies:
% 135.48/19.94 | (5) all_30_0 = e3
% 135.48/19.94 |
% 135.48/19.94 | REDUCE: (3), (5) imply:
% 135.48/19.94 | (6) $false
% 135.48/19.94 |
% 135.48/19.94 | CLOSE: (6) is inconsistent.
% 135.48/19.94 |
% 135.48/19.94 End of proof
% 135.48/19.94
% 135.48/19.94 Sub-proof #55 shows that the following formulas are inconsistent:
% 135.48/19.94 ----------------------------------------------------------------
% 135.48/19.94 (1) op(e2, e1) = e1
% 135.48/19.94 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.94 (3) op(e0, e0) = e1
% 135.48/19.94 (4) op(e0, e1) = all_52_11
% 135.48/19.94 (5) ~ (all_52_14 = e1)
% 135.48/19.94 (6) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2)
% 135.48/19.94 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.48/19.94 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25
% 135.48/19.94 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.48/19.94 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3)
% 135.48/19.94 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.48/19.94 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 135.48/19.94 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) &
% 135.48/19.94 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 &
% 135.48/19.94 all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~
% 135.48/19.94 (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) =
% 135.48/19.94 e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) =
% 135.48/19.94 all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23
% 135.48/19.94 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.48/19.94 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1,
% 135.48/19.94 e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 135.48/19.94 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.48/19.94 $i(all_56_29))
% 135.48/19.94 (7) ~ (all_52_11 = e0)
% 135.48/19.94 (8) ~ (e3 = e1)
% 135.48/19.94 (9) op(e1, e0) = all_52_14
% 135.48/19.94 (10) op(e0, e0) = all_56_31
% 135.48/19.94
% 135.48/19.94 Begin of proof
% 135.48/19.94 |
% 135.48/19.94 | BETA: splitting (6) gives:
% 135.48/19.94 |
% 135.48/19.94 | Case 1:
% 135.48/19.94 | |
% 135.48/19.94 | | (11) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 135.48/19.94 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.48/19.94 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.48/19.94 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9)
% 135.48/19.94 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 135.48/19.94 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.48/19.94 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 135.48/19.94 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 135.48/19.94 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.48/19.94 | | $i(all_56_27))
% 135.48/19.94 | |
% 135.48/19.94 | | REF_CLOSE: (1), (2), (3), (8), (10), (11) are inconsistent by sub-proof #56.
% 135.48/19.94 | |
% 135.48/19.94 | Case 2:
% 135.48/19.94 | |
% 135.48/19.94 | | (12) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.48/19.94 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.48/19.94 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.48/19.94 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 135.48/19.94 | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 135.48/19.94 | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 135.48/19.94 | | ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.48/19.94 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 135.48/19.94 | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.48/19.94 | | $i(all_56_29))
% 135.48/19.94 | |
% 135.48/19.94 | | BETA: splitting (12) gives:
% 135.48/19.94 | |
% 135.48/19.94 | | Case 1:
% 135.48/19.94 | | |
% 135.48/19.94 | | | (13) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.48/19.94 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.48/19.94 | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.48/19.94 | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 135.48/19.94 | | | $i(all_56_15) & $i(all_56_23)
% 135.48/19.94 | | |
% 135.48/19.94 | | | ALPHA: (13) implies:
% 135.48/19.94 | | | (14) op(e1, e0) = e1
% 135.48/19.94 | | |
% 135.48/19.94 | | | REF_CLOSE: (2), (5), (9), (14) are inconsistent by sub-proof #327.
% 135.48/19.94 | | |
% 135.48/19.94 | | Case 2:
% 135.48/19.94 | | |
% 135.48/19.94 | | | (15) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 135.48/19.94 | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 135.48/19.94 | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.48/19.94 | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.48/19.94 | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 135.48/19.94 | | |
% 135.48/19.94 | | | ALPHA: (15) implies:
% 135.48/19.94 | | | (16) op(e0, e1) = e0
% 135.48/19.94 | | |
% 135.48/19.94 | | | GROUND_INST: instantiating (2) with all_52_11, e0, e1, e0, simplifying
% 135.48/19.94 | | | with (4), (16) gives:
% 135.48/19.94 | | | (17) all_52_11 = e0
% 135.48/19.94 | | |
% 135.48/19.94 | | | REDUCE: (7), (17) imply:
% 135.48/19.94 | | | (18) $false
% 135.48/19.94 | | |
% 135.48/19.94 | | | CLOSE: (18) is inconsistent.
% 135.48/19.94 | | |
% 135.48/19.94 | | End of split
% 135.48/19.94 | |
% 135.48/19.94 | End of split
% 135.48/19.94 |
% 135.48/19.94 End of proof
% 135.48/19.94
% 135.48/19.94 Sub-proof #56 shows that the following formulas are inconsistent:
% 135.48/19.94 ----------------------------------------------------------------
% 135.48/19.94 (1) op(e2, e1) = e1
% 135.48/19.94 (2) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2)
% 135.48/19.94 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.48/19.94 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25
% 135.48/19.94 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.48/19.94 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3)
% 135.48/19.94 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.48/19.94 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 135.48/19.94 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) &
% 135.48/19.94 $i(all_56_11) & $i(all_56_19) & $i(all_56_27))
% 135.48/19.94 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.94 (4) op(e0, e0) = e1
% 135.48/19.94 (5) ~ (e3 = e1)
% 135.48/19.94 (6) op(e0, e0) = all_56_31
% 135.48/19.94
% 135.48/19.94 Begin of proof
% 135.48/19.94 |
% 135.48/19.94 | BETA: splitting (2) gives:
% 135.48/19.94 |
% 135.48/19.94 | Case 1:
% 135.48/19.94 | |
% 135.48/19.94 | | (7) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 135.48/19.94 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.48/19.94 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.48/19.94 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.48/19.94 | | $i(all_56_17) & $i(all_56_25)
% 135.48/19.94 | |
% 135.48/19.94 | | ALPHA: (7) implies:
% 135.48/19.94 | | (8) all_56_31 = e3
% 135.48/19.94 | |
% 135.48/19.94 | | REDUCE: (6), (8) imply:
% 135.48/19.94 | | (9) op(e0, e0) = e3
% 135.48/19.94 | |
% 135.48/19.94 | | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #606.
% 135.48/19.94 | |
% 135.48/19.94 | Case 2:
% 135.48/19.94 | |
% 135.48/19.94 | | (10) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11
% 135.48/19.94 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.48/19.94 | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 135.48/19.94 | | e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.48/19.94 | | $i(all_56_19) & $i(all_56_27)
% 135.48/19.94 | |
% 135.48/19.94 | | ALPHA: (10) implies:
% 135.48/19.94 | | (11) ~ (all_56_19 = e1)
% 135.48/19.94 | | (12) op(e2, e1) = all_56_19
% 135.48/19.94 | |
% 135.48/19.94 | | REF_CLOSE: (1), (3), (11), (12) are inconsistent by sub-proof #106.
% 135.48/19.94 | |
% 135.48/19.94 | End of split
% 135.48/19.94 |
% 135.48/19.94 End of proof
% 135.48/19.94
% 135.48/19.94 Sub-proof #57 shows that the following formulas are inconsistent:
% 135.48/19.94 ----------------------------------------------------------------
% 135.48/19.94 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.94 (2) op(e2, e2) = all_8_2
% 135.48/19.94 (3) op(e2, e2) = e1
% 135.48/19.94 (4) ~ (all_8_2 = e1)
% 135.48/19.94
% 135.48/19.94 Begin of proof
% 135.48/19.94 |
% 135.48/19.94 | GROUND_INST: instantiating (1) with all_8_2, e1, e2, e2, simplifying with (2),
% 135.48/19.94 | (3) gives:
% 135.48/19.94 | (5) all_8_2 = e1
% 135.48/19.94 |
% 135.48/19.94 | REDUCE: (4), (5) imply:
% 135.48/19.94 | (6) $false
% 135.48/19.94 |
% 135.48/19.94 | CLOSE: (6) is inconsistent.
% 135.48/19.94 |
% 135.48/19.94 End of proof
% 135.48/19.94
% 135.48/19.94 Sub-proof #58 shows that the following formulas are inconsistent:
% 135.48/19.94 ----------------------------------------------------------------
% 135.48/19.94 (1) op(e2, e2) = all_8_2
% 135.48/19.94 (2) op(e1, e1) = all_6_2
% 135.48/19.94 (3) ~ (all_8_2 = e1)
% 135.48/19.94 (4) ~ (all_6_2 = e3)
% 135.48/19.94 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.94 (6) ~ (all_52_11 = all_6_2)
% 135.48/19.94 (7) op(e0, e1) = all_52_11
% 135.48/19.94 (8) op(e0, e2) = all_52_7
% 135.48/19.94 (9) all_54_10 = all_6_2
% 135.48/19.94 (10) ~ (all_6_2 = e2)
% 135.48/19.94 (11) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 135.48/19.94 (12) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 135.48/19.94 (13) all_54_5 = all_8_2
% 135.48/19.94 (14) op(e3, e3) = e3
% 135.48/19.94 (15) ~ (all_52_14 = e1)
% 135.48/19.94 (16) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 135.48/19.94 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.48/19.94 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0)
% 135.48/19.94 = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.48/19.94 $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~
% 135.48/19.94 (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.48/19.94 (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.48/19.94 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.48/19.94 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.48/19.94 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 135.48/19.94 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 135.48/19.94 op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 135.48/19.94 op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 135.48/19.94 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13
% 135.48/19.94 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 135.48/19.94 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1,
% 135.48/19.94 e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.48/19.94 $i(all_56_21) & $i(all_56_29))
% 135.48/19.94 (17) ~ (all_52_7 = all_8_2)
% 135.48/19.94 (18) ~ (all_8_2 = e3)
% 135.48/19.94 (19) op(e1, e0) = all_52_14
% 135.48/19.94
% 135.48/19.94 Begin of proof
% 135.48/19.94 |
% 135.48/19.94 | BETA: splitting (16) gives:
% 135.48/19.94 |
% 135.48/19.94 | Case 1:
% 135.48/19.94 | |
% 135.48/19.94 | | (20) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 135.48/19.94 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.48/19.94 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.48/19.94 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9)
% 135.48/19.94 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 135.48/19.94 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.48/19.94 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 135.48/19.94 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 135.48/19.94 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.48/19.94 | | $i(all_56_27))
% 135.48/19.94 | |
% 135.48/19.94 | | BETA: splitting (20) gives:
% 135.48/19.94 | |
% 135.48/19.94 | | Case 1:
% 135.48/19.94 | | |
% 135.48/19.94 | | | (21) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 135.48/19.94 | | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.48/19.94 | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.48/19.94 | | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9)
% 135.48/19.94 | | | & $i(all_56_17) & $i(all_56_25)
% 135.48/19.94 | | |
% 135.48/19.94 | | | ALPHA: (21) implies:
% 135.48/19.94 | | | (22) ~ (all_56_1 = e3)
% 135.48/19.94 | | | (23) op(e3, e3) = all_56_1
% 135.48/19.94 | | |
% 135.48/19.94 | | | REF_CLOSE: (5), (14), (22), (23) are inconsistent by sub-proof #766.
% 135.48/19.94 | | |
% 135.48/19.94 | | Case 2:
% 135.48/19.94 | | |
% 135.48/19.94 | | | (24) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 135.48/19.94 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.48/19.94 | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.48/19.94 | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.48/19.94 | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)
% 135.48/19.94 | | |
% 135.48/19.94 | | | ALPHA: (24) implies:
% 135.48/19.94 | | | (25) ~ (all_56_11 = e2)
% 135.48/19.94 | | | (26) op(e0, e2) = e0
% 135.48/19.94 | | | (27) op(e2, e2) = all_56_11
% 135.48/19.94 | | |
% 135.48/19.94 | | | REF_CLOSE: (1), (3), (5), (8), (11), (13), (17), (18), (25), (26), (27)
% 135.48/19.94 | | | are inconsistent by sub-proof #227.
% 135.48/19.94 | | |
% 135.48/19.94 | | End of split
% 135.48/19.94 | |
% 135.48/19.94 | Case 2:
% 135.48/19.94 | |
% 135.48/19.94 | | (28) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.48/19.94 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.48/19.94 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.48/19.94 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 135.48/19.94 | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 135.48/19.94 | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 135.48/19.94 | | ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.48/19.94 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 135.48/19.94 | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.48/19.94 | | $i(all_56_29))
% 135.48/19.94 | |
% 135.48/19.94 | | REF_CLOSE: (2), (4), (5), (6), (7), (9), (10), (12), (15), (19), (28) are
% 135.48/19.94 | | inconsistent by sub-proof #59.
% 135.48/19.94 | |
% 135.48/19.94 | End of split
% 135.48/19.94 |
% 135.48/19.94 End of proof
% 135.48/19.94
% 135.48/19.94 Sub-proof #59 shows that the following formulas are inconsistent:
% 135.48/19.94 ----------------------------------------------------------------
% 135.48/19.94 (1) op(e1, e1) = all_6_2
% 135.48/19.94 (2) ~ (all_6_2 = e3)
% 135.48/19.94 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.94 (4) ~ (all_52_11 = all_6_2)
% 135.48/19.94 (5) op(e0, e1) = all_52_11
% 135.48/19.94 (6) all_54_10 = all_6_2
% 135.48/19.94 (7) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 135.48/19.94 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 135.48/19.94 op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 135.48/19.94 op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 135.48/19.94 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.48/19.94 e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 135.48/19.94 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.48/19.94 = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.48/19.94 $i(all_56_21) & $i(all_56_29))
% 135.48/19.94 (8) ~ (all_6_2 = e2)
% 135.48/19.94 (9) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 135.48/19.94 (10) ~ (all_52_14 = e1)
% 135.48/19.94 (11) op(e1, e0) = all_52_14
% 135.48/19.94
% 135.48/19.94 Begin of proof
% 135.48/19.94 |
% 135.48/19.94 | BETA: splitting (7) gives:
% 135.48/19.94 |
% 135.48/19.95 | Case 1:
% 135.48/19.95 | |
% 135.48/19.95 | | (12) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15
% 135.48/19.95 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) =
% 135.48/19.95 | | e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.48/19.95 | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 135.48/19.95 | | $i(all_56_23)
% 135.48/19.95 | |
% 135.48/19.95 | | ALPHA: (12) implies:
% 135.48/19.95 | | (13) op(e1, e0) = e1
% 135.48/19.95 | |
% 135.48/19.95 | | REF_CLOSE: (3), (10), (11), (13) are inconsistent by sub-proof #327.
% 135.48/19.95 | |
% 135.48/19.95 | Case 2:
% 135.48/19.95 | |
% 135.48/19.95 | | (14) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13
% 135.48/19.95 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 135.48/19.95 | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1,
% 135.48/19.95 | | e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.48/19.95 | | $i(all_56_21) & $i(all_56_29)
% 135.48/19.95 | |
% 135.48/19.95 | | ALPHA: (14) implies:
% 135.48/19.95 | | (15) ~ (all_56_21 = e1)
% 135.48/19.95 | | (16) op(e0, e1) = e0
% 135.48/19.95 | | (17) op(e1, e1) = all_56_21
% 135.48/19.95 | |
% 135.48/19.95 | | GROUND_INST: instantiating (3) with all_52_11, e0, e1, e0, simplifying with
% 135.48/19.95 | | (5), (16) gives:
% 135.48/19.95 | | (18) all_52_11 = e0
% 135.48/19.95 | |
% 135.48/19.95 | | GROUND_INST: instantiating (3) with all_6_2, all_56_21, e1, e1, simplifying
% 135.48/19.95 | | with (1), (17) gives:
% 135.48/19.95 | | (19) all_56_21 = all_6_2
% 135.48/19.95 | |
% 135.48/19.95 | | REDUCE: (4), (18) imply:
% 135.48/19.95 | | (20) ~ (all_6_2 = e0)
% 135.48/19.95 | |
% 135.48/19.95 | | SIMP: (20) implies:
% 135.48/19.95 | | (21) ~ (all_6_2 = e0)
% 135.48/19.95 | |
% 135.48/19.95 | | REF_CLOSE: (1), (2), (3), (6), (8), (9), (15), (17), (21) are inconsistent
% 135.48/19.95 | | by sub-proof #124.
% 135.48/19.95 | |
% 135.48/19.95 | End of split
% 135.48/19.95 |
% 135.48/19.95 End of proof
% 135.48/19.95
% 135.48/19.95 Sub-proof #60 shows that the following formulas are inconsistent:
% 135.48/19.95 ----------------------------------------------------------------
% 135.48/19.95 (1) op(e2, e0) = all_52_13
% 135.48/19.95 (2) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 135.48/19.95 (3) ~ (all_8_2 = e1)
% 135.48/19.95 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.95 (5) op(e2, e0) = e2
% 135.48/19.95 (6) all_54_5 = all_8_2
% 135.48/19.95 (7) ~ (all_8_2 = e0)
% 135.48/19.95 (8) ~ (all_52_13 = all_8_2)
% 135.48/19.95
% 135.48/19.95 Begin of proof
% 135.48/19.95 |
% 135.48/19.95 | BETA: splitting (2) gives:
% 135.48/19.95 |
% 135.48/19.95 | Case 1:
% 135.48/19.95 | |
% 135.48/19.95 | | (9) all_54_5 = e2
% 135.48/19.95 | |
% 135.48/19.95 | | COMBINE_EQS: (6), (9) imply:
% 135.48/19.95 | | (10) all_8_2 = e2
% 135.48/19.95 | |
% 135.48/19.95 | | SIMP: (10) implies:
% 135.48/19.95 | | (11) all_8_2 = e2
% 135.48/19.95 | |
% 135.48/19.95 | | REDUCE: (8), (11) imply:
% 135.48/19.95 | | (12) ~ (all_52_13 = e2)
% 135.48/19.95 | |
% 135.48/19.95 | | REF_CLOSE: (1), (4), (5), (12) are inconsistent by sub-proof #768.
% 135.48/19.95 | |
% 135.48/19.95 | Case 2:
% 135.48/19.95 | |
% 135.48/19.95 | | (13) all_54_5 = e1 | all_54_5 = e0
% 135.48/19.95 | |
% 135.48/19.95 | | REF_CLOSE: (3), (6), (7), (13) are inconsistent by sub-proof #624.
% 135.48/19.95 | |
% 135.48/19.95 | End of split
% 135.48/19.95 |
% 135.48/19.95 End of proof
% 135.48/19.95
% 135.48/19.95 Sub-proof #61 shows that the following formulas are inconsistent:
% 135.48/19.95 ----------------------------------------------------------------
% 135.48/19.95 (1) all_57_6 = e3 & op(e1, e3) = e3
% 135.48/19.95 (2) all_57_6 = e1
% 135.48/19.95 (3) ~ (e3 = e1)
% 135.48/19.95
% 135.48/19.95 Begin of proof
% 135.48/19.95 |
% 135.48/19.95 | ALPHA: (1) implies:
% 135.48/19.95 | (4) all_57_6 = e3
% 135.48/19.95 |
% 135.48/19.95 | COMBINE_EQS: (2), (4) imply:
% 135.48/19.95 | (5) e3 = e1
% 135.48/19.95 |
% 135.48/19.95 | REDUCE: (3), (5) imply:
% 135.48/19.95 | (6) $false
% 135.48/19.95 |
% 135.48/19.95 | CLOSE: (6) is inconsistent.
% 135.48/19.95 |
% 135.48/19.95 End of proof
% 135.48/19.95
% 135.48/19.95 Sub-proof #62 shows that the following formulas are inconsistent:
% 135.48/19.95 ----------------------------------------------------------------
% 135.48/19.95 (1) all_54_7 = all_20_0
% 135.48/19.95 (2) all_54_7 = e1
% 135.48/19.95 (3) ~ (all_20_0 = e1)
% 135.48/19.95
% 135.48/19.95 Begin of proof
% 135.48/19.95 |
% 135.48/19.95 | COMBINE_EQS: (1), (2) imply:
% 135.48/19.95 | (4) all_20_0 = e1
% 135.48/19.95 |
% 135.48/19.95 | SIMP: (4) implies:
% 135.48/19.95 | (5) all_20_0 = e1
% 135.48/19.95 |
% 135.48/19.95 | REDUCE: (3), (5) imply:
% 135.48/19.95 | (6) $false
% 135.48/19.95 |
% 135.48/19.95 | CLOSE: (6) is inconsistent.
% 135.48/19.95 |
% 135.48/19.95 End of proof
% 135.48/19.95
% 135.48/19.95 Sub-proof #63 shows that the following formulas are inconsistent:
% 135.48/19.95 ----------------------------------------------------------------
% 135.48/19.95 (1) all_54_7 = all_20_0
% 135.48/19.95 (2) all_54_7 = e2
% 135.48/19.95 (3) ~ (all_20_0 = e2)
% 135.48/19.95
% 135.48/19.95 Begin of proof
% 135.48/19.95 |
% 135.48/19.95 | COMBINE_EQS: (1), (2) imply:
% 135.48/19.95 | (4) all_20_0 = e2
% 135.48/19.95 |
% 135.48/19.95 | SIMP: (4) implies:
% 135.48/19.95 | (5) all_20_0 = e2
% 135.48/19.95 |
% 135.48/19.95 | REDUCE: (3), (5) imply:
% 135.48/19.95 | (6) $false
% 135.48/19.95 |
% 135.48/19.95 | CLOSE: (6) is inconsistent.
% 135.48/19.95 |
% 135.48/19.95 End of proof
% 135.48/19.95
% 135.48/19.95 Sub-proof #64 shows that the following formulas are inconsistent:
% 135.48/19.95 ----------------------------------------------------------------
% 135.48/19.95 (1) all_54_9 = all_52_6
% 135.48/19.95 (2) all_54_9 = e3
% 135.48/19.95 (3) ~ (all_52_6 = e3)
% 135.48/19.95
% 135.48/19.95 Begin of proof
% 135.48/19.95 |
% 135.48/19.95 | COMBINE_EQS: (1), (2) imply:
% 135.48/19.95 | (4) all_52_6 = e3
% 135.48/19.95 |
% 135.48/19.95 | SIMP: (4) implies:
% 135.48/19.95 | (5) all_52_6 = e3
% 135.48/19.95 |
% 135.48/19.95 | REDUCE: (3), (5) imply:
% 135.48/19.95 | (6) $false
% 135.48/19.95 |
% 135.48/19.95 | CLOSE: (6) is inconsistent.
% 135.48/19.95 |
% 135.48/19.95 End of proof
% 135.48/19.95
% 135.48/19.95 Sub-proof #65 shows that the following formulas are inconsistent:
% 135.48/19.95 ----------------------------------------------------------------
% 135.48/19.95 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.95 (2) op(e1, e2) = all_52_6
% 135.48/19.95 (3) op(e1, e2) = e1
% 135.48/19.95 (4) ~ (all_52_6 = e1)
% 135.48/19.95
% 135.48/19.95 Begin of proof
% 135.48/19.95 |
% 135.48/19.95 | GROUND_INST: instantiating (1) with all_52_6, e1, e2, e1, simplifying with
% 135.48/19.95 | (2), (3) gives:
% 135.48/19.95 | (5) all_52_6 = e1
% 135.48/19.95 |
% 135.48/19.95 | REDUCE: (4), (5) imply:
% 135.48/19.95 | (6) $false
% 135.48/19.95 |
% 135.48/19.95 | CLOSE: (6) is inconsistent.
% 135.48/19.95 |
% 135.48/19.95 End of proof
% 135.48/19.95
% 135.48/19.95 Sub-proof #66 shows that the following formulas are inconsistent:
% 135.48/19.95 ----------------------------------------------------------------
% 135.48/19.95 (1) all_54_0 = all_10_2
% 135.48/19.95 (2) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2)
% 135.48/19.95 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3,
% 135.48/19.95 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 135.48/19.95 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.48/19.95 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 135.48/19.95 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.48/19.95 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) =
% 135.48/19.95 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.48/19.95 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.48/19.95 $i(all_56_21) & $i(all_56_29))
% 135.48/19.95 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.95 (4) ~ (all_10_2 = e0)
% 135.48/19.95 (5) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 135.48/19.95 (6) op(e3, e3) = all_10_2
% 135.48/19.95 (7) ~ (all_10_2 = e2)
% 135.48/19.95 (8) ~ (all_10_2 = e1)
% 135.48/19.95
% 135.48/19.95 Begin of proof
% 135.48/19.95 |
% 135.48/19.95 | BETA: splitting (2) gives:
% 135.48/19.95 |
% 135.48/19.95 | Case 1:
% 135.48/19.95 | |
% 135.48/19.95 | | (9) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.48/19.95 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.48/19.95 | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.48/19.95 | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.48/19.95 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)
% 135.48/19.95 | |
% 135.48/19.95 | | ALPHA: (9) implies:
% 135.48/19.95 | | (10) op(e3, e3) = e2
% 135.48/19.95 | |
% 135.48/19.95 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10) are inconsistent by
% 135.48/19.95 | | sub-proof #776.
% 135.48/19.95 | |
% 135.48/19.95 | Case 2:
% 135.48/19.95 | |
% 135.48/19.95 | | (11) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13
% 135.48/19.95 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) =
% 135.48/19.95 | | e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.48/19.95 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 135.48/19.95 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 135.48/19.95 | |
% 135.48/19.95 | | ALPHA: (11) implies:
% 135.48/19.95 | | (12) op(e3, e3) = e1
% 135.48/19.95 | |
% 135.48/19.95 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (12) are inconsistent by
% 135.48/19.95 | | sub-proof #774.
% 135.48/19.95 | |
% 135.48/19.95 | End of split
% 135.48/19.95 |
% 135.48/19.95 End of proof
% 135.48/19.95
% 135.48/19.95 Sub-proof #67 shows that the following formulas are inconsistent:
% 135.48/19.95 ----------------------------------------------------------------
% 135.48/19.95 (1) op(e1, e1) = all_6_2
% 135.48/19.95 (2) ~ (all_40_2 = e0) | ( ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 &
% 135.48/19.95 $i(all_40_0)) | ( ~ (all_40_1 = e2) & op(e0, e0) = all_40_1 &
% 135.48/19.95 $i(all_40_1))
% 135.48/19.95 (3) ~ (all_52_11 = e2)
% 135.48/19.95 (4) all_40_2 = all_6_2
% 135.48/19.95 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.95 (6) ~ (e2 = e1)
% 135.48/19.95 (7) ~ (e3 = e2)
% 135.48/19.95 (8) ~ (all_52_11 = all_6_2)
% 135.48/19.95 (9) op(e0, e1) = all_52_11
% 135.48/19.95 (10) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 135.48/19.95 (11) op(e2, e0) = e0
% 135.48/19.95 (12) op(e0, e0) = e2
% 135.48/19.95 (13) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.48/19.95 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.48/19.95 all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 135.48/19.95 e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 135.48/19.95 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 135.48/19.95 all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~
% 135.48/19.95 (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 135.48/19.95 (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 &
% 135.48/19.95 op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0
% 135.48/19.95 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 135.48/19.95 (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 135.48/19.95 (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.48/19.95 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.48/19.95 all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.48/19.95 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.48/19.95 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.48/19.95 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.48/19.95 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.48/19.95 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 135.48/19.95 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 135.48/19.95 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 135.48/19.95 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.48/19.95 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 135.48/19.95 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.48/19.95 $i(all_56_29))))
% 135.48/19.95 (14) all_54_14 = all_52_11
% 135.48/19.95
% 135.48/19.95 Begin of proof
% 135.48/19.95 |
% 135.48/19.95 | BETA: splitting (13) gives:
% 135.48/19.95 |
% 135.48/19.95 | Case 1:
% 135.48/19.95 | |
% 135.48/19.95 | | (15) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11
% 135.48/19.95 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.48/19.95 | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 135.48/19.95 | | e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3)
% 135.48/19.95 | | & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)
% 135.48/19.95 | |
% 135.48/19.95 | | ALPHA: (15) implies:
% 135.48/19.95 | | (16) ~ (all_56_27 = e0)
% 135.48/19.95 | | (17) op(e2, e0) = all_56_27
% 135.48/19.95 | |
% 135.48/19.95 | | REF_CLOSE: (5), (11), (16), (17) are inconsistent by sub-proof #275.
% 135.48/19.95 | |
% 135.48/19.95 | Case 2:
% 135.48/19.95 | |
% 135.48/19.95 | | (18) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31
% 135.48/19.95 | | = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 135.48/19.95 | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2)
% 135.48/19.95 | | = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.48/19.95 | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.48/19.95 | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3
% 135.48/19.95 | | = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.48/19.95 | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 135.48/19.95 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 135.48/19.95 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.48/19.95 | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7
% 135.48/19.95 | | = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.48/19.95 | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 135.48/19.95 | | e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) =
% 135.48/19.95 | | all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 135.48/19.95 | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 135.48/19.95 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 135.48/19.95 | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.48/19.95 | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.48/19.95 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)))
% 135.48/19.95 | |
% 135.48/19.95 | | ALPHA: (18) implies:
% 135.48/19.95 | | (19) op(e0, e0) = all_56_31
% 135.48/19.95 | | (20) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 135.48/19.95 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.48/19.95 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.48/19.95 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9)
% 135.48/19.95 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 135.48/19.95 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.48/19.95 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 135.48/19.95 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 135.48/19.95 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.48/19.95 | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 135.48/19.95 | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31
% 135.48/19.95 | | = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 135.48/19.95 | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.48/19.95 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 &
% 135.48/19.95 | | all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.48/19.95 | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 135.48/19.95 | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 135.48/19.95 | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.48/19.95 | | $i(all_56_21) & $i(all_56_29))
% 135.48/19.95 | |
% 135.48/19.95 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 135.48/19.95 | | (14), (19), (20) are inconsistent by sub-proof #273.
% 135.48/19.95 | |
% 135.48/19.95 | End of split
% 135.48/19.95 |
% 135.48/19.95 End of proof
% 135.48/19.95
% 135.48/19.95 Sub-proof #68 shows that the following formulas are inconsistent:
% 135.48/19.95 ----------------------------------------------------------------
% 135.48/19.95 (1) op(e2, e2) = all_8_2
% 135.48/19.95 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.95 (3) op(e0, e3) = e3
% 135.48/19.95 (4) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 135.48/19.95 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.48/19.95 op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 135.48/19.95 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.48/19.95 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 &
% 135.48/19.95 all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~
% 135.48/19.95 (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3,
% 135.48/19.95 e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.48/19.95 op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.48/19.95 $i(all_56_17) & $i(all_56_25))
% 135.48/19.95 (5) ~ (all_8_2 = e3)
% 135.48/19.95
% 135.48/19.95 Begin of proof
% 135.48/19.95 |
% 135.48/19.95 | BETA: splitting (4) gives:
% 135.48/19.95 |
% 135.48/19.95 | Case 1:
% 135.48/19.95 | |
% 135.48/19.95 | | (6) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 135.48/19.95 | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.48/19.95 | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 135.48/19.95 | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.48/19.95 | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)
% 135.48/19.95 | |
% 135.48/19.95 | | ALPHA: (6) implies:
% 135.48/19.95 | | (7) ~ (all_56_7 = e3)
% 135.48/19.95 | | (8) op(e0, e3) = all_56_7
% 135.48/19.95 | |
% 135.48/19.95 | | REF_CLOSE: (2), (3), (7), (8) are inconsistent by sub-proof #209.
% 135.48/19.95 | |
% 135.48/19.95 | Case 2:
% 135.48/19.95 | |
% 135.48/19.95 | | (9) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 135.48/19.95 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.48/19.95 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.48/19.95 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1)
% 135.48/19.95 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)
% 135.48/19.95 | |
% 135.48/19.95 | | ALPHA: (9) implies:
% 135.48/19.95 | | (10) op(e2, e2) = e3
% 135.48/19.95 | |
% 135.48/19.95 | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #228.
% 135.48/19.95 | |
% 135.48/19.95 | End of split
% 135.48/19.95 |
% 135.48/19.95 End of proof
% 135.48/19.95
% 135.48/19.95 Sub-proof #69 shows that the following formulas are inconsistent:
% 135.48/19.95 ----------------------------------------------------------------
% 135.48/19.95 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.95 (2) ~ (e2 = e1)
% 135.48/19.95 (3) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1)
% 135.48/19.95 (4) op(e3, e3) = e0
% 135.48/19.95 (5) ~ (e1 = e0)
% 135.48/19.95 (6) op(e2, e3) = e2
% 135.48/19.95
% 135.48/19.95 Begin of proof
% 135.48/19.95 |
% 135.48/19.95 | BETA: splitting (3) gives:
% 135.48/19.95 |
% 135.48/19.95 | Case 1:
% 135.48/19.95 | |
% 135.48/19.95 | | (7) all_57_0 = e1 & op(e3, e3) = e1
% 135.48/19.95 | |
% 135.48/19.95 | | ALPHA: (7) implies:
% 135.48/19.95 | | (8) op(e3, e3) = e1
% 135.48/19.95 | |
% 135.48/19.95 | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #717.
% 135.48/19.95 | |
% 135.48/19.95 | Case 2:
% 135.48/19.95 | |
% 135.48/19.95 | | (9) all_57_2 = e1 & op(e2, e3) = e1
% 135.48/19.95 | |
% 135.48/19.95 | | ALPHA: (9) implies:
% 135.48/19.95 | | (10) op(e2, e3) = e1
% 135.48/19.95 | |
% 135.48/19.95 | | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #450.
% 135.48/19.95 | |
% 135.48/19.95 | End of split
% 135.48/19.95 |
% 135.48/19.95 End of proof
% 135.48/19.95
% 135.48/19.95 Sub-proof #70 shows that the following formulas are inconsistent:
% 135.48/19.95 ----------------------------------------------------------------
% 135.48/19.95 (1) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3)
% 135.48/19.95 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.95 (3) ~ (e3 = e0)
% 135.48/19.95 (4) ~ (e3 = e2)
% 135.48/19.95 (5) all_57_2 = e2
% 135.48/19.95 (6) op(e3, e3) = e0
% 135.48/19.95
% 135.48/19.95 Begin of proof
% 135.48/19.95 |
% 135.48/19.95 | BETA: splitting (1) gives:
% 135.48/19.95 |
% 135.48/19.95 | Case 1:
% 135.48/19.95 | |
% 135.48/19.95 | | (7) all_57_0 = e3 & op(e3, e3) = e3
% 135.48/19.95 | |
% 135.48/19.95 | | ALPHA: (7) implies:
% 135.48/19.95 | | (8) op(e3, e3) = e3
% 135.48/19.95 | |
% 135.48/19.95 | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #773.
% 135.48/19.95 | |
% 135.48/19.95 | Case 2:
% 135.48/19.95 | |
% 135.48/19.95 | | (9) all_57_2 = e3 & op(e2, e3) = e3
% 135.48/19.95 | |
% 135.48/19.95 | | ALPHA: (9) implies:
% 135.48/19.95 | | (10) all_57_2 = e3
% 135.48/19.95 | |
% 135.48/19.95 | | COMBINE_EQS: (5), (10) imply:
% 135.48/19.95 | | (11) e3 = e2
% 135.48/19.95 | |
% 135.48/19.95 | | REDUCE: (4), (11) imply:
% 135.48/19.95 | | (12) $false
% 135.48/19.95 | |
% 135.48/19.95 | | CLOSE: (12) is inconsistent.
% 135.48/19.95 | |
% 135.48/19.95 | End of split
% 135.48/19.95 |
% 135.48/19.95 End of proof
% 135.48/19.95
% 135.48/19.95 Sub-proof #71 shows that the following formulas are inconsistent:
% 135.48/19.95 ----------------------------------------------------------------
% 135.48/19.95 (1) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 135.48/19.95 (2) ~ (all_52_8 = e0)
% 135.48/19.95 (3) all_54_2 = all_52_8
% 135.48/19.95 (4) ~ (all_52_8 = e2)
% 135.48/19.95 (5) ~ (all_52_8 = e1)
% 135.48/19.95
% 135.48/19.95 Begin of proof
% 135.48/19.95 |
% 135.48/19.95 | BETA: splitting (1) gives:
% 135.48/19.95 |
% 135.48/19.95 | Case 1:
% 135.48/19.95 | |
% 135.48/19.95 | | (6) all_54_2 = e2
% 135.48/19.95 | |
% 135.48/19.95 | | REF_CLOSE: (3), (4), (6) are inconsistent by sub-proof #317.
% 135.48/19.95 | |
% 135.48/19.95 | Case 2:
% 135.48/19.95 | |
% 135.48/19.95 | | (7) all_54_2 = e1 | all_54_2 = e0
% 135.48/19.95 | |
% 135.48/19.95 | | BETA: splitting (7) gives:
% 135.48/19.95 | |
% 135.48/19.95 | | Case 1:
% 135.48/19.95 | | |
% 135.48/19.95 | | | (8) all_54_2 = e1
% 135.48/19.95 | | |
% 135.48/19.95 | | | REF_CLOSE: (3), (5), (8) are inconsistent by sub-proof #316.
% 135.48/19.95 | | |
% 135.48/19.95 | | Case 2:
% 135.48/19.95 | | |
% 135.48/19.95 | | | (9) all_54_2 = e0
% 135.48/19.95 | | |
% 135.48/19.95 | | | COMBINE_EQS: (3), (9) imply:
% 135.48/19.95 | | | (10) all_52_8 = e0
% 135.48/19.95 | | |
% 135.48/19.95 | | | SIMP: (10) implies:
% 135.48/19.95 | | | (11) all_52_8 = e0
% 135.48/19.95 | | |
% 135.48/19.95 | | | REDUCE: (2), (11) imply:
% 135.48/19.95 | | | (12) $false
% 135.48/19.95 | | |
% 135.48/19.95 | | | CLOSE: (12) is inconsistent.
% 135.48/19.95 | | |
% 135.48/19.95 | | End of split
% 135.48/19.95 | |
% 135.48/19.95 | End of split
% 135.48/19.95 |
% 135.48/19.95 End of proof
% 135.48/19.95
% 135.48/19.95 Sub-proof #72 shows that the following formulas are inconsistent:
% 135.48/19.95 ----------------------------------------------------------------
% 135.48/19.95 (1) op(e2, e2) = e0
% 135.48/19.95 (2) ~ (all_52_13 = e0)
% 135.48/19.95 (3) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 135.48/19.95 (4) ~ (all_42_0 = e1)
% 135.48/19.95 (5) ~ (all_52_4 = all_52_12)
% 135.48/19.95 (6) ~ (all_52_13 = e1)
% 135.48/19.95 (7) ~ (all_52_7 = e3)
% 135.48/19.95 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.95 (9) ~ (e3 = e0)
% 135.48/19.95 (10) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 135.48/19.95 (11) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 135.48/19.95 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 135.48/19.95 (12) all_54_3 = all_52_12
% 135.48/19.95 (13) ~ (all_52_12 = e0)
% 135.48/19.95 (14) op(e0, e2) = all_52_7
% 135.48/19.95 (15) ~ (all_52_4 = e3)
% 135.48/19.95 (16) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 135.48/19.95 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 135.48/19.96 (17) ~ (all_52_12 = all_52_13)
% 135.48/19.96 (18) op(e3, e2) = all_52_4
% 135.48/19.96 (19) op(e0, e2) = all_42_0
% 135.48/19.96 (20) ~ (all_52_13 = e3)
% 135.48/19.96 (21) op(e0, e2) = all_56_15
% 135.48/19.96 (22) all_57_2 = e3
% 135.48/19.96 (23) all_54_7 = all_52_13
% 135.48/19.96 (24) ~ (e3 = e1)
% 135.48/19.96 (25) ~ (e1 = e0)
% 135.48/19.96 (26) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 135.48/19.96 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 135.48/19.96 (27) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 135.48/19.96 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 135.48/19.96 (28) all_57_10 = e2
% 135.48/19.96 (29) ~ (all_52_12 = e3)
% 135.48/19.96
% 135.48/19.96 Begin of proof
% 135.48/19.96 |
% 135.48/19.96 | BETA: splitting (3) gives:
% 135.48/19.96 |
% 135.48/19.96 | Case 1:
% 135.48/19.96 | |
% 135.48/19.96 | | (30) all_54_7 = e3
% 135.48/19.96 | |
% 135.48/19.96 | | REF_CLOSE: (20), (23), (30) are inconsistent by sub-proof #338.
% 135.48/19.96 | |
% 135.48/19.96 | Case 2:
% 135.48/19.96 | |
% 135.48/19.96 | | (31) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 135.48/19.96 | |
% 135.48/19.96 | | BETA: splitting (31) gives:
% 135.48/19.96 | |
% 135.48/19.96 | | Case 1:
% 135.48/19.96 | | |
% 135.48/19.96 | | | (32) all_54_7 = e2
% 135.48/19.96 | | |
% 135.48/19.96 | | | COMBINE_EQS: (23), (32) imply:
% 135.48/19.96 | | | (33) all_52_13 = e2
% 135.48/19.96 | | |
% 135.48/19.96 | | | SIMP: (33) implies:
% 135.48/19.96 | | | (34) all_52_13 = e2
% 135.48/19.96 | | |
% 135.48/19.96 | | | REDUCE: (17), (34) imply:
% 135.48/19.96 | | | (35) ~ (all_52_12 = e2)
% 135.48/19.96 | | |
% 135.48/19.96 | | | REDUCE: (6), (34) imply:
% 135.48/19.96 | | | (36) ~ (e2 = e1)
% 135.48/19.96 | | |
% 135.48/19.96 | | | REDUCE: (2), (34) imply:
% 135.48/19.96 | | | (37) ~ (e2 = e0)
% 135.48/19.96 | | |
% 135.48/19.96 | | | BETA: splitting (10) gives:
% 135.48/19.96 | | |
% 135.48/19.96 | | | Case 1:
% 135.48/19.96 | | | |
% 135.48/19.96 | | | | (38) all_54_3 = e3
% 135.48/19.96 | | | |
% 135.48/19.96 | | | | COMBINE_EQS: (12), (38) imply:
% 135.48/19.96 | | | | (39) all_52_12 = e3
% 135.48/19.96 | | | |
% 135.48/19.96 | | | | REDUCE: (29), (39) imply:
% 135.48/19.96 | | | | (40) $false
% 135.48/19.96 | | | |
% 135.48/19.96 | | | | CLOSE: (40) is inconsistent.
% 135.48/19.96 | | | |
% 135.48/19.96 | | | Case 2:
% 135.48/19.96 | | | |
% 135.48/19.96 | | | | (41) ~ (all_54_3 = e3)
% 135.48/19.96 | | | | (42) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 135.48/19.96 | | | |
% 135.48/19.96 | | | | BETA: splitting (42) gives:
% 135.48/19.96 | | | |
% 135.48/19.96 | | | | Case 1:
% 135.48/19.96 | | | | |
% 135.48/19.96 | | | | | (43) all_54_3 = e2
% 135.48/19.96 | | | | |
% 135.48/19.96 | | | | | COMBINE_EQS: (12), (43) imply:
% 135.48/19.96 | | | | | (44) all_52_12 = e2
% 135.48/19.96 | | | | |
% 135.48/19.96 | | | | | REDUCE: (35), (44) imply:
% 135.48/19.96 | | | | | (45) $false
% 135.48/19.96 | | | | |
% 135.48/19.96 | | | | | CLOSE: (45) is inconsistent.
% 135.48/19.96 | | | | |
% 135.48/19.96 | | | | Case 2:
% 135.48/19.96 | | | | |
% 135.48/19.96 | | | | | (46) all_54_3 = e1 | all_54_3 = e0
% 135.48/19.96 | | | | |
% 135.48/19.96 | | | | | BETA: splitting (11) gives:
% 135.48/19.96 | | | | |
% 135.48/19.96 | | | | | Case 1:
% 135.48/19.96 | | | | | |
% 135.48/19.96 | | | | | | (47) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2,
% 135.48/19.96 | | | | | | e2) = e3)
% 135.48/19.96 | | | | | |
% 135.48/19.96 | | | | | | BETA: splitting (47) gives:
% 135.48/19.96 | | | | | |
% 135.48/19.96 | | | | | | Case 1:
% 135.48/19.96 | | | | | | |
% 135.48/19.96 | | | | | | | (48) all_57_1 = e3 & op(e3, e2) = e3
% 135.48/19.96 | | | | | | |
% 135.48/19.96 | | | | | | | ALPHA: (48) implies:
% 135.48/19.96 | | | | | | | (49) op(e3, e2) = e3
% 135.48/19.96 | | | | | | |
% 135.48/19.96 | | | | | | | REF_CLOSE: (8), (15), (18), (49) are inconsistent by sub-proof
% 135.48/19.96 | | | | | | | #738.
% 135.48/19.96 | | | | | | |
% 135.48/19.96 | | | | | | Case 2:
% 135.48/19.96 | | | | | | |
% 135.48/19.96 | | | | | | | (50) all_57_3 = e3 & op(e2, e2) = e3
% 135.48/19.96 | | | | | | |
% 135.48/19.96 | | | | | | | ALPHA: (50) implies:
% 135.48/19.96 | | | | | | | (51) all_57_3 = e3
% 135.48/19.96 | | | | | | |
% 135.48/19.96 | | | | | | | REF_CLOSE: (9), (22), (24), (25), (26), (27), (28), (36), (37),
% 135.48/19.96 | | | | | | | (51) are inconsistent by sub-proof #362.
% 135.48/19.96 | | | | | | |
% 135.48/19.96 | | | | | | End of split
% 135.48/19.96 | | | | | |
% 135.48/19.96 | | | | | Case 2:
% 135.48/19.96 | | | | | |
% 135.48/19.96 | | | | | | (52) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0,
% 135.48/19.96 | | | | | | e2) = e3)
% 135.48/19.96 | | | | | |
% 135.48/19.96 | | | | | | BETA: splitting (52) gives:
% 135.48/19.96 | | | | | |
% 135.48/19.96 | | | | | | Case 1:
% 135.48/19.96 | | | | | | |
% 135.48/19.96 | | | | | | | (53) all_57_7 = e3 & op(e1, e2) = e3
% 135.48/19.96 | | | | | | |
% 135.48/19.96 | | | | | | | ALPHA: (53) implies:
% 135.48/19.96 | | | | | | | (54) all_57_7 = e3
% 135.48/19.96 | | | | | | |
% 135.48/19.96 | | | | | | | BETA: splitting (46) gives:
% 135.48/19.96 | | | | | | |
% 135.48/19.96 | | | | | | | Case 1:
% 135.48/19.96 | | | | | | | |
% 135.48/19.96 | | | | | | | | (55) all_54_3 = e1
% 135.48/19.96 | | | | | | | |
% 135.48/19.96 | | | | | | | | COMBINE_EQS: (12), (55) imply:
% 135.48/19.96 | | | | | | | | (56) all_52_12 = e1
% 135.48/19.96 | | | | | | | |
% 135.48/19.96 | | | | | | | | REDUCE: (5), (56) imply:
% 135.48/19.96 | | | | | | | | (57) ~ (all_52_4 = e1)
% 135.48/19.96 | | | | | | | |
% 135.48/19.96 | | | | | | | | REDUCE: (29), (56) imply:
% 135.48/19.96 | | | | | | | | (58) ~ (e3 = e1)
% 135.48/19.96 | | | | | | | |
% 135.48/19.96 | | | | | | | | BETA: splitting (16) gives:
% 135.48/19.96 | | | | | | | |
% 135.48/19.96 | | | | | | | | Case 1:
% 135.48/19.96 | | | | | | | | |
% 135.48/19.96 | | | | | | | | | (59) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 &
% 135.48/19.96 | | | | | | | | | op(e2, e2) = e1)
% 135.48/19.96 | | | | | | | | |
% 135.48/19.96 | | | | | | | | | REF_CLOSE: (1), (8), (18), (25), (57), (59) are inconsistent
% 135.48/19.96 | | | | | | | | | by sub-proof #564.
% 135.48/19.96 | | | | | | | | |
% 135.48/19.96 | | | | | | | | Case 2:
% 135.48/19.96 | | | | | | | | |
% 135.48/19.96 | | | | | | | | | (60) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 &
% 135.48/19.96 | | | | | | | | | op(e0, e2) = e1)
% 135.48/19.96 | | | | | | | | |
% 135.48/19.96 | | | | | | | | | BETA: splitting (60) gives:
% 135.48/19.96 | | | | | | | | |
% 135.48/19.96 | | | | | | | | | Case 1:
% 135.48/19.96 | | | | | | | | | |
% 135.48/19.96 | | | | | | | | | | (61) all_57_7 = e1 & op(e1, e2) = e1
% 135.48/19.96 | | | | | | | | | |
% 135.48/19.96 | | | | | | | | | | REF_CLOSE: (24), (54), (61) are inconsistent by sub-proof
% 135.48/19.96 | | | | | | | | | | #603.
% 135.48/19.96 | | | | | | | | | |
% 135.48/19.96 | | | | | | | | | Case 2:
% 135.48/19.96 | | | | | | | | | |
% 135.48/19.96 | | | | | | | | | | (62) all_57_13 = e1 & op(e0, e2) = e1
% 135.48/19.96 | | | | | | | | | |
% 135.48/19.96 | | | | | | | | | | ALPHA: (62) implies:
% 135.48/19.96 | | | | | | | | | | (63) op(e0, e2) = e1
% 135.48/19.96 | | | | | | | | | |
% 135.48/19.96 | | | | | | | | | | GROUND_INST: instantiating (8) with all_42_0, all_56_15, e2,
% 135.48/19.96 | | | | | | | | | | e0, simplifying with (19), (21) gives:
% 135.48/19.96 | | | | | | | | | | (64) all_56_15 = all_42_0
% 135.48/19.96 | | | | | | | | | |
% 135.48/19.96 | | | | | | | | | | GROUND_INST: instantiating (8) with e1, all_56_15, e2, e0,
% 135.48/19.96 | | | | | | | | | | simplifying with (21), (63) gives:
% 135.48/19.96 | | | | | | | | | | (65) all_56_15 = e1
% 135.48/19.96 | | | | | | | | | |
% 135.48/19.96 | | | | | | | | | | COMBINE_EQS: (64), (65) imply:
% 135.48/19.96 | | | | | | | | | | (66) all_42_0 = e1
% 135.48/19.96 | | | | | | | | | |
% 135.48/19.96 | | | | | | | | | | REDUCE: (4), (66) imply:
% 135.48/19.96 | | | | | | | | | | (67) $false
% 135.48/19.96 | | | | | | | | | |
% 135.48/19.96 | | | | | | | | | | CLOSE: (67) is inconsistent.
% 135.48/19.96 | | | | | | | | | |
% 135.48/19.96 | | | | | | | | | End of split
% 135.48/19.96 | | | | | | | | |
% 135.48/19.96 | | | | | | | | End of split
% 135.48/19.96 | | | | | | | |
% 135.48/19.96 | | | | | | | Case 2:
% 135.48/19.96 | | | | | | | |
% 135.48/19.96 | | | | | | | | (68) all_54_3 = e0
% 135.48/19.96 | | | | | | | |
% 135.48/19.96 | | | | | | | | COMBINE_EQS: (12), (68) imply:
% 135.48/19.96 | | | | | | | | (69) all_52_12 = e0
% 135.48/19.96 | | | | | | | |
% 135.48/19.96 | | | | | | | | REDUCE: (13), (69) imply:
% 135.48/19.96 | | | | | | | | (70) $false
% 135.48/19.96 | | | | | | | |
% 135.48/19.96 | | | | | | | | CLOSE: (70) is inconsistent.
% 135.48/19.96 | | | | | | | |
% 135.48/19.96 | | | | | | | End of split
% 135.48/19.96 | | | | | | |
% 135.48/19.96 | | | | | | Case 2:
% 135.48/19.96 | | | | | | |
% 135.48/19.96 | | | | | | | (71) all_57_13 = e3 & op(e0, e2) = e3
% 135.48/19.96 | | | | | | |
% 135.48/19.96 | | | | | | | REF_CLOSE: (7), (8), (14), (71) are inconsistent by sub-proof
% 135.48/19.96 | | | | | | | #556.
% 135.48/19.96 | | | | | | |
% 135.48/19.96 | | | | | | End of split
% 135.48/19.96 | | | | | |
% 135.48/19.96 | | | | | End of split
% 135.48/19.96 | | | | |
% 135.48/19.96 | | | | End of split
% 135.48/19.96 | | | |
% 135.48/19.96 | | | End of split
% 135.48/19.96 | | |
% 135.48/19.96 | | Case 2:
% 135.48/19.96 | | |
% 135.48/19.96 | | | (72) all_54_7 = e1 | all_54_7 = e0
% 135.48/19.96 | | |
% 135.48/19.96 | | | REF_CLOSE: (2), (6), (23), (72) are inconsistent by sub-proof #313.
% 135.48/19.96 | | |
% 135.48/19.96 | | End of split
% 135.48/19.96 | |
% 135.48/19.96 | End of split
% 135.48/19.96 |
% 135.48/19.96 End of proof
% 135.48/19.96
% 135.48/19.96 Sub-proof #73 shows that the following formulas are inconsistent:
% 135.48/19.96 ----------------------------------------------------------------
% 135.48/19.96 (1) all_57_6 = e0 & op(e1, e3) = e0
% 135.48/19.96 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.96 (3) op(e1, e3) = all_52_2
% 135.48/19.96 (4) ~ (all_52_2 = e0)
% 135.48/19.96
% 135.48/19.96 Begin of proof
% 135.48/19.96 |
% 135.48/19.96 | ALPHA: (1) implies:
% 135.48/19.96 | (5) op(e1, e3) = e0
% 135.48/19.96 |
% 135.48/19.96 | GROUND_INST: instantiating (2) with all_52_2, e0, e3, e1, simplifying with
% 135.48/19.96 | (3), (5) gives:
% 135.48/19.96 | (6) all_52_2 = e0
% 135.48/19.96 |
% 135.48/19.96 | REDUCE: (4), (6) imply:
% 135.48/19.96 | (7) $false
% 135.48/19.96 |
% 135.48/19.96 | CLOSE: (7) is inconsistent.
% 135.48/19.96 |
% 135.48/19.96 End of proof
% 135.48/19.96
% 135.48/19.96 Sub-proof #74 shows that the following formulas are inconsistent:
% 135.48/19.96 ----------------------------------------------------------------
% 135.48/19.96 (1) ~ (all_6_1 = e3) & op(e2, e2) = all_6_1 & $i(all_6_1)
% 135.48/19.96 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.96 (3) op(e2, e2) = e3
% 135.48/19.96
% 135.48/19.96 Begin of proof
% 135.48/19.96 |
% 135.48/19.96 | ALPHA: (1) implies:
% 135.48/19.96 | (4) ~ (all_6_1 = e3)
% 135.48/19.96 | (5) op(e2, e2) = all_6_1
% 135.48/19.96 |
% 135.48/19.96 | GROUND_INST: instantiating (2) with e3, all_6_1, e2, e2, simplifying with (3),
% 135.48/19.96 | (5) gives:
% 135.48/19.96 | (6) all_6_1 = e3
% 135.48/19.96 |
% 135.48/19.96 | REDUCE: (4), (6) imply:
% 135.48/19.96 | (7) $false
% 135.48/19.96 |
% 135.48/19.96 | CLOSE: (7) is inconsistent.
% 135.48/19.96 |
% 135.48/19.96 End of proof
% 135.48/19.96
% 135.48/19.96 Sub-proof #75 shows that the following formulas are inconsistent:
% 135.48/19.96 ----------------------------------------------------------------
% 135.48/19.96 (1) all_54_6 = all_6_0
% 135.48/19.96 (2) all_54_6 = e0
% 135.48/19.96 (3) ~ (all_6_0 = e0)
% 135.48/19.96
% 135.48/19.96 Begin of proof
% 135.48/19.96 |
% 135.48/19.96 | COMBINE_EQS: (1), (2) imply:
% 135.48/19.96 | (4) all_6_0 = e0
% 135.48/19.96 |
% 135.48/19.96 | SIMP: (4) implies:
% 135.48/19.96 | (5) all_6_0 = e0
% 135.48/19.96 |
% 135.48/19.96 | REDUCE: (3), (5) imply:
% 135.48/19.96 | (6) $false
% 135.48/19.96 |
% 135.48/19.96 | CLOSE: (6) is inconsistent.
% 135.48/19.96 |
% 135.48/19.96 End of proof
% 135.48/19.96
% 135.48/19.96 Sub-proof #76 shows that the following formulas are inconsistent:
% 135.48/19.96 ----------------------------------------------------------------
% 135.48/19.96 (1) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 135.48/19.96 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 135.48/19.96 (2) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 135.48/19.96 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 135.48/19.96 (3) all_57_5 = e1
% 135.48/19.96 (4) ~ (e2 = e0)
% 135.48/19.96 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.96 (6) ~ (e2 = e1)
% 135.48/19.96 (7) ~ (e3 = e0)
% 135.48/19.96 (8) ~ (e3 = e2)
% 135.48/19.96 (9) all_57_8 = e2
% 135.48/19.96 (10) op(e1, e1) = e2
% 135.48/19.96 (11) ~ (all_52_9 = e3)
% 135.48/19.96 (12) op(e2, e1) = all_52_9
% 135.48/19.96 (13) op(e3, e1) = all_52_8
% 135.48/19.96 (14) ~ (e3 = e1)
% 135.48/19.96 (15) ~ (e1 = e0)
% 135.48/19.96 (16) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 135.48/19.96 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 135.48/19.96 (17) all_57_14 = e1
% 135.48/19.96
% 135.48/19.96 Begin of proof
% 135.48/19.96 |
% 135.48/19.96 | BETA: splitting (16) gives:
% 135.48/19.96 |
% 135.48/19.96 | Case 1:
% 135.48/19.96 | |
% 135.48/19.96 | | (18) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 135.48/19.96 | | e3)
% 135.48/19.96 | |
% 135.48/19.96 | | BETA: splitting (18) gives:
% 135.48/19.96 | |
% 135.48/19.96 | | Case 1:
% 135.48/19.96 | | |
% 135.48/19.96 | | | (19) all_57_4 = e3 & op(e3, e1) = e3
% 135.48/19.96 | | |
% 135.48/19.96 | | | ALPHA: (19) implies:
% 135.48/19.96 | | | (20) all_57_4 = e3
% 135.48/19.96 | | | (21) op(e3, e1) = e3
% 135.48/19.96 | | |
% 135.48/19.96 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (13), (14), (15), (17),
% 135.48/19.96 | | | (20), (21) are inconsistent by sub-proof #82.
% 135.48/19.96 | | |
% 135.48/19.96 | | Case 2:
% 135.48/19.96 | | |
% 135.48/19.96 | | | (22) all_57_5 = e3 & op(e2, e1) = e3
% 135.48/19.96 | | |
% 135.48/19.96 | | | REF_CLOSE: (5), (11), (12), (22) are inconsistent by sub-proof #547.
% 135.48/19.96 | | |
% 135.48/19.96 | | End of split
% 135.48/19.96 | |
% 135.48/19.96 | Case 2:
% 135.48/19.96 | |
% 135.48/19.96 | | (23) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 135.48/19.96 | | e3)
% 135.48/19.96 | |
% 135.48/19.96 | | REF_CLOSE: (5), (8), (10), (14), (17), (23) are inconsistent by sub-proof
% 135.48/19.96 | | #81.
% 135.48/19.96 | |
% 135.48/19.96 | End of split
% 135.48/19.96 |
% 135.48/19.96 End of proof
% 135.48/19.96
% 135.48/19.96 Sub-proof #77 shows that the following formulas are inconsistent:
% 135.48/19.96 ----------------------------------------------------------------
% 135.48/19.96 (1) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 135.48/19.96 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.96 (3) op(e2, e2) = e3
% 135.48/19.96 (4) ~ (all_52_1 = e1)
% 135.48/19.96 (5) op(e2, e3) = all_52_1
% 135.48/19.96 (6) ~ (e3 = e1)
% 135.48/19.96
% 135.48/19.96 Begin of proof
% 135.48/19.96 |
% 135.48/19.96 | BETA: splitting (1) gives:
% 135.48/19.96 |
% 135.48/19.96 | Case 1:
% 135.48/19.96 | |
% 135.48/19.96 | | (7) all_57_2 = e1 & op(e2, e3) = e1
% 135.48/19.96 | |
% 135.48/19.96 | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #676.
% 135.48/19.96 | |
% 135.48/19.96 | Case 2:
% 135.48/19.96 | |
% 135.48/19.96 | | (8) all_57_3 = e1 & op(e2, e2) = e1
% 135.48/19.96 | |
% 135.48/19.96 | | ALPHA: (8) implies:
% 135.48/19.96 | | (9) op(e2, e2) = e1
% 135.48/19.96 | |
% 135.48/19.96 | | REF_CLOSE: (2), (3), (6), (9) are inconsistent by sub-proof #325.
% 135.48/19.96 | |
% 135.48/19.96 | End of split
% 135.48/19.96 |
% 135.48/19.96 End of proof
% 135.48/19.96
% 135.48/19.96 Sub-proof #78 shows that the following formulas are inconsistent:
% 135.48/19.96 ----------------------------------------------------------------
% 135.48/19.96 (1) all_54_6 = all_6_0
% 135.48/19.96 (2) all_54_6 = e2
% 135.48/19.96 (3) ~ (all_6_0 = e2)
% 135.48/19.96
% 135.48/19.96 Begin of proof
% 135.48/19.96 |
% 135.48/19.96 | COMBINE_EQS: (1), (2) imply:
% 135.48/19.96 | (4) all_6_0 = e2
% 135.48/19.96 |
% 135.48/19.96 | SIMP: (4) implies:
% 135.48/19.96 | (5) all_6_0 = e2
% 135.48/19.96 |
% 135.48/19.96 | REDUCE: (3), (5) imply:
% 135.48/19.96 | (6) $false
% 135.48/19.96 |
% 135.48/19.96 | CLOSE: (6) is inconsistent.
% 135.48/19.96 |
% 135.48/19.96 End of proof
% 135.48/19.96
% 135.48/19.96 Sub-proof #79 shows that the following formulas are inconsistent:
% 135.48/19.96 ----------------------------------------------------------------
% 135.48/19.96 (1) all_54_6 = all_6_0
% 135.48/19.96 (2) all_54_6 = e3
% 135.48/19.96 (3) ~ (all_6_0 = e3)
% 135.48/19.96
% 135.48/19.96 Begin of proof
% 135.48/19.96 |
% 135.48/19.96 | COMBINE_EQS: (1), (2) imply:
% 135.48/19.96 | (4) all_6_0 = e3
% 135.48/19.96 |
% 135.48/19.96 | SIMP: (4) implies:
% 135.48/19.96 | (5) all_6_0 = e3
% 135.48/19.96 |
% 135.48/19.96 | REDUCE: (3), (5) imply:
% 135.48/19.96 | (6) $false
% 135.48/19.96 |
% 135.48/19.96 | CLOSE: (6) is inconsistent.
% 135.48/19.96 |
% 135.48/19.96 End of proof
% 135.48/19.96
% 135.48/19.96 Sub-proof #80 shows that the following formulas are inconsistent:
% 135.48/19.96 ----------------------------------------------------------------
% 135.48/19.96 (1) op(e2, e2) = all_8_2
% 135.48/19.96 (2) op(e3, e3) = e2
% 135.48/19.96 (3) ~ (e2 = e0)
% 135.48/19.96 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.96 (5) ~ (e2 = e1)
% 135.48/19.96 (6) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2)
% 135.48/19.96 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3,
% 135.48/19.96 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 135.48/19.96 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.48/19.96 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 135.48/19.96 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.48/19.96 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) =
% 135.48/19.96 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.48/19.96 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.48/19.96 $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~
% 135.48/19.96 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.48/19.96 (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) =
% 135.48/19.96 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 135.48/19.96 = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 135.48/19.96 $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) &
% 135.48/19.96 ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3,
% 135.48/19.96 e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.48/19.96 op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 135.48/19.96 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25))
% 135.48/19.96 (7) op(e2, e2) = e2
% 135.48/19.96 (8) ~ (all_8_2 = e3)
% 135.48/19.96
% 135.48/19.96 Begin of proof
% 135.48/19.96 |
% 135.48/19.96 | BETA: splitting (6) gives:
% 135.48/19.96 |
% 135.48/19.96 | Case 1:
% 135.48/19.96 | |
% 135.48/19.96 | | (9) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.48/19.96 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2
% 135.48/19.96 | | & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11
% 135.48/19.96 | | & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.48/19.96 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 135.48/19.96 | | all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.48/19.96 | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 135.48/19.96 | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 135.48/19.96 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.48/19.96 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 135.48/19.96 | |
% 135.48/19.96 | | REF_CLOSE: (2), (4), (5), (7), (9) are inconsistent by sub-proof #444.
% 135.48/19.96 | |
% 135.48/19.96 | Case 2:
% 135.48/19.96 | |
% 135.48/19.96 | | (10) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15
% 135.48/19.96 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) =
% 135.48/19.96 | | e0 & op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.48/19.96 | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 &
% 135.48/19.96 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.48/19.96 | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 135.48/19.96 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.48/19.96 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.48/19.96 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 135.48/19.96 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25))
% 135.48/19.96 | |
% 135.48/19.96 | | BETA: splitting (10) gives:
% 135.48/19.96 | |
% 135.48/19.96 | | Case 1:
% 135.48/19.96 | | |
% 135.48/19.96 | | | (11) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~
% 135.48/19.96 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.48/19.96 | | | op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 135.48/19.96 | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 135.48/19.96 | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 135.48/19.96 | | | $i(all_56_31)
% 135.48/19.96 | | |
% 135.48/19.96 | | | ALPHA: (11) implies:
% 135.48/19.96 | | | (12) op(e3, e3) = e0
% 135.48/19.96 | | |
% 135.48/19.96 | | | REF_CLOSE: (2), (3), (4), (12) are inconsistent by sub-proof #495.
% 135.48/19.96 | | |
% 135.48/19.96 | | Case 2:
% 135.48/19.96 | | |
% 135.48/19.96 | | | (13) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 135.48/19.96 | | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.48/19.96 | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.48/19.96 | | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 135.48/19.96 | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)
% 135.48/19.96 | | |
% 135.48/19.96 | | | ALPHA: (13) implies:
% 135.48/19.96 | | | (14) op(e2, e2) = e3
% 135.48/19.96 | | |
% 135.48/19.96 | | | REF_CLOSE: (1), (4), (8), (14) are inconsistent by sub-proof #228.
% 135.48/19.96 | | |
% 135.48/19.96 | | End of split
% 135.48/19.96 | |
% 135.48/19.96 | End of split
% 135.48/19.96 |
% 135.48/19.96 End of proof
% 135.48/19.96
% 135.48/19.96 Sub-proof #81 shows that the following formulas are inconsistent:
% 135.48/19.96 ----------------------------------------------------------------
% 135.48/19.96 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.96 (2) ~ (e3 = e2)
% 135.48/19.96 (3) op(e1, e1) = e2
% 135.48/19.96 (4) ~ (e3 = e1)
% 135.48/19.96 (5) all_57_14 = e1
% 135.48/19.96 (6) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 135.48/19.96
% 135.48/19.96 Begin of proof
% 135.48/19.96 |
% 135.48/19.96 | BETA: splitting (6) gives:
% 135.48/19.96 |
% 135.48/19.96 | Case 1:
% 135.48/19.96 | |
% 135.48/19.96 | | (7) all_57_8 = e3 & op(e1, e1) = e3
% 135.48/19.96 | |
% 135.48/19.96 | | ALPHA: (7) implies:
% 135.48/19.96 | | (8) op(e1, e1) = e3
% 135.48/19.96 | |
% 135.48/19.96 | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #109.
% 135.48/19.96 | |
% 135.48/19.96 | Case 2:
% 135.48/19.96 | |
% 135.48/19.96 | | (9) all_57_14 = e3 & op(e0, e1) = e3
% 135.48/19.96 | |
% 135.48/19.96 | | ALPHA: (9) implies:
% 135.48/19.96 | | (10) all_57_14 = e3
% 135.48/19.96 | |
% 135.48/19.96 | | REF_CLOSE: (4), (5), (10) are inconsistent by sub-proof #561.
% 135.48/19.96 | |
% 135.48/19.96 | End of split
% 135.48/19.96 |
% 135.48/19.96 End of proof
% 135.48/19.96
% 135.48/19.96 Sub-proof #82 shows that the following formulas are inconsistent:
% 135.48/19.96 ----------------------------------------------------------------
% 135.48/19.96 (1) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 135.48/19.96 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 135.48/19.96 (2) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 135.48/19.96 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 135.48/19.96 (3) all_57_5 = e1
% 135.48/19.96 (4) ~ (e2 = e0)
% 135.48/19.96 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.48/19.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.48/19.96 (6) ~ (e2 = e1)
% 135.48/19.96 (7) ~ (e3 = e0)
% 135.48/19.96 (8) all_57_8 = e2
% 135.48/19.96 (9) all_57_4 = e3
% 135.48/19.96 (10) op(e3, e1) = all_52_8
% 135.48/19.96 (11) ~ (e3 = e1)
% 135.48/19.96 (12) ~ (e1 = e0)
% 135.48/19.96 (13) all_57_14 = e1
% 135.48/19.96 (14) op(e3, e1) = e3
% 135.48/19.96
% 135.48/19.96 Begin of proof
% 135.48/19.96 |
% 135.48/19.96 | BETA: splitting (2) gives:
% 135.48/19.96 |
% 135.48/19.96 | Case 1:
% 135.48/19.96 | |
% 135.48/19.96 | | (15) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) =
% 135.48/19.96 | | e0)
% 135.48/19.96 | |
% 135.48/19.96 | | BETA: splitting (15) gives:
% 135.48/19.96 | |
% 135.48/19.96 | | Case 1:
% 135.48/19.96 | | |
% 135.48/19.96 | | | (16) all_57_4 = e0 & op(e3, e1) = e0
% 135.48/19.96 | | |
% 135.48/19.96 | | | ALPHA: (16) implies:
% 135.48/19.96 | | | (17) op(e3, e1) = e0
% 135.48/19.96 | | |
% 135.48/19.96 | | | REF_CLOSE: (5), (7), (10), (14), (17) are inconsistent by sub-proof #600.
% 135.48/19.96 | | |
% 135.48/19.96 | | Case 2:
% 135.48/19.96 | | |
% 135.48/19.96 | | | (18) all_57_5 = e0 & op(e2, e1) = e0
% 135.48/19.96 | | |
% 135.48/19.96 | | | ALPHA: (18) implies:
% 135.48/19.96 | | | (19) all_57_5 = e0
% 135.48/19.96 | | |
% 135.48/19.96 | | | COMBINE_EQS: (3), (19) imply:
% 135.48/19.96 | | | (20) e1 = e0
% 135.48/19.96 | | |
% 135.48/19.96 | | | COMBINE_EQS: (13), (20) imply:
% 135.48/19.96 | | | (21) all_57_14 = e0
% 135.48/19.96 | | |
% 135.48/19.96 | | | REF_CLOSE: (1), (6), (8), (9), (11), (12), (19), (21) are inconsistent by
% 135.48/19.96 | | | sub-proof #84.
% 135.48/19.96 | | |
% 135.48/19.96 | | End of split
% 135.48/19.96 | |
% 135.48/19.96 | Case 2:
% 135.48/19.96 | |
% 135.48/19.96 | | (22) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 135.48/19.96 | | e0)
% 135.48/19.96 | |
% 135.48/19.96 | | BETA: splitting (22) gives:
% 135.48/19.96 | |
% 135.48/19.96 | | Case 1:
% 135.48/19.96 | | |
% 135.48/19.96 | | | (23) all_57_8 = e0 & op(e1, e1) = e0
% 135.48/19.96 | | |
% 135.48/19.96 | | | REF_CLOSE: (4), (8), (23) are inconsistent by sub-proof #83.
% 135.48/19.96 | | |
% 135.48/19.96 | | Case 2:
% 135.48/19.96 | | |
% 135.48/19.96 | | | (24) all_57_14 = e0 & op(e0, e1) = e0
% 135.48/19.96 | | |
% 135.48/19.96 | | | ALPHA: (24) implies:
% 135.48/19.97 | | | (25) all_57_14 = e0
% 135.48/19.97 | | |
% 135.48/19.97 | | | COMBINE_EQS: (13), (25) imply:
% 135.48/19.97 | | | (26) e1 = e0
% 135.48/19.97 | | |
% 135.48/19.97 | | | SIMP: (26) implies:
% 135.48/19.97 | | | (27) e1 = e0
% 135.48/19.97 | | |
% 135.48/19.97 | | | COMBINE_EQS: (3), (27) imply:
% 135.48/19.97 | | | (28) all_57_5 = e0
% 135.48/19.97 | | |
% 135.48/19.97 | | | REF_CLOSE: (1), (6), (8), (9), (11), (12), (25), (28) are inconsistent by
% 135.48/19.97 | | | sub-proof #84.
% 135.48/19.97 | | |
% 135.48/19.97 | | End of split
% 135.48/19.97 | |
% 135.48/19.97 | End of split
% 135.48/19.97 |
% 135.80/19.97 End of proof
% 135.80/19.97
% 135.80/19.97 Sub-proof #83 shows that the following formulas are inconsistent:
% 135.80/19.97 ----------------------------------------------------------------
% 135.80/19.97 (1) all_57_8 = e0 & op(e1, e1) = e0
% 135.80/19.97 (2) all_57_8 = e2
% 135.80/19.97 (3) ~ (e2 = e0)
% 135.80/19.97
% 135.80/19.97 Begin of proof
% 135.80/19.97 |
% 135.80/19.97 | ALPHA: (1) implies:
% 135.80/19.97 | (4) all_57_8 = e0
% 135.80/19.97 |
% 135.80/19.97 | COMBINE_EQS: (2), (4) imply:
% 135.80/19.97 | (5) e2 = e0
% 135.80/19.97 |
% 135.80/19.97 | REDUCE: (3), (5) imply:
% 135.80/19.97 | (6) $false
% 135.80/19.97 |
% 135.80/19.97 | CLOSE: (6) is inconsistent.
% 135.80/19.97 |
% 135.80/19.97 End of proof
% 135.80/19.97
% 135.80/19.97 Sub-proof #84 shows that the following formulas are inconsistent:
% 135.80/19.97 ----------------------------------------------------------------
% 135.80/19.97 (1) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 135.80/19.97 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 135.80/19.97 (2) ~ (e2 = e1)
% 135.80/19.97 (3) all_57_8 = e2
% 135.80/19.97 (4) all_57_14 = e0
% 135.80/19.97 (5) all_57_4 = e3
% 135.80/19.97 (6) ~ (e3 = e1)
% 135.80/19.97 (7) ~ (e1 = e0)
% 135.80/19.97 (8) all_57_5 = e0
% 135.80/19.97
% 135.80/19.97 Begin of proof
% 135.80/19.97 |
% 135.80/19.97 | BETA: splitting (1) gives:
% 135.80/19.97 |
% 135.80/19.97 | Case 1:
% 135.80/19.97 | |
% 135.80/19.97 | | (9) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1)
% 135.80/19.97 | |
% 135.80/19.97 | | BETA: splitting (9) gives:
% 135.80/19.97 | |
% 135.80/19.97 | | Case 1:
% 135.80/19.97 | | |
% 135.80/19.97 | | | (10) all_57_4 = e1 & op(e3, e1) = e1
% 135.80/19.97 | | |
% 135.80/19.97 | | | ALPHA: (10) implies:
% 135.80/19.97 | | | (11) all_57_4 = e1
% 135.80/19.97 | | |
% 135.80/19.97 | | | REF_CLOSE: (5), (6), (11) are inconsistent by sub-proof #671.
% 135.80/19.97 | | |
% 135.80/19.97 | | Case 2:
% 135.80/19.97 | | |
% 135.80/19.97 | | | (12) all_57_5 = e1 & op(e2, e1) = e1
% 135.80/19.97 | | |
% 135.80/19.97 | | | ALPHA: (12) implies:
% 135.80/19.97 | | | (13) all_57_5 = e1
% 135.80/19.97 | | |
% 135.80/19.97 | | | COMBINE_EQS: (8), (13) imply:
% 135.80/19.97 | | | (14) e1 = e0
% 135.80/19.97 | | |
% 135.80/19.97 | | | SIMP: (14) implies:
% 135.80/19.97 | | | (15) e1 = e0
% 135.80/19.97 | | |
% 135.80/19.97 | | | REDUCE: (7), (15) imply:
% 135.80/19.97 | | | (16) $false
% 135.80/19.97 | | |
% 135.80/19.97 | | | CLOSE: (16) is inconsistent.
% 135.80/19.97 | | |
% 135.80/19.97 | | End of split
% 135.80/19.97 | |
% 135.80/19.97 | Case 2:
% 135.80/19.97 | |
% 135.80/19.97 | | (17) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) =
% 135.80/19.97 | | e1)
% 135.80/19.97 | |
% 135.80/19.97 | | BETA: splitting (17) gives:
% 135.80/19.97 | |
% 135.80/19.97 | | Case 1:
% 135.80/19.97 | | |
% 135.80/19.97 | | | (18) all_57_8 = e1 & op(e1, e1) = e1
% 135.80/19.97 | | |
% 135.80/19.97 | | | REF_CLOSE: (2), (3), (18) are inconsistent by sub-proof #85.
% 135.80/19.97 | | |
% 135.80/19.97 | | Case 2:
% 135.80/19.97 | | |
% 135.80/19.97 | | | (19) all_57_14 = e1 & op(e0, e1) = e1
% 135.80/19.97 | | |
% 135.80/19.97 | | | REF_CLOSE: (4), (7), (19) are inconsistent by sub-proof #231.
% 135.80/19.97 | | |
% 135.80/19.97 | | End of split
% 135.80/19.97 | |
% 135.80/19.97 | End of split
% 135.80/19.97 |
% 135.80/19.97 End of proof
% 135.80/19.97
% 135.80/19.97 Sub-proof #85 shows that the following formulas are inconsistent:
% 135.80/19.97 ----------------------------------------------------------------
% 135.80/19.97 (1) all_57_8 = e1 & op(e1, e1) = e1
% 135.80/19.97 (2) all_57_8 = e2
% 135.80/19.97 (3) ~ (e2 = e1)
% 135.80/19.97
% 135.80/19.97 Begin of proof
% 135.80/19.97 |
% 135.80/19.97 | ALPHA: (1) implies:
% 135.80/19.97 | (4) all_57_8 = e1
% 135.80/19.97 |
% 135.80/19.97 | COMBINE_EQS: (2), (4) imply:
% 135.80/19.97 | (5) e2 = e1
% 135.80/19.97 |
% 135.80/19.97 | SIMP: (5) implies:
% 135.80/19.97 | (6) e2 = e1
% 135.80/19.97 |
% 135.80/19.97 | REDUCE: (3), (6) imply:
% 135.80/19.97 | (7) $false
% 135.80/19.97 |
% 135.80/19.97 | CLOSE: (7) is inconsistent.
% 135.80/19.97 |
% 135.80/19.97 End of proof
% 135.80/19.97
% 135.80/19.97 Sub-proof #86 shows that the following formulas are inconsistent:
% 135.80/19.97 ----------------------------------------------------------------
% 135.80/19.97 (1) ~ (e2 = e0)
% 135.80/19.97 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.80/19.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.80/19.97 (3) op(e1, e1) = e2
% 135.80/19.97 (4) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 135.80/19.97 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 135.80/19.97 op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 135.80/19.97 op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 135.80/19.97 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.80/19.97 e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 135.80/19.97 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.80/19.97 = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.80/19.97 $i(all_56_21) & $i(all_56_29))
% 135.80/19.97 (5) ~ (all_4_2 = e1)
% 135.80/19.97 (6) all_56_31 = all_4_2
% 135.80/19.97
% 135.80/19.97 Begin of proof
% 135.80/19.97 |
% 135.80/19.97 | BETA: splitting (4) gives:
% 135.80/19.97 |
% 135.80/19.97 | Case 1:
% 135.80/19.97 | |
% 135.80/19.97 | | (7) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15
% 135.80/19.97 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0
% 135.80/19.97 | | & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 135.80/19.97 | | op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)
% 135.80/19.97 | |
% 135.80/19.97 | | ALPHA: (7) implies:
% 135.80/19.97 | | (8) op(e1, e1) = e0
% 135.80/19.97 | |
% 135.80/19.97 | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #98.
% 135.80/19.97 | |
% 135.80/19.97 | Case 2:
% 135.80/19.97 | |
% 135.80/19.97 | | (9) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13
% 135.80/19.97 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 135.80/19.97 | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1,
% 135.80/19.97 | | e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.80/19.97 | | $i(all_56_21) & $i(all_56_29)
% 135.80/19.97 | |
% 135.80/19.97 | | REF_CLOSE: (5), (6), (9) are inconsistent by sub-proof #745.
% 135.80/19.97 | |
% 135.80/19.97 | End of split
% 135.80/19.97 |
% 135.80/19.97 End of proof
% 135.80/19.97
% 135.80/19.97 Sub-proof #87 shows that the following formulas are inconsistent:
% 135.80/19.97 ----------------------------------------------------------------
% 135.80/19.97 (1) op(e2, e2) = e0
% 135.80/19.97 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.80/19.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.80/19.97 (3) ~ (e2 = e1)
% 135.80/19.97 (4) all_57_5 = e3 & op(e2, e1) = e3
% 135.80/19.97 (5) all_57_2 = e3
% 135.80/19.97 (6) ~ (e3 = e1)
% 135.80/19.97 (7) ~ (e1 = e0)
% 135.80/19.97 (8) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 135.80/19.97 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 135.80/19.97 (9) all_57_10 = e2
% 135.80/19.97
% 135.80/19.97 Begin of proof
% 135.80/19.97 |
% 135.80/19.97 | ALPHA: (4) implies:
% 135.80/19.97 | (10) all_57_5 = e3
% 135.80/19.97 |
% 135.80/19.97 | BETA: splitting (8) gives:
% 135.80/19.97 |
% 135.80/19.97 | Case 1:
% 135.80/19.97 | |
% 135.80/19.97 | | (11) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 135.80/19.97 | | e1)
% 135.80/19.97 | |
% 135.80/19.97 | | BETA: splitting (11) gives:
% 135.80/19.97 | |
% 135.80/19.97 | | Case 1:
% 135.80/19.97 | | |
% 135.80/19.97 | | | (12) all_57_2 = e1 & op(e2, e3) = e1
% 135.80/19.97 | | |
% 135.80/19.97 | | | REF_CLOSE: (5), (6), (12) are inconsistent by sub-proof #371.
% 135.80/19.97 | | |
% 135.80/19.97 | | Case 2:
% 135.80/19.97 | | |
% 135.80/19.97 | | | (13) all_57_3 = e1 & op(e2, e2) = e1
% 135.80/19.97 | | |
% 135.80/19.97 | | | ALPHA: (13) implies:
% 135.80/19.97 | | | (14) op(e2, e2) = e1
% 135.80/19.97 | | |
% 135.80/19.97 | | | REF_CLOSE: (1), (2), (7), (14) are inconsistent by sub-proof #675.
% 135.80/19.97 | | |
% 135.80/19.97 | | End of split
% 135.80/19.97 | |
% 135.80/19.97 | Case 2:
% 135.80/19.97 | |
% 135.80/19.97 | | (15) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 135.80/19.97 | | e1)
% 135.80/19.97 | |
% 135.80/19.97 | | BETA: splitting (15) gives:
% 135.80/19.97 | |
% 135.80/19.97 | | Case 1:
% 135.80/19.97 | | |
% 135.80/19.97 | | | (16) all_57_5 = e1 & op(e2, e1) = e1
% 135.80/19.97 | | |
% 135.80/19.97 | | | ALPHA: (16) implies:
% 135.80/19.97 | | | (17) all_57_5 = e1
% 135.80/19.97 | | |
% 135.80/19.97 | | | REF_CLOSE: (6), (10), (17) are inconsistent by sub-proof #88.
% 135.80/19.97 | | |
% 135.80/19.97 | | Case 2:
% 135.80/19.97 | | |
% 135.80/19.97 | | | (18) all_57_10 = e1 & op(e2, e0) = e1
% 135.80/19.97 | | |
% 135.80/19.97 | | | ALPHA: (18) implies:
% 135.80/19.97 | | | (19) all_57_10 = e1
% 135.80/19.97 | | |
% 135.80/19.97 | | | REF_CLOSE: (3), (9), (19) are inconsistent by sub-proof #414.
% 135.80/19.97 | | |
% 135.80/19.97 | | End of split
% 135.80/19.97 | |
% 135.80/19.97 | End of split
% 135.80/19.97 |
% 135.80/19.97 End of proof
% 135.80/19.97
% 135.80/19.97 Sub-proof #88 shows that the following formulas are inconsistent:
% 135.80/19.97 ----------------------------------------------------------------
% 135.80/19.97 (1) all_57_5 = e3
% 135.80/19.97 (2) all_57_5 = e1
% 135.80/19.97 (3) ~ (e3 = e1)
% 135.80/19.97
% 135.80/19.97 Begin of proof
% 135.80/19.97 |
% 135.80/19.97 | COMBINE_EQS: (1), (2) imply:
% 135.80/19.97 | (4) e3 = e1
% 135.80/19.97 |
% 135.80/19.97 | SIMP: (4) implies:
% 135.80/19.97 | (5) e3 = e1
% 135.80/19.97 |
% 135.80/19.97 | REDUCE: (3), (5) imply:
% 135.80/19.97 | (6) $false
% 135.80/19.97 |
% 135.80/19.97 | CLOSE: (6) is inconsistent.
% 135.80/19.97 |
% 135.80/19.97 End of proof
% 135.80/19.97
% 135.80/19.97 Sub-proof #89 shows that the following formulas are inconsistent:
% 135.80/19.97 ----------------------------------------------------------------
% 135.80/19.97 (1) op(e3, e3) = e2
% 135.80/19.97 (2) ~ (e2 = e0)
% 135.80/19.97 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.80/19.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.80/19.97 (4) ~ (all_52_1 = e0)
% 135.80/19.97 (5) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0)
% 135.80/19.97 (6) op(e2, e3) = all_52_1
% 135.80/19.97
% 135.80/19.97 Begin of proof
% 135.80/19.97 |
% 135.80/19.97 | BETA: splitting (5) gives:
% 135.80/19.97 |
% 135.80/19.97 | Case 1:
% 135.80/19.97 | |
% 135.80/19.97 | | (7) all_57_0 = e0 & op(e3, e3) = e0
% 135.80/19.97 | |
% 135.80/19.97 | | ALPHA: (7) implies:
% 135.80/19.97 | | (8) op(e3, e3) = e0
% 135.80/19.97 | |
% 135.80/19.97 | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #495.
% 135.80/19.97 | |
% 135.80/19.97 | Case 2:
% 135.80/19.97 | |
% 135.80/19.97 | | (9) all_57_2 = e0 & op(e2, e3) = e0
% 135.80/19.97 | |
% 135.80/19.97 | | REF_CLOSE: (3), (4), (6), (9) are inconsistent by sub-proof #225.
% 135.80/19.97 | |
% 135.80/19.97 | End of split
% 135.80/19.97 |
% 135.80/19.97 End of proof
% 135.80/19.97
% 135.80/19.97 Sub-proof #90 shows that the following formulas are inconsistent:
% 135.80/19.97 ----------------------------------------------------------------
% 135.80/19.97 (1) ( ~ (all_20_0 = e3) & op(e2, e0) = all_20_0 & $i(all_20_0)) | ( ~
% 135.80/19.97 (all_20_1 = e1) & op(e2, e2) = all_20_1 & $i(all_20_1))
% 135.80/19.97 (2) op(e2, e2) = e0
% 135.80/19.97 (3) op(e2, e0) = all_52_13
% 135.80/19.97 (4) ~ (all_52_8 = all_52_9)
% 135.80/19.97 (5) ~ (e2 = e0)
% 135.80/19.97 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.80/19.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.80/19.97 (7) ~ (e2 = e1)
% 135.80/19.97 (8) ~ (e3 = e0)
% 135.80/19.97 (9) ~ (e3 = e2)
% 135.80/19.97 (10) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 135.80/19.97 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 135.80/19.97 (11) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 135.80/19.97 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 135.80/19.97 (12) op(e1, e1) = e2
% 135.80/19.97 (13) ~ (all_10_2 = e0)
% 135.80/19.97 (14) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 135.80/19.97 (15) all_57_2 = e2
% 135.80/19.97 (16) ~ (all_52_9 = e2)
% 135.80/19.97 (17) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.80/19.97 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.80/19.97 op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.80/19.97 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.80/19.97 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 135.80/19.97 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.80/19.97 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 135.80/19.97 = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.80/19.97 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.80/19.97 $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~
% 135.80/19.97 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.80/19.97 (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) =
% 135.80/19.97 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0,
% 135.80/19.97 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 135.80/19.97 $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3)
% 135.80/19.97 & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 135.80/19.97 op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17
% 135.80/19.97 & op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 135.80/19.97 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 135.80/19.97 (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 135.80/19.97 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.80/19.97 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0)
% 135.80/19.97 = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) &
% 135.80/19.97 $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 &
% 135.80/19.97 all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.80/19.97 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 135.80/19.97 = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.80/19.97 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.80/19.97 $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~
% 135.80/19.97 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.80/19.97 (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 135.80/19.97 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0,
% 135.80/19.97 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 135.80/19.97 $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3)
% 135.80/19.97 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.80/19.97 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.80/19.97 all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2
% 135.80/19.97 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.80/19.97 (op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 =
% 135.80/19.97 e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.80/19.97 & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) =
% 135.80/19.97 all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.80/19.97 op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.80/19.97 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 135.80/19.97 e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.80/19.97 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 135.80/19.97 e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.80/19.97 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.80/19.97 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.80/19.97 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.80/19.97 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.80/19.97 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 135.80/19.97 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 135.80/19.97 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 135.80/19.97 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.80/19.97 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 135.80/19.97 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.80/19.97 $i(all_56_29))))
% 135.80/19.97 (18) op(e3, e3) = all_10_2
% 135.80/19.97 (19) op(e2, e1) = all_52_9
% 135.80/19.97 (20) ~ (all_52_8 = e2)
% 135.80/19.97 (21) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 135.80/19.97 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 135.80/19.97 (22) all_32_2 = all_10_2
% 135.80/19.97 (23) all_54_6 = all_52_9
% 135.80/19.97 (24) op(e0, e0) = e2
% 135.80/19.97 (25) ~ (all_10_2 = e2)
% 135.80/19.97 (26) ~ (all_32_2 = e1) | ( ~ (all_32_0 = e0) & op(e1, e3) = all_32_0 &
% 135.80/19.97 $i(all_32_0)) | ( ~ (all_32_1 = e2) & op(e1, e1) = all_32_1 &
% 135.80/19.97 $i(all_32_1))
% 135.80/19.97 (27) ( ~ (all_18_0 = e3) & op(e2, e1) = all_18_0 & $i(all_18_0)) | ( ~
% 135.80/19.97 (all_18_1 = e0) & op(e2, e2) = all_18_1 & $i(all_18_1))
% 135.80/19.97 (28) op(e3, e1) = all_52_8
% 135.80/19.97 (29) ~ (all_52_9 = e0)
% 135.80/19.97 (30) ~ (e3 = e1)
% 135.80/19.97 (31) ~ (e1 = e0)
% 135.80/19.97 (32) op(e2, e3) = e2
% 135.80/19.97 (33) ~ (all_52_9 = all_52_13)
% 135.80/19.97 (34) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 135.80/19.97 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 135.80/19.97 (35) op(e3, e2) = e2
% 135.80/19.97
% 135.80/19.97 Begin of proof
% 135.80/19.97 |
% 135.80/19.97 | BETA: splitting (27) gives:
% 135.80/19.97 |
% 135.80/19.97 | Case 1:
% 135.80/19.97 | |
% 135.80/19.97 | | (36) ~ (all_18_0 = e3) & op(e2, e1) = all_18_0 & $i(all_18_0)
% 135.80/19.97 | |
% 135.80/19.97 | | ALPHA: (36) implies:
% 135.80/19.97 | | (37) ~ (all_18_0 = e3)
% 135.80/19.97 | | (38) op(e2, e1) = all_18_0
% 135.80/19.97 | |
% 135.80/19.97 | | GROUND_INST: instantiating (6) with all_52_9, all_18_0, e1, e2, simplifying
% 135.80/19.97 | | with (19), (38) gives:
% 135.80/19.97 | | (39) all_52_9 = all_18_0
% 135.80/19.97 | |
% 135.80/19.97 | | COMBINE_EQS: (23), (39) imply:
% 135.80/19.97 | | (40) all_54_6 = all_18_0
% 135.80/19.97 | |
% 135.80/19.97 | | REDUCE: (4), (39) imply:
% 135.80/19.97 | | (41) ~ (all_52_8 = all_18_0)
% 135.80/19.97 | |
% 135.80/19.97 | | REDUCE: (33), (39) imply:
% 135.80/19.97 | | (42) ~ (all_52_13 = all_18_0)
% 135.80/19.97 | |
% 135.80/19.97 | | SIMP: (42) implies:
% 135.80/19.97 | | (43) ~ (all_52_13 = all_18_0)
% 135.80/19.97 | |
% 135.80/19.97 | | REDUCE: (16), (39) imply:
% 135.80/19.97 | | (44) ~ (all_18_0 = e2)
% 135.80/19.97 | |
% 135.80/19.97 | | REDUCE: (29), (39) imply:
% 135.80/19.97 | | (45) ~ (all_18_0 = e0)
% 135.80/19.97 | |
% 135.80/19.97 | | BETA: splitting (14) gives:
% 135.80/19.97 | |
% 135.80/19.97 | | Case 1:
% 135.80/19.97 | | |
% 135.80/19.97 | | | (46) all_54_6 = e3
% 135.80/19.97 | | |
% 135.80/19.97 | | | COMBINE_EQS: (40), (46) imply:
% 135.80/19.97 | | | (47) all_18_0 = e3
% 135.80/19.97 | | |
% 135.80/19.97 | | | SIMP: (47) implies:
% 135.80/19.97 | | | (48) all_18_0 = e3
% 135.80/19.97 | | |
% 135.80/19.97 | | | REDUCE: (37), (48) imply:
% 135.80/19.97 | | | (49) $false
% 135.80/19.97 | | |
% 135.80/19.97 | | | CLOSE: (49) is inconsistent.
% 135.80/19.97 | | |
% 135.80/19.97 | | Case 2:
% 135.80/19.97 | | |
% 135.80/19.97 | | | (50) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 135.80/19.97 | | |
% 135.80/19.97 | | | BETA: splitting (50) gives:
% 135.80/19.97 | | |
% 135.80/19.97 | | | Case 1:
% 135.80/19.97 | | | |
% 135.80/19.97 | | | | (51) all_54_6 = e2
% 135.80/19.97 | | | |
% 135.80/19.97 | | | | COMBINE_EQS: (40), (51) imply:
% 135.80/19.97 | | | | (52) all_18_0 = e2
% 135.80/19.97 | | | |
% 135.80/19.97 | | | | SIMP: (52) implies:
% 135.80/19.97 | | | | (53) all_18_0 = e2
% 135.80/19.97 | | | |
% 135.80/19.97 | | | | REDUCE: (44), (53) imply:
% 135.80/19.97 | | | | (54) $false
% 135.80/19.97 | | | |
% 135.80/19.97 | | | | CLOSE: (54) is inconsistent.
% 135.80/19.97 | | | |
% 135.80/19.97 | | | Case 2:
% 135.80/19.97 | | | |
% 135.80/19.97 | | | | (55) ~ (all_54_6 = e2)
% 135.80/19.97 | | | | (56) all_54_6 = e1 | all_54_6 = e0
% 135.80/19.97 | | | |
% 135.80/19.97 | | | | BETA: splitting (11) gives:
% 135.80/19.97 | | | |
% 135.80/19.97 | | | | Case 1:
% 135.80/19.97 | | | | |
% 135.80/19.97 | | | | | (57) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2,
% 135.80/19.97 | | | | | e2) = e3)
% 135.80/19.97 | | | | |
% 135.80/19.97 | | | | | REF_CLOSE: (2), (6), (8), (9), (15), (57) are inconsistent by
% 135.80/19.97 | | | | | sub-proof #94.
% 135.80/19.97 | | | | |
% 135.80/19.97 | | | | Case 2:
% 135.80/19.97 | | | | |
% 135.80/19.97 | | | | | (58) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2,
% 135.80/19.97 | | | | | e0) = e3)
% 135.80/19.97 | | | | |
% 135.80/19.97 | | | | | BETA: splitting (58) gives:
% 135.80/19.97 | | | | |
% 135.80/19.97 | | | | | Case 1:
% 135.80/19.97 | | | | | |
% 135.80/19.97 | | | | | | (59) all_57_5 = e3 & op(e2, e1) = e3
% 135.80/19.97 | | | | | |
% 135.80/19.97 | | | | | | ALPHA: (59) implies:
% 135.80/19.97 | | | | | | (60) all_57_5 = e3
% 135.80/19.97 | | | | | |
% 135.80/19.97 | | | | | | BETA: splitting (34) gives:
% 135.80/19.97 | | | | | |
% 135.80/19.97 | | | | | | Case 1:
% 135.80/19.97 | | | | | | |
% 135.80/19.97 | | | | | | | (61) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 &
% 135.80/19.97 | | | | | | | op(e2, e2) = e1)
% 135.80/19.97 | | | | | | |
% 135.80/19.97 | | | | | | | REF_CLOSE: (2), (6), (7), (31), (32), (61) are inconsistent by
% 135.80/19.97 | | | | | | | sub-proof #93.
% 135.80/19.97 | | | | | | |
% 135.80/19.97 | | | | | | Case 2:
% 135.80/19.97 | | | | | | |
% 135.80/19.97 | | | | | | | (62) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 &
% 135.80/19.97 | | | | | | | op(e2, e0) = e1)
% 135.80/19.97 | | | | | | |
% 135.80/19.97 | | | | | | | BETA: splitting (62) gives:
% 135.80/19.97 | | | | | | |
% 135.80/19.97 | | | | | | | Case 1:
% 135.80/19.97 | | | | | | | |
% 135.80/19.97 | | | | | | | | (63) all_57_5 = e1 & op(e2, e1) = e1
% 135.80/19.97 | | | | | | | |
% 135.80/19.97 | | | | | | | | REF_CLOSE: (30), (60), (63) are inconsistent by sub-proof #673.
% 135.80/19.97 | | | | | | | |
% 135.80/19.97 | | | | | | | Case 2:
% 135.80/19.97 | | | | | | | |
% 135.80/19.97 | | | | | | | | (64) all_57_10 = e1 & op(e2, e0) = e1
% 135.80/19.97 | | | | | | | |
% 135.80/19.97 | | | | | | | | ALPHA: (64) implies:
% 135.80/19.97 | | | | | | | | (65) op(e2, e0) = e1
% 135.80/19.97 | | | | | | | |
% 135.80/19.97 | | | | | | | | BETA: splitting (56) gives:
% 135.80/19.97 | | | | | | | |
% 135.80/19.97 | | | | | | | | Case 1:
% 135.80/19.97 | | | | | | | | |
% 135.80/19.97 | | | | | | | | | (66) all_54_6 = e1
% 135.80/19.97 | | | | | | | | |
% 135.80/19.97 | | | | | | | | | COMBINE_EQS: (40), (66) imply:
% 135.80/19.97 | | | | | | | | | (67) all_18_0 = e1
% 135.80/19.97 | | | | | | | | |
% 135.80/19.97 | | | | | | | | | SIMP: (67) implies:
% 135.80/19.97 | | | | | | | | | (68) all_18_0 = e1
% 135.80/19.97 | | | | | | | | |
% 135.80/19.97 | | | | | | | | | REDUCE: (43), (68) imply:
% 135.80/19.97 | | | | | | | | | (69) ~ (all_52_13 = e1)
% 135.80/19.97 | | | | | | | | |
% 135.80/19.97 | | | | | | | | | REF_CLOSE: (3), (6), (65), (69) are inconsistent by sub-proof
% 135.80/19.97 | | | | | | | | | #180.
% 135.80/19.97 | | | | | | | | |
% 135.80/19.97 | | | | | | | | Case 2:
% 135.80/19.97 | | | | | | | | |
% 135.80/19.97 | | | | | | | | | (70) all_54_6 = e0
% 135.80/19.97 | | | | | | | | |
% 135.80/19.97 | | | | | | | | | REF_CLOSE: (40), (45), (70) are inconsistent by sub-proof #92.
% 135.80/19.97 | | | | | | | | |
% 135.80/19.97 | | | | | | | | End of split
% 135.80/19.97 | | | | | | | |
% 135.80/19.97 | | | | | | | End of split
% 135.80/19.97 | | | | | | |
% 135.80/19.97 | | | | | | End of split
% 135.80/19.97 | | | | | |
% 135.80/19.97 | | | | | Case 2:
% 135.80/19.97 | | | | | |
% 135.80/19.97 | | | | | | (71) all_57_10 = e3 & op(e2, e0) = e3
% 135.80/19.97 | | | | | |
% 135.80/19.97 | | | | | | ALPHA: (71) implies:
% 135.80/19.97 | | | | | | (72) op(e2, e0) = e3
% 135.80/19.97 | | | | | |
% 135.80/19.97 | | | | | | BETA: splitting (56) gives:
% 135.80/19.97 | | | | | |
% 135.80/19.97 | | | | | | Case 1:
% 135.80/19.97 | | | | | | |
% 135.80/19.97 | | | | | | | (73) all_54_6 = e1
% 135.80/19.97 | | | | | | |
% 135.80/19.97 | | | | | | | COMBINE_EQS: (40), (73) imply:
% 135.80/19.97 | | | | | | | (74) all_18_0 = e1
% 135.80/19.97 | | | | | | |
% 135.80/19.97 | | | | | | | SIMP: (74) implies:
% 135.80/19.97 | | | | | | | (75) all_18_0 = e1
% 135.80/19.97 | | | | | | |
% 135.80/19.97 | | | | | | | REDUCE: (41), (75) imply:
% 135.80/19.97 | | | | | | | (76) ~ (all_52_8 = e1)
% 135.80/19.97 | | | | | | |
% 135.80/19.97 | | | | | | | REDUCE: (44), (75) imply:
% 135.80/19.97 | | | | | | | (77) ~ (e2 = e1)
% 135.80/19.97 | | | | | | |
% 135.80/19.97 | | | | | | | REDUCE: (38), (75) imply:
% 135.80/19.97 | | | | | | | (78) op(e2, e1) = e1
% 135.80/19.97 | | | | | | |
% 135.80/19.97 | | | | | | | BETA: splitting (17) gives:
% 135.80/19.97 | | | | | | |
% 135.80/19.97 | | | | | | | Case 1:
% 135.80/19.97 | | | | | | | |
% 135.80/19.97 | | | | | | | | (79) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~
% 135.80/19.97 | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.80/19.97 | | | | | | | | = e0) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2,
% 135.80/19.97 | | | | | | | | e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1)
% 135.80/19.97 | | | | | | | | = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.80/19.97 | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.80/19.97 | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) &
% 135.80/19.97 | | | | | | | | ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.80/19.97 | | | | | | | | (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 135.80/19.97 | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 135.80/19.97 | | | | | | | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 135.80/19.97 | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.80/19.97 | | | | | | | | $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~
% 135.80/19.97 | | | | | | | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23
% 135.80/19.97 | | | | | | | | = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.80/19.97 | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.80/19.97 | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 135.80/19.97 | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 135.80/19.97 | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 &
% 135.80/19.98 | | | | | | | | all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 135.80/19.98 | | | | | | | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 135.80/19.98 | | | | | | | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 135.80/19.98 | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e2,
% 135.80/19.98 | | | | | | | | e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) &
% 135.80/19.98 | | | | | | | | $i(all_56_9) & $i(all_56_17) & $i(all_56_25))
% 135.80/19.98 | | | | | | | |
% 135.80/19.98 | | | | | | | | BETA: splitting (79) gives:
% 135.80/19.98 | | | | | | | |
% 135.80/19.98 | | | | | | | | Case 1:
% 135.80/19.98 | | | | | | | | |
% 135.80/19.98 | | | | | | | | | (80) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) &
% 135.80/19.98 | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.80/19.98 | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = e3
% 135.80/19.98 | | | | | | | | | & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.80/19.98 | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 135.80/19.98 | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.80/19.98 | | | | | | | | | $i(all_56_27)) | (all_56_1 = e1 & all_56_17 = e3 &
% 135.80/19.98 | | | | | | | | | ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.80/19.98 | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3)
% 135.80/19.98 | | | | | | | | | = e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 &
% 135.80/19.98 | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 135.80/19.98 | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.80/19.98 | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 135.80/19.98 | | | | | | | | |
% 135.80/19.98 | | | | | | | | | BETA: splitting (80) gives:
% 135.80/19.98 | | | | | | | | |
% 135.80/19.98 | | | | | | | | | Case 1:
% 135.80/19.98 | | | | | | | | | |
% 135.80/19.98 | | | | | | | | | | (81) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) &
% 135.80/19.98 | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.80/19.98 | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = e3
% 135.80/19.98 | | | | | | | | | | & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.80/19.98 | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 135.80/19.98 | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.80/19.98 | | | | | | | | | | $i(all_56_27)
% 135.80/19.98 | | | | | | | | | |
% 135.80/19.98 | | | | | | | | | | ALPHA: (81) implies:
% 135.80/19.98 | | | | | | | | | | (82) op(e3, e3) = e2
% 135.80/19.98 | | | | | | | | | |
% 135.80/19.98 | | | | | | | | | | REF_CLOSE: (6), (18), (25), (82) are inconsistent by
% 135.80/19.98 | | | | | | | | | | sub-proof #536.
% 135.80/19.98 | | | | | | | | | |
% 135.80/19.98 | | | | | | | | | Case 2:
% 135.80/19.98 | | | | | | | | | |
% 135.80/19.98 | | | | | | | | | | (83) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3)
% 135.80/19.98 | | | | | | | | | | & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.80/19.98 | | | | | | | | | | (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3
% 135.80/19.98 | | | | | | | | | | & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 135.80/19.98 | | | | | | | | | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 135.80/19.98 | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.80/19.98 | | | | | | | | | | $i(all_56_29)
% 135.80/19.98 | | | | | | | | | |
% 135.80/19.98 | | | | | | | | | | ALPHA: (83) implies:
% 135.80/19.98 | | | | | | | | | | (84) ~ (all_56_5 = e3)
% 135.84/19.98 | | | | | | | | | | (85) op(e1, e1) = all_56_21
% 135.84/19.98 | | | | | | | | | | (86) op(e1, e3) = all_56_5
% 135.84/19.98 | | | | | | | | | | (87) op(e3, e1) = e3
% 135.84/19.98 | | | | | | | | | | (88) op(e3, e3) = e1
% 135.84/19.98 | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | BETA: splitting (1) gives:
% 135.84/19.98 | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | Case 1:
% 135.84/19.98 | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | (89) ~ (all_20_0 = e3) & op(e2, e0) = all_20_0 &
% 135.84/19.98 | | | | | | | | | | | $i(all_20_0)
% 135.84/19.98 | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | ALPHA: (89) implies:
% 135.84/19.98 | | | | | | | | | | | (90) ~ (all_20_0 = e3)
% 135.84/19.98 | | | | | | | | | | | (91) op(e2, e0) = all_20_0
% 135.84/19.98 | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | GROUND_INST: instantiating (6) with e3, all_20_0, e0, e2,
% 135.84/19.98 | | | | | | | | | | | simplifying with (72), (91) gives:
% 135.84/19.98 | | | | | | | | | | | (92) all_20_0 = e3
% 135.84/19.98 | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | REDUCE: (90), (92) imply:
% 135.84/19.98 | | | | | | | | | | | (93) $false
% 135.84/19.98 | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | CLOSE: (93) is inconsistent.
% 135.84/19.98 | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | Case 2:
% 135.84/19.98 | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | GROUND_INST: instantiating (6) with e2, all_56_21, e1, e1,
% 135.84/19.98 | | | | | | | | | | | simplifying with (12), (85) gives:
% 135.84/19.98 | | | | | | | | | | | (94) all_56_21 = e2
% 135.84/19.98 | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | GROUND_INST: instantiating (6) with all_52_8, e3, e1, e3,
% 135.84/19.98 | | | | | | | | | | | simplifying with (28), (87) gives:
% 135.84/19.98 | | | | | | | | | | | (95) all_52_8 = e3
% 135.84/19.98 | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | GROUND_INST: instantiating (6) with all_10_2, e1, e3, e3,
% 135.84/19.98 | | | | | | | | | | | simplifying with (18), (88) gives:
% 135.84/19.98 | | | | | | | | | | | (96) all_10_2 = e1
% 135.84/19.98 | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | COMBINE_EQS: (22), (96) imply:
% 135.84/19.98 | | | | | | | | | | | (97) all_32_2 = e1
% 135.84/19.98 | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | BETA: splitting (26) gives:
% 135.84/19.98 | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | Case 1:
% 135.84/19.98 | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | (98) ~ (all_32_2 = e1)
% 135.84/19.98 | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | REDUCE: (97), (98) imply:
% 135.84/19.98 | | | | | | | | | | | | (99) $false
% 135.84/19.98 | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | CLOSE: (99) is inconsistent.
% 135.84/19.98 | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | Case 2:
% 135.84/19.98 | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | (100) ( ~ (all_32_0 = e0) & op(e1, e3) = all_32_0 &
% 135.84/19.98 | | | | | | | | | | | | $i(all_32_0)) | ( ~ (all_32_1 = e2) & op(e1, e1)
% 135.84/19.98 | | | | | | | | | | | | = all_32_1 & $i(all_32_1))
% 135.84/19.98 | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | BETA: splitting (100) gives:
% 135.84/19.98 | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | Case 1:
% 135.84/19.98 | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | (101) ~ (all_32_0 = e0) & op(e1, e3) = all_32_0 &
% 135.84/19.98 | | | | | | | | | | | | | $i(all_32_0)
% 135.84/19.98 | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | ALPHA: (101) implies:
% 135.84/19.98 | | | | | | | | | | | | | (102) ~ (all_32_0 = e0)
% 135.84/19.98 | | | | | | | | | | | | | (103) op(e1, e3) = all_32_0
% 135.84/19.98 | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | BETA: splitting (21) gives:
% 135.84/19.98 | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | Case 1:
% 135.84/19.98 | | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | | (104) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 135.84/19.98 | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 135.84/19.98 | | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | | BETA: splitting (104) gives:
% 135.84/19.98 | | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | | Case 1:
% 135.84/19.98 | | | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | | | (105) all_57_0 = e0 & op(e3, e3) = e0
% 135.84/19.98 | | | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | | | ALPHA: (105) implies:
% 135.84/19.98 | | | | | | | | | | | | | | | (106) op(e3, e3) = e0
% 135.84/19.98 | | | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | | | REF_CLOSE: (6), (31), (88), (106) are inconsistent by
% 135.84/19.98 | | | | | | | | | | | | | | | sub-proof #717.
% 135.84/19.98 | | | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | | Case 2:
% 135.84/19.98 | | | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | | | (107) all_57_2 = e0 & op(e2, e3) = e0
% 135.84/19.98 | | | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | | | REF_CLOSE: (5), (15), (107) are inconsistent by sub-proof
% 135.84/19.98 | | | | | | | | | | | | | | | #494.
% 135.84/19.98 | | | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | | End of split
% 135.84/19.98 | | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | Case 2:
% 135.84/19.98 | | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | | (108) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 135.84/19.98 | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 135.84/19.98 | | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 135.84/19.98 | | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | | Case 1:
% 135.84/19.98 | | | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | | | (109) all_57_6 = e0 & op(e1, e3) = e0
% 135.84/19.98 | | | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | | | ALPHA: (109) implies:
% 135.84/19.98 | | | | | | | | | | | | | | | (110) op(e1, e3) = e0
% 135.84/19.98 | | | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_32_0, all_56_5, e3, e1,
% 135.84/19.98 | | | | | | | | | | | | | | | simplifying with (86), (103) gives:
% 135.84/19.98 | | | | | | | | | | | | | | | (111) all_56_5 = all_32_0
% 135.84/19.98 | | | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with e0, all_56_5, e3, e1,
% 135.84/19.98 | | | | | | | | | | | | | | | simplifying with (86), (110) gives:
% 135.84/19.98 | | | | | | | | | | | | | | | (112) all_56_5 = e0
% 135.84/19.98 | | | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | | | COMBINE_EQS: (111), (112) imply:
% 135.84/19.98 | | | | | | | | | | | | | | | (113) all_32_0 = e0
% 135.84/19.98 | | | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | | | SIMP: (113) implies:
% 135.84/19.98 | | | | | | | | | | | | | | | (114) all_32_0 = e0
% 135.84/19.98 | | | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | | | REDUCE: (102), (114) imply:
% 135.84/19.98 | | | | | | | | | | | | | | | (115) $false
% 135.84/19.98 | | | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | | | CLOSE: (115) is inconsistent.
% 135.84/19.98 | | | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | | Case 2:
% 135.84/19.98 | | | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | | | (116) all_57_12 = e0 & op(e0, e3) = e0
% 135.84/19.98 | | | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | | | ALPHA: (116) implies:
% 135.84/19.98 | | | | | | | | | | | | | | | (117) all_57_12 = e0
% 135.84/19.98 | | | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (10), (15), (30), (84), (86), (88),
% 135.84/19.98 | | | | | | | | | | | | | | | (117) are inconsistent by sub-proof #144.
% 135.84/19.98 | | | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | | End of split
% 135.84/19.98 | | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | End of split
% 135.84/19.98 | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | Case 2:
% 135.84/19.98 | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | (118) ~ (all_32_1 = e2) & op(e1, e1) = all_32_1 &
% 135.84/19.98 | | | | | | | | | | | | | $i(all_32_1)
% 135.84/19.98 | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | REF_CLOSE: (6), (12), (118) are inconsistent by sub-proof
% 135.84/19.98 | | | | | | | | | | | | | #95.
% 135.84/19.98 | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | End of split
% 135.84/19.98 | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | End of split
% 135.84/19.98 | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | End of split
% 135.84/19.98 | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | End of split
% 135.84/19.98 | | | | | | | | |
% 135.84/19.98 | | | | | | | | Case 2:
% 135.84/19.98 | | | | | | | | |
% 135.84/19.98 | | | | | | | | | (119) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3)
% 135.84/19.98 | | | | | | | | | & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.84/19.98 | | | | | | | | | (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 135.84/19.98 | | | | | | | | | e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15
% 135.84/19.98 | | | | | | | | | & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 &
% 135.84/19.98 | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 135.84/19.98 | | | | | | | | | $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 &
% 135.84/19.98 | | | | | | | | | ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~
% 135.84/19.98 | | | | | | | | | (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3)
% 135.84/19.98 | | | | | | | | | = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) =
% 135.84/19.98 | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e2, e3) =
% 135.84/19.98 | | | | | | | | | e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9)
% 135.84/19.98 | | | | | | | | | & $i(all_56_17) & $i(all_56_25))
% 135.84/19.98 | | | | | | | | |
% 135.84/19.98 | | | | | | | | | REF_CLOSE: (2), (6), (8), (13), (18), (119) are inconsistent
% 135.84/19.98 | | | | | | | | | by sub-proof #457.
% 135.84/19.98 | | | | | | | | |
% 135.84/19.98 | | | | | | | | End of split
% 135.84/19.98 | | | | | | | |
% 135.84/19.98 | | | | | | | Case 2:
% 135.84/19.98 | | | | | | | |
% 135.84/19.98 | | | | | | | | (120) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) &
% 135.84/19.98 | | | | | | | | ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 135.84/19.98 | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2)
% 135.84/19.98 | | | | | | | | = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) =
% 135.84/19.98 | | | | | | | | all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 135.84/19.98 | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.84/19.98 | | | | | | | | $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 &
% 135.84/19.98 | | | | | | | | ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.84/19.98 | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) =
% 135.84/19.98 | | | | | | | | e1 & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1,
% 135.84/19.98 | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1,
% 135.84/19.98 | | | | | | | | e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.84/19.98 | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 &
% 135.84/19.98 | | | | | | | | all_56_27 = e2 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 135.84/19.98 | | | | | | | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.84/19.98 | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 135.84/19.98 | | | | | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) =
% 135.84/19.98 | | | | | | | | all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.84/19.98 | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.84/19.98 | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) &
% 135.84/19.98 | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.84/19.98 | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 135.84/19.98 | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 135.84/19.98 | | | | | | | | all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 135.84/19.98 | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.84/19.98 | | | | | | | | $i(all_56_27)) | (op(e0, e0) = all_56_31 &
% 135.84/19.98 | | | | | | | | $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~
% 135.84/19.98 | | | | | | | | (all_56_1 = e3) & ~ (all_56_9 = e2) & ~
% 135.84/19.98 | | | | | | | | (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3,
% 135.84/19.98 | | | | | | | | e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 135.84/19.98 | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.84/19.98 | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.84/19.98 | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0
% 135.84/19.98 | | | | | | | | & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 135.84/19.98 | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.84/19.98 | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2,
% 135.84/19.98 | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.84/19.98 | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.84/19.98 | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.84/19.98 | | | | | | | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1
% 135.84/19.98 | | | | | | | | & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~
% 135.84/19.98 | | | | | | | | (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1,
% 135.84/19.98 | | | | | | | | e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 135.84/19.98 | | | | | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) =
% 135.84/19.98 | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 135.84/19.98 | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 135.84/19.98 | | | | | | | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.84/19.98 | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1,
% 135.84/19.98 | | | | | | | | e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 135.84/19.98 | | | | | | | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 135.84/19.98 | | | | | | | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.84/19.98 | | | | | | | | $i(all_56_21) & $i(all_56_29))))
% 135.84/19.98 | | | | | | | |
% 135.84/19.98 | | | | | | | | BETA: splitting (120) gives:
% 135.84/19.98 | | | | | | | |
% 135.84/19.98 | | | | | | | | Case 1:
% 135.84/19.98 | | | | | | | | |
% 135.84/19.98 | | | | | | | | | (121) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3)
% 135.84/19.98 | | | | | | | | | & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 135.84/19.98 | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3,
% 135.84/19.98 | | | | | | | | | e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.84/19.98 | | | | | | | | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) =
% 135.84/19.98 | | | | | | | | | e3 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.84/19.98 | | | | | | | | | $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 &
% 135.84/19.98 | | | | | | | | | ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.84/19.98 | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2)
% 135.84/19.98 | | | | | | | | | = e1 & op(e2, e1) = e2 & op(e1, e3) = all_56_5 &
% 135.84/19.98 | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 135.84/19.98 | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.84/19.98 | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 135.84/19.98 | | | | | | | | |
% 135.84/19.98 | | | | | | | | | REF_CLOSE: (6), (9), (12), (16), (19), (121) are inconsistent
% 135.84/19.98 | | | | | | | | | by sub-proof #108.
% 135.84/19.98 | | | | | | | | |
% 135.84/19.98 | | | | | | | | Case 2:
% 135.84/19.98 | | | | | | | | |
% 135.84/19.98 | | | | | | | | | (122) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3)
% 135.84/19.98 | | | | | | | | | & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.84/19.98 | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) =
% 135.84/19.98 | | | | | | | | | e2 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15
% 135.84/19.98 | | | | | | | | | & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 &
% 135.84/19.98 | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 135.84/19.98 | | | | | | | | | $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 &
% 135.84/19.98 | | | | | | | | | ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~
% 135.84/19.98 | | | | | | | | | (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3)
% 135.84/19.98 | | | | | | | | | = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.84/19.98 | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) =
% 135.84/19.98 | | | | | | | | | e1 & op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11)
% 135.84/19.98 | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 135.84/19.98 | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 135.84/19.98 | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 135.84/19.98 | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 135.84/19.98 | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.84/19.98 | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17
% 135.84/19.98 | | | | | | | | | & op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 135.84/19.98 | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.84/19.98 | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 135.84/19.98 | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 135.84/19.98 | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.84/19.98 | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11
% 135.84/19.98 | | | | | | | | | & op(e2, e1) = all_56_19 & op(e2, e0) =
% 135.84/19.98 | | | | | | | | | all_56_27 & op(e0, e2) = e0 & $i(all_56_3) &
% 135.84/19.98 | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27))
% 135.84/19.98 | | | | | | | | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7
% 135.84/19.98 | | | | | | | | | = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.84/19.98 | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 135.84/19.98 | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 135.84/19.98 | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23
% 135.84/19.98 | | | | | | | | | & $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 135.84/19.98 | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5
% 135.84/19.98 | | | | | | | | | = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.84/19.98 | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 135.84/19.98 | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1)
% 135.84/19.98 | | | | | | | | | = all_56_21 & op(e1, e0) = all_56_29 & op(e0,
% 135.84/19.98 | | | | | | | | | e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.84/19.98 | | | | | | | | | $i(all_56_21) & $i(all_56_29))))
% 135.84/19.98 | | | | | | | | |
% 135.84/19.98 | | | | | | | | | BETA: splitting (122) gives:
% 135.84/19.98 | | | | | | | | |
% 135.84/19.98 | | | | | | | | | Case 1:
% 135.84/19.98 | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | (123) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 135.84/19.98 | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 135.84/19.98 | | | | | | | | | | ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 135.84/19.98 | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.84/19.98 | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 135.84/19.98 | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 135.84/19.98 | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 135.84/19.98 | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | ALPHA: (123) implies:
% 135.84/19.98 | | | | | | | | | | (124) op(e2, e0) = e2
% 135.84/19.98 | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | REF_CLOSE: (3), (6), (9), (72), (124) are inconsistent by
% 135.84/19.98 | | | | | | | | | | sub-proof #546.
% 135.84/19.98 | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | Case 2:
% 135.84/19.98 | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | (125) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.84/19.98 | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 135.84/19.98 | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.84/19.98 | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.84/19.98 | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 135.84/19.98 | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 135.84/19.98 | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 135.84/19.98 | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 135.84/19.98 | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 135.84/19.98 | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 135.84/19.98 | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.84/19.98 | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 135.84/19.98 | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 135.84/19.98 | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.84/19.98 | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 135.84/19.98 | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 135.84/19.98 | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.84/19.98 | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.84/19.98 | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.84/19.98 | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 135.84/19.98 | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.84/19.98 | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 135.84/19.98 | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.84/19.98 | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.84/19.98 | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.84/19.98 | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.84/19.98 | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.84/19.98 | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 135.84/19.98 | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 135.84/19.98 | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.84/19.98 | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 135.84/19.98 | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.84/19.98 | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1,
% 135.84/19.98 | | | | | | | | | | e0) = all_56_29 & op(e0, e1) = e0 &
% 135.84/19.98 | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.84/19.98 | | | | | | | | | | & $i(all_56_29))))
% 135.84/19.98 | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | BETA: splitting (125) gives:
% 135.84/19.98 | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | Case 1:
% 135.84/19.98 | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | (126) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.84/19.98 | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 135.84/19.98 | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.84/19.98 | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.84/19.98 | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 135.84/19.98 | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 135.84/19.98 | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 135.84/19.98 | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | ALPHA: (126) implies:
% 135.84/19.98 | | | | | | | | | | | (127) ~ (all_56_19 = e1)
% 135.84/19.98 | | | | | | | | | | | (128) op(e2, e1) = all_56_19
% 135.84/19.98 | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | REF_CLOSE: (6), (78), (127), (128) are inconsistent by
% 135.84/19.98 | | | | | | | | | | | sub-proof #106.
% 135.84/19.98 | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | Case 2:
% 135.84/19.98 | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | (129) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.84/19.98 | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 135.84/19.98 | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 135.84/19.98 | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.84/19.98 | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 135.84/19.98 | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 135.84/19.98 | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.84/19.98 | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 135.84/19.98 | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 135.84/19.98 | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.84/19.98 | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.84/19.98 | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.84/19.98 | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 135.84/19.98 | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.84/19.98 | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 135.84/19.98 | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.84/19.98 | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.84/19.98 | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.84/19.98 | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.84/19.98 | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.84/19.98 | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 135.84/19.98 | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 135.84/19.98 | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.84/19.98 | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 135.84/19.98 | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 135.84/19.98 | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 135.84/19.98 | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 135.84/19.98 | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 135.84/19.98 | | | | | | | | | | | $i(all_56_29)))
% 135.84/19.98 | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | ALPHA: (129) implies:
% 135.84/19.98 | | | | | | | | | | | (130) op(e0, e0) = all_56_31
% 135.84/19.98 | | | | | | | | | | | (131) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 135.84/19.98 | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.84/19.98 | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.84/19.98 | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.84/19.98 | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 135.84/19.98 | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.84/19.98 | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 135.84/19.98 | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 135.84/19.98 | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.84/19.98 | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.84/19.98 | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 135.84/19.98 | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 135.84/19.98 | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 135.84/19.98 | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.84/19.98 | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.84/19.98 | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 135.84/19.98 | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.84/19.98 | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 135.84/19.98 | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 135.84/19.98 | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 135.84/19.98 | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.84/19.98 | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 135.84/19.98 | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.84/19.98 | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 135.84/19.98 | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.84/19.98 | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 135.84/19.98 | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | BETA: splitting (131) gives:
% 135.84/19.98 | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | Case 1:
% 135.84/19.98 | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | (132) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 135.84/19.98 | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.84/19.98 | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.84/19.98 | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.84/19.98 | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 135.84/19.98 | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.84/19.98 | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 135.84/19.98 | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 135.84/19.98 | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.84/19.98 | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.84/19.98 | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 135.84/19.98 | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 135.84/19.98 | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27))
% 135.84/19.98 | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | REF_CLOSE: (6), (35), (78), (132) are inconsistent by
% 135.84/19.98 | | | | | | | | | | | | sub-proof #91.
% 135.84/19.98 | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | Case 2:
% 135.84/19.98 | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | (133) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 135.84/19.98 | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.84/19.98 | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 135.84/19.98 | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.84/19.98 | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.84/19.98 | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 135.84/19.98 | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 135.84/19.98 | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.84/19.98 | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 135.84/19.98 | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.84/19.98 | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 135.84/19.98 | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.84/19.98 | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 135.84/19.98 | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | BETA: splitting (133) gives:
% 135.84/19.98 | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | Case 1:
% 135.84/19.98 | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | (134) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 135.84/19.98 | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 135.84/19.98 | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 135.84/19.98 | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 135.84/19.98 | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7)
% 135.84/19.98 | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23)
% 135.84/19.98 | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | ALPHA: (134) implies:
% 135.84/19.98 | | | | | | | | | | | | | (135) op(e1, e1) = e0
% 135.84/19.98 | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | REF_CLOSE: (5), (6), (12), (135) are inconsistent by
% 135.84/19.98 | | | | | | | | | | | | | sub-proof #98.
% 135.84/19.98 | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | Case 2:
% 135.84/19.98 | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | (136) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 135.84/19.98 | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1)
% 135.84/19.98 | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 135.84/19.98 | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 135.84/19.98 | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.84/19.98 | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.84/19.98 | | | | | | | | | | | | | $i(all_56_29)
% 135.84/19.98 | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | ALPHA: (136) implies:
% 135.84/19.98 | | | | | | | | | | | | | (137) all_56_31 = e1
% 135.84/19.98 | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | REDUCE: (130), (137) imply:
% 135.84/19.98 | | | | | | | | | | | | | (138) op(e0, e0) = e1
% 135.84/19.98 | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | | REF_CLOSE: (6), (7), (24), (138) are inconsistent by
% 135.84/19.98 | | | | | | | | | | | | | sub-proof #636.
% 135.84/19.98 | | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | | End of split
% 135.84/19.98 | | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | | End of split
% 135.84/19.98 | | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | | End of split
% 135.84/19.98 | | | | | | | | | |
% 135.84/19.98 | | | | | | | | | End of split
% 135.84/19.98 | | | | | | | | |
% 135.84/19.98 | | | | | | | | End of split
% 135.84/19.98 | | | | | | | |
% 135.84/19.98 | | | | | | | End of split
% 135.84/19.98 | | | | | | |
% 135.84/19.98 | | | | | | Case 2:
% 135.84/19.98 | | | | | | |
% 135.84/19.98 | | | | | | | (139) all_54_6 = e0
% 135.84/19.98 | | | | | | |
% 135.84/19.98 | | | | | | | REF_CLOSE: (40), (45), (139) are inconsistent by sub-proof #92.
% 135.84/19.98 | | | | | | |
% 135.84/19.98 | | | | | | End of split
% 135.84/19.98 | | | | | |
% 135.84/19.98 | | | | | End of split
% 135.84/19.98 | | | | |
% 135.84/19.98 | | | | End of split
% 135.84/19.98 | | | |
% 135.84/19.98 | | | End of split
% 135.84/19.98 | | |
% 135.84/19.98 | | End of split
% 135.84/19.98 | |
% 135.84/19.98 | Case 2:
% 135.84/19.98 | |
% 135.84/19.98 | | (140) ~ (all_18_1 = e0) & op(e2, e2) = all_18_1 & $i(all_18_1)
% 135.84/19.98 | |
% 135.84/19.98 | | REF_CLOSE: (2), (6), (140) are inconsistent by sub-proof #103.
% 135.84/19.98 | |
% 135.84/19.98 | End of split
% 135.84/19.98 |
% 135.84/19.98 End of proof
% 135.84/19.98
% 135.84/19.98 Sub-proof #91 shows that the following formulas are inconsistent:
% 135.84/19.98 ----------------------------------------------------------------
% 135.84/19.98 (1) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2)
% 135.84/19.98 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.84/19.98 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25
% 135.84/19.98 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.84/19.98 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3)
% 135.84/19.98 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.84/19.98 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 135.84/19.98 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) &
% 135.84/19.98 $i(all_56_11) & $i(all_56_19) & $i(all_56_27))
% 135.84/19.98 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.84/19.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.84/19.98 (3) op(e3, e2) = e2
% 135.84/19.98 (4) op(e2, e1) = e1
% 135.84/19.98
% 135.84/19.98 Begin of proof
% 135.84/19.98 |
% 135.84/19.98 | BETA: splitting (1) gives:
% 135.84/19.98 |
% 135.84/19.98 | Case 1:
% 135.84/19.98 | |
% 135.84/19.98 | | (5) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 135.84/19.98 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.84/19.98 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.84/19.98 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.84/19.98 | | $i(all_56_17) & $i(all_56_25)
% 135.84/19.98 | |
% 135.84/19.98 | | ALPHA: (5) implies:
% 135.84/19.98 | | (6) ~ (all_56_9 = e2)
% 135.84/19.98 | | (7) op(e3, e2) = all_56_9
% 135.84/19.98 | |
% 135.84/19.98 | | REF_CLOSE: (2), (3), (6), (7) are inconsistent by sub-proof #199.
% 135.84/19.98 | |
% 135.84/19.98 | Case 2:
% 135.84/19.98 | |
% 135.84/19.99 | | (8) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11
% 135.84/19.99 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.84/19.99 | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 135.84/19.99 | | e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.84/19.99 | | $i(all_56_19) & $i(all_56_27)
% 135.84/19.99 | |
% 135.84/19.99 | | ALPHA: (8) implies:
% 135.84/19.99 | | (9) ~ (all_56_19 = e1)
% 135.84/19.99 | | (10) op(e2, e1) = all_56_19
% 135.84/19.99 | |
% 135.84/19.99 | | REF_CLOSE: (2), (4), (9), (10) are inconsistent by sub-proof #106.
% 135.84/19.99 | |
% 135.84/19.99 | End of split
% 135.84/19.99 |
% 135.84/19.99 End of proof
% 135.84/19.99
% 135.84/19.99 Sub-proof #92 shows that the following formulas are inconsistent:
% 135.84/19.99 ----------------------------------------------------------------
% 135.84/19.99 (1) all_54_6 = all_18_0
% 135.84/19.99 (2) all_54_6 = e0
% 135.84/19.99 (3) ~ (all_18_0 = e0)
% 135.84/19.99
% 135.84/19.99 Begin of proof
% 135.84/19.99 |
% 135.84/19.99 | COMBINE_EQS: (1), (2) imply:
% 135.84/19.99 | (4) all_18_0 = e0
% 135.84/19.99 |
% 135.84/19.99 | SIMP: (4) implies:
% 135.84/19.99 | (5) all_18_0 = e0
% 135.84/19.99 |
% 135.84/19.99 | REDUCE: (3), (5) imply:
% 135.84/19.99 | (6) $false
% 135.84/19.99 |
% 135.84/19.99 | CLOSE: (6) is inconsistent.
% 135.84/19.99 |
% 135.84/19.99 End of proof
% 135.84/19.99
% 135.84/19.99 Sub-proof #93 shows that the following formulas are inconsistent:
% 135.84/19.99 ----------------------------------------------------------------
% 135.84/19.99 (1) op(e2, e2) = e0
% 135.84/19.99 (2) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 135.84/19.99 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.84/19.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.84/19.99 (4) ~ (e2 = e1)
% 135.84/19.99 (5) ~ (e1 = e0)
% 135.84/19.99 (6) op(e2, e3) = e2
% 135.84/19.99
% 135.84/19.99 Begin of proof
% 135.84/19.99 |
% 135.84/19.99 | BETA: splitting (2) gives:
% 135.84/19.99 |
% 135.84/19.99 | Case 1:
% 135.84/19.99 | |
% 135.84/19.99 | | (7) all_57_2 = e1 & op(e2, e3) = e1
% 135.84/19.99 | |
% 135.84/19.99 | | ALPHA: (7) implies:
% 135.84/19.99 | | (8) op(e2, e3) = e1
% 135.84/19.99 | |
% 135.84/19.99 | | REF_CLOSE: (3), (4), (6), (8) are inconsistent by sub-proof #450.
% 135.84/19.99 | |
% 135.84/19.99 | Case 2:
% 135.84/19.99 | |
% 135.84/19.99 | | (9) all_57_3 = e1 & op(e2, e2) = e1
% 135.84/19.99 | |
% 135.84/19.99 | | ALPHA: (9) implies:
% 135.84/19.99 | | (10) op(e2, e2) = e1
% 135.84/19.99 | |
% 135.84/19.99 | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #675.
% 135.84/19.99 | |
% 135.84/19.99 | End of split
% 135.84/19.99 |
% 135.84/19.99 End of proof
% 135.84/19.99
% 135.84/19.99 Sub-proof #94 shows that the following formulas are inconsistent:
% 135.84/19.99 ----------------------------------------------------------------
% 135.84/19.99 (1) op(e2, e2) = e0
% 135.84/19.99 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.84/19.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.84/19.99 (3) ~ (e3 = e0)
% 135.84/19.99 (4) ~ (e3 = e2)
% 135.84/19.99 (5) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 135.84/19.99 (6) all_57_2 = e2
% 135.84/19.99
% 135.84/19.99 Begin of proof
% 135.84/19.99 |
% 135.84/19.99 | BETA: splitting (5) gives:
% 135.84/19.99 |
% 135.84/19.99 | Case 1:
% 135.84/19.99 | |
% 135.84/19.99 | | (7) all_57_2 = e3 & op(e2, e3) = e3
% 135.84/19.99 | |
% 135.84/19.99 | | REF_CLOSE: (4), (6), (7) are inconsistent by sub-proof #590.
% 135.84/19.99 | |
% 135.84/19.99 | Case 2:
% 135.84/19.99 | |
% 135.84/19.99 | | (8) all_57_3 = e3 & op(e2, e2) = e3
% 135.84/19.99 | |
% 135.84/19.99 | | ALPHA: (8) implies:
% 135.84/19.99 | | (9) op(e2, e2) = e3
% 135.84/19.99 | |
% 135.84/19.99 | | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #641.
% 135.84/19.99 | |
% 135.84/19.99 | End of split
% 135.84/19.99 |
% 135.84/19.99 End of proof
% 135.84/19.99
% 135.84/19.99 Sub-proof #95 shows that the following formulas are inconsistent:
% 135.84/19.99 ----------------------------------------------------------------
% 135.84/19.99 (1) ~ (all_32_1 = e2) & op(e1, e1) = all_32_1 & $i(all_32_1)
% 135.84/19.99 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.84/19.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.84/19.99 (3) op(e1, e1) = e2
% 135.84/19.99
% 135.84/19.99 Begin of proof
% 135.84/19.99 |
% 135.84/19.99 | ALPHA: (1) implies:
% 135.84/19.99 | (4) ~ (all_32_1 = e2)
% 135.84/19.99 | (5) op(e1, e1) = all_32_1
% 135.84/19.99 |
% 135.84/19.99 | GROUND_INST: instantiating (2) with e2, all_32_1, e1, e1, simplifying with
% 135.84/19.99 | (3), (5) gives:
% 135.84/19.99 | (6) all_32_1 = e2
% 135.84/19.99 |
% 135.84/19.99 | REDUCE: (4), (6) imply:
% 135.84/19.99 | (7) $false
% 135.84/19.99 |
% 135.84/19.99 | CLOSE: (7) is inconsistent.
% 135.84/19.99 |
% 135.84/19.99 End of proof
% 135.84/19.99
% 135.84/19.99 Sub-proof #96 shows that the following formulas are inconsistent:
% 135.84/19.99 ----------------------------------------------------------------
% 135.84/19.99 (1) all_54_8 = all_32_0
% 135.84/19.99 (2) ~ (all_32_0 = e2)
% 135.84/19.99 (3) ~ (all_32_0 = e0)
% 135.84/19.99 (4) ~ (all_32_0 = e1)
% 135.84/19.99 (5) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 135.84/19.99
% 135.84/19.99 Begin of proof
% 135.84/19.99 |
% 135.84/19.99 | BETA: splitting (5) gives:
% 135.84/19.99 |
% 135.84/19.99 | Case 1:
% 135.84/19.99 | |
% 135.84/19.99 | | (6) all_54_8 = e2
% 135.84/19.99 | |
% 135.84/19.99 | | COMBINE_EQS: (1), (6) imply:
% 135.84/19.99 | | (7) all_32_0 = e2
% 135.84/19.99 | |
% 135.84/19.99 | | REDUCE: (2), (7) imply:
% 135.84/19.99 | | (8) $false
% 135.84/19.99 | |
% 135.84/19.99 | | CLOSE: (8) is inconsistent.
% 135.84/19.99 | |
% 135.84/19.99 | Case 2:
% 135.84/19.99 | |
% 135.84/19.99 | | (9) all_54_8 = e1 | all_54_8 = e0
% 135.84/19.99 | |
% 135.84/19.99 | | BETA: splitting (9) gives:
% 135.84/19.99 | |
% 135.84/19.99 | | Case 1:
% 135.84/19.99 | | |
% 135.84/19.99 | | | (10) all_54_8 = e1
% 135.84/19.99 | | |
% 135.84/19.99 | | | COMBINE_EQS: (1), (10) imply:
% 135.84/19.99 | | | (11) all_32_0 = e1
% 135.84/19.99 | | |
% 135.84/19.99 | | | REDUCE: (4), (11) imply:
% 135.84/19.99 | | | (12) $false
% 135.84/19.99 | | |
% 135.84/19.99 | | | CLOSE: (12) is inconsistent.
% 135.84/19.99 | | |
% 135.84/19.99 | | Case 2:
% 135.84/19.99 | | |
% 135.84/19.99 | | | (13) all_54_8 = e0
% 135.84/19.99 | | |
% 135.84/19.99 | | | COMBINE_EQS: (1), (13) imply:
% 135.84/19.99 | | | (14) all_32_0 = e0
% 135.84/19.99 | | |
% 135.84/19.99 | | | REDUCE: (3), (14) imply:
% 135.84/19.99 | | | (15) $false
% 135.84/19.99 | | |
% 135.84/19.99 | | | CLOSE: (15) is inconsistent.
% 135.84/19.99 | | |
% 135.84/19.99 | | End of split
% 135.84/19.99 | |
% 135.84/19.99 | End of split
% 135.84/19.99 |
% 135.84/19.99 End of proof
% 135.84/19.99
% 135.84/19.99 Sub-proof #97 shows that the following formulas are inconsistent:
% 135.84/19.99 ----------------------------------------------------------------
% 135.84/19.99 (1) all_57_12 = e2 & op(e0, e3) = e2
% 135.84/19.99 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.84/19.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.84/19.99 (3) op(e0, e3) = all_52_3
% 135.84/19.99 (4) ~ (all_52_3 = e2)
% 135.84/19.99
% 135.84/19.99 Begin of proof
% 135.84/19.99 |
% 135.84/19.99 | ALPHA: (1) implies:
% 135.84/19.99 | (5) op(e0, e3) = e2
% 135.84/19.99 |
% 135.84/19.99 | GROUND_INST: instantiating (2) with all_52_3, e2, e3, e0, simplifying with
% 135.84/19.99 | (3), (5) gives:
% 135.84/19.99 | (6) all_52_3 = e2
% 135.84/19.99 |
% 135.84/19.99 | REDUCE: (4), (6) imply:
% 135.84/19.99 | (7) $false
% 135.84/19.99 |
% 135.84/19.99 | CLOSE: (7) is inconsistent.
% 135.84/19.99 |
% 135.84/19.99 End of proof
% 135.84/19.99
% 135.84/19.99 Sub-proof #98 shows that the following formulas are inconsistent:
% 135.84/19.99 ----------------------------------------------------------------
% 135.84/19.99 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.84/19.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.84/19.99 (2) op(e1, e1) = e2
% 135.84/19.99 (3) op(e1, e1) = e0
% 135.84/19.99 (4) ~ (e2 = e0)
% 135.84/19.99
% 135.84/19.99 Begin of proof
% 135.84/19.99 |
% 135.84/19.99 | GROUND_INST: instantiating (1) with e2, e0, e1, e1, simplifying with (2), (3)
% 135.84/19.99 | gives:
% 135.84/19.99 | (5) e2 = e0
% 135.84/19.99 |
% 135.84/19.99 | REDUCE: (4), (5) imply:
% 135.84/19.99 | (6) $false
% 135.84/19.99 |
% 135.84/19.99 | CLOSE: (6) is inconsistent.
% 135.84/19.99 |
% 135.84/19.99 End of proof
% 135.84/19.99
% 135.84/19.99 Sub-proof #99 shows that the following formulas are inconsistent:
% 135.84/19.99 ----------------------------------------------------------------
% 135.84/19.99 (1) all_54_12 = all_52_3
% 135.84/19.99 (2) all_54_12 = e1
% 135.84/19.99 (3) ~ (all_52_3 = e1)
% 135.84/19.99
% 135.84/19.99 Begin of proof
% 135.84/19.99 |
% 135.84/19.99 | COMBINE_EQS: (1), (2) imply:
% 135.84/19.99 | (4) all_52_3 = e1
% 135.84/19.99 |
% 135.84/19.99 | SIMP: (4) implies:
% 135.84/19.99 | (5) all_52_3 = e1
% 135.84/19.99 |
% 135.84/19.99 | REDUCE: (3), (5) imply:
% 135.84/19.99 | (6) $false
% 135.84/19.99 |
% 135.84/19.99 | CLOSE: (6) is inconsistent.
% 135.84/19.99 |
% 135.84/19.99 End of proof
% 135.84/19.99
% 135.84/19.99 Sub-proof #100 shows that the following formulas are inconsistent:
% 135.84/19.99 ----------------------------------------------------------------
% 135.84/19.99 (1) all_57_13 = e2 & op(e0, e2) = e2
% 135.84/19.99 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.84/19.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.84/19.99 (3) op(e0, e2) = all_52_7
% 135.84/19.99 (4) ~ (all_52_7 = e2)
% 135.84/19.99
% 135.84/19.99 Begin of proof
% 135.84/19.99 |
% 135.84/19.99 | ALPHA: (1) implies:
% 135.84/19.99 | (5) op(e0, e2) = e2
% 135.84/19.99 |
% 135.84/19.99 | GROUND_INST: instantiating (2) with all_52_7, e2, e2, e0, simplifying with
% 135.84/19.99 | (3), (5) gives:
% 135.84/19.99 | (6) all_52_7 = e2
% 135.84/19.99 |
% 135.84/19.99 | REDUCE: (4), (6) imply:
% 135.84/19.99 | (7) $false
% 135.84/19.99 |
% 135.84/19.99 | CLOSE: (7) is inconsistent.
% 135.84/19.99 |
% 135.84/19.99 End of proof
% 135.84/19.99
% 135.84/19.99 Sub-proof #101 shows that the following formulas are inconsistent:
% 135.84/19.99 ----------------------------------------------------------------
% 135.84/19.99 (1) op(e0, e0) = all_4_2
% 135.84/19.99 (2) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 135.84/19.99 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 135.84/19.99 (3) op(e2, e0) = all_52_13
% 135.84/19.99 (4) ~ (e2 = e0)
% 135.84/19.99 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.84/19.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.84/19.99 (6) op(e1, e1) = e2
% 135.84/19.99 (7) ~ (all_52_9 = e2)
% 135.84/19.99 (8) ~ (all_4_2 = e1)
% 135.84/19.99 (9) ~ (all_52_13 = e2)
% 135.84/19.99 (10) op(e2, e1) = all_52_9
% 135.84/19.99 (11) ~ (all_52_1 = e2)
% 135.84/19.99 (12) op(e0, e3) = all_52_3
% 135.84/19.99 (13) op(e2, e3) = all_52_1
% 135.84/19.99 (14) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 135.84/19.99 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.84/19.99 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0)
% 135.84/19.99 = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.84/19.99 $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~
% 135.84/19.99 (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.84/19.99 (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.84/19.99 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.84/19.99 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.84/19.99 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 135.84/19.99 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 135.84/19.99 op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 135.84/19.99 op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 135.84/19.99 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13
% 135.84/19.99 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 135.84/19.99 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1,
% 135.84/19.99 e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.84/19.99 $i(all_56_21) & $i(all_56_29))
% 135.84/19.99 (15) all_57_3 = e2
% 135.84/19.99 (16) op(e2, e2) = e2
% 135.84/19.99 (17) ~ (all_52_3 = e0)
% 135.84/19.99 (18) op(e0, e0) = all_56_31
% 135.84/19.99
% 135.84/19.99 Begin of proof
% 135.84/19.99 |
% 135.84/19.99 | BETA: splitting (14) gives:
% 135.84/19.99 |
% 135.84/19.99 | Case 1:
% 135.84/19.99 | |
% 135.84/19.99 | | (19) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 135.84/19.99 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.84/19.99 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.84/19.99 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9)
% 135.84/19.99 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 135.84/19.99 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.84/19.99 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 135.84/19.99 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 135.84/19.99 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.84/19.99 | | $i(all_56_27))
% 135.84/19.99 | |
% 135.84/19.99 | | BETA: splitting (19) gives:
% 135.84/19.99 | |
% 135.84/19.99 | | Case 1:
% 135.84/19.99 | | |
% 135.84/19.99 | | | (20) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 135.84/19.99 | | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.84/19.99 | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.84/19.99 | | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9)
% 135.84/19.99 | | | & $i(all_56_17) & $i(all_56_25)
% 135.84/19.99 | | |
% 135.84/19.99 | | | ALPHA: (20) implies:
% 135.84/19.99 | | | (21) op(e0, e3) = e0
% 135.84/19.99 | | |
% 135.84/19.99 | | | REF_CLOSE: (5), (12), (17), (21) are inconsistent by sub-proof #219.
% 135.84/19.99 | | |
% 135.84/19.99 | | Case 2:
% 135.84/19.99 | | |
% 135.84/19.99 | | | (22) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 135.84/19.99 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.84/19.99 | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.84/19.99 | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.84/19.99 | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)
% 135.84/19.99 | | |
% 135.84/19.99 | | | ALPHA: (22) implies:
% 135.84/19.99 | | | (23) ~ (all_56_11 = e2)
% 135.84/19.99 | | | (24) op(e2, e2) = all_56_11
% 135.84/19.99 | | |
% 135.84/19.99 | | | REF_CLOSE: (5), (16), (23), (24) are inconsistent by sub-proof #531.
% 135.84/19.99 | | |
% 135.84/19.99 | | End of split
% 135.84/19.99 | |
% 135.84/19.99 | Case 2:
% 135.84/19.99 | |
% 135.84/19.99 | | (25) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.84/19.99 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.84/19.99 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.84/19.99 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 135.84/19.99 | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 135.84/19.99 | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 135.84/19.99 | | ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.84/19.99 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 135.84/19.99 | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.84/19.99 | | $i(all_56_29))
% 135.84/19.99 | |
% 135.84/19.99 | | BETA: splitting (25) gives:
% 135.84/19.99 | |
% 135.84/19.99 | | Case 1:
% 135.84/19.99 | | |
% 135.84/19.99 | | | (26) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.84/19.99 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.84/19.99 | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.84/19.99 | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 135.84/19.99 | | | $i(all_56_15) & $i(all_56_23)
% 135.84/19.99 | | |
% 135.84/19.99 | | | ALPHA: (26) implies:
% 135.84/19.99 | | | (27) op(e1, e1) = e0
% 135.84/19.99 | | |
% 135.84/19.99 | | | GROUND_INST: instantiating (5) with e2, e0, e1, e1, simplifying with (6),
% 135.84/19.99 | | | (27) gives:
% 135.84/19.99 | | | (28) e2 = e0
% 135.84/19.99 | | |
% 135.84/19.99 | | | REF_CLOSE: (2), (3), (4), (5), (7), (9), (10), (11), (13), (15), (28) are
% 135.84/19.99 | | | inconsistent by sub-proof #359.
% 135.84/19.99 | | |
% 135.84/19.99 | | Case 2:
% 135.84/19.99 | | |
% 135.84/19.99 | | | (29) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 135.84/19.99 | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 135.84/19.99 | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.84/19.99 | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.84/19.99 | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 135.84/19.99 | | |
% 135.84/19.99 | | | ALPHA: (29) implies:
% 135.84/19.99 | | | (30) all_56_31 = e1
% 135.84/19.99 | | |
% 135.84/19.99 | | | REDUCE: (18), (30) imply:
% 135.84/19.99 | | | (31) op(e0, e0) = e1
% 135.84/19.99 | | |
% 135.84/19.99 | | | REF_CLOSE: (1), (5), (8), (31) are inconsistent by sub-proof #354.
% 135.84/19.99 | | |
% 135.84/19.99 | | End of split
% 135.84/19.99 | |
% 135.84/19.99 | End of split
% 135.84/19.99 |
% 135.84/19.99 End of proof
% 135.84/19.99
% 135.84/19.99 Sub-proof #102 shows that the following formulas are inconsistent:
% 135.84/19.99 ----------------------------------------------------------------
% 135.84/19.99 (1) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2)
% 135.84/19.99 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3,
% 135.84/19.99 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 135.84/19.99 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.84/19.99 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 135.84/19.99 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.84/19.99 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) =
% 135.84/19.99 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.84/19.99 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.84/19.99 $i(all_56_21) & $i(all_56_29))
% 135.84/19.99 (2) ~ (e2 = e0)
% 135.84/19.99 (3) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 135.84/19.99 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 135.84/19.99 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.84/19.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.84/19.99 (5) ~ (e2 = e1)
% 135.84/19.99 (6) ~ (e3 = e0)
% 135.84/19.99 (7) ~ (e3 = e2)
% 135.84/19.99 (8) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 135.84/19.99 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 135.84/19.99 (9) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 135.84/19.99 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 135.84/19.99 (10) ~ (e3 = e1)
% 135.84/19.99 (11) ~ (e1 = e0)
% 135.84/19.99 (12) all_57_12 = e2
% 135.84/19.99 (13) op(e1, e3) = e3
% 135.84/19.99
% 135.84/19.99 Begin of proof
% 135.84/19.99 |
% 135.84/19.99 | BETA: splitting (1) gives:
% 135.84/19.99 |
% 135.84/19.99 | Case 1:
% 135.84/19.99 | |
% 135.84/19.99 | | (14) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.84/19.99 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2
% 135.84/19.99 | | & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.84/19.99 | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.84/19.99 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)
% 135.84/19.99 | |
% 135.84/19.99 | | ALPHA: (14) implies:
% 135.84/19.99 | | (15) op(e3, e3) = e2
% 135.84/19.99 | |
% 135.84/19.99 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (15)
% 135.84/19.99 | | are inconsistent by sub-proof #290.
% 135.84/19.99 | |
% 135.84/19.99 | Case 2:
% 135.84/19.99 | |
% 135.84/19.99 | | (16) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13
% 135.84/19.99 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) =
% 135.84/19.99 | | e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.84/19.99 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 135.84/19.99 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 135.84/19.99 | |
% 135.84/19.99 | | ALPHA: (16) implies:
% 135.84/19.99 | | (17) ~ (all_56_5 = e3)
% 135.84/19.99 | | (18) op(e1, e3) = all_56_5
% 135.84/19.99 | |
% 135.84/19.99 | | REF_CLOSE: (4), (13), (17), (18) are inconsistent by sub-proof #724.
% 135.84/19.99 | |
% 135.84/19.99 | End of split
% 135.84/19.99 |
% 135.84/19.99 End of proof
% 135.84/19.99
% 135.84/19.99 Sub-proof #103 shows that the following formulas are inconsistent:
% 135.84/19.99 ----------------------------------------------------------------
% 135.84/19.99 (1) ~ (all_18_1 = e0) & op(e2, e2) = all_18_1 & $i(all_18_1)
% 135.84/19.99 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.84/19.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.84/19.99 (3) op(e2, e2) = e0
% 135.84/19.99
% 135.84/19.99 Begin of proof
% 135.84/19.99 |
% 135.84/19.99 | ALPHA: (1) implies:
% 135.84/19.99 | (4) ~ (all_18_1 = e0)
% 135.84/19.99 | (5) op(e2, e2) = all_18_1
% 135.84/19.99 |
% 135.84/19.99 | GROUND_INST: instantiating (2) with e0, all_18_1, e2, e2, simplifying with
% 135.84/19.99 | (3), (5) gives:
% 135.84/19.99 | (6) all_18_1 = e0
% 135.84/19.99 |
% 135.84/19.99 | REDUCE: (4), (6) imply:
% 135.84/19.99 | (7) $false
% 135.84/19.99 |
% 135.84/19.99 | CLOSE: (7) is inconsistent.
% 135.84/19.99 |
% 135.84/19.99 End of proof
% 135.84/19.99
% 135.84/19.99 Sub-proof #104 shows that the following formulas are inconsistent:
% 135.84/19.99 ----------------------------------------------------------------
% 135.84/19.99 (1) op(e2, e1) = e1
% 135.84/19.99 (2) all_54_0 = all_10_2
% 135.84/19.99 (3) op(e0, e0) = all_4_2
% 135.84/19.99 (4) op(e1, e1) = all_6_2
% 135.84/19.99 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.84/19.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.84/19.99 (6) op(e2, e2) = e3
% 135.84/19.99 (7) all_54_2 = all_52_8
% 135.84/19.99 (8) op(e1, e1) = e2
% 135.84/19.99 (9) ~ (all_52_12 = all_10_2)
% 135.84/19.99 (10) ~ (all_10_2 = e0)
% 135.84/19.99 (11) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 135.84/19.99 (12) ~ (all_52_9 = e2)
% 135.84/19.99 (13) ~ (all_4_2 = e1)
% 135.84/20.00 (14) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.84/20.00 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 135.84/20.00 op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.84/20.00 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.84/20.00 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 135.84/20.00 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.84/20.00 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 135.84/20.00 = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.84/20.00 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.84/20.00 $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~
% 135.84/20.00 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.84/20.00 (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) =
% 135.84/20.00 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0,
% 135.84/20.00 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 135.84/20.00 $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3)
% 135.84/20.00 & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 135.84/20.00 op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17
% 135.84/20.00 & op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 135.84/20.00 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 135.84/20.00 (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 135.84/20.00 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.84/20.00 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0)
% 135.84/20.00 = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) &
% 135.84/20.00 $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 &
% 135.84/20.00 all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.84/20.00 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 135.84/20.00 = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.84/20.00 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.84/20.00 $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~
% 135.84/20.00 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 135.84/20.00 (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 135.84/20.00 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0,
% 135.84/20.00 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 135.84/20.00 $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3)
% 135.84/20.00 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.84/20.00 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.84/20.00 all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2
% 135.84/20.00 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.84/20.00 (op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 =
% 135.84/20.00 e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 135.84/20.00 & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) =
% 135.84/20.00 all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.84/20.00 op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.84/20.00 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 135.84/20.00 e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.84/20.00 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 135.84/20.00 e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.84/20.00 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.84/20.00 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.84/20.00 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.84/20.00 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.84/20.00 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 135.84/20.00 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 135.84/20.00 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 135.84/20.00 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.84/20.00 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 135.84/20.00 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.84/20.00 $i(all_56_29))))
% 135.84/20.00 (15) ~ (all_52_8 = all_6_2)
% 135.84/20.00 (16) op(e3, e3) = all_10_2
% 135.84/20.00 (17) op(e2, e1) = all_52_9
% 135.84/20.00 (18) ~ (all_52_8 = e2)
% 135.84/20.00 (19) op(e3, e0) = all_52_12
% 135.84/20.00 (20) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 135.84/20.00 (21) ~ (all_10_2 = e2)
% 135.84/20.00 (22) op(e3, e1) = all_52_8
% 135.84/20.00 (23) ~ (all_52_8 = all_10_2)
% 135.84/20.00 (24) ~ (all_10_2 = e1)
% 135.84/20.00 (25) ~ (all_52_8 = e1)
% 135.84/20.00
% 135.84/20.00 Begin of proof
% 135.84/20.00 |
% 135.84/20.00 | BETA: splitting (11) gives:
% 135.84/20.00 |
% 135.84/20.00 | Case 1:
% 135.84/20.00 | |
% 135.84/20.00 | | (26) all_54_0 = e3
% 135.84/20.00 | |
% 135.84/20.00 | | COMBINE_EQS: (2), (26) imply:
% 135.84/20.00 | | (27) all_10_2 = e3
% 135.84/20.00 | |
% 135.84/20.00 | | REDUCE: (23), (27) imply:
% 135.84/20.00 | | (28) ~ (all_52_8 = e3)
% 135.84/20.00 | |
% 135.84/20.00 | | REDUCE: (9), (27) imply:
% 135.84/20.00 | | (29) ~ (all_52_12 = e3)
% 135.84/20.00 | |
% 135.84/20.00 | | REDUCE: (21), (27) imply:
% 135.84/20.00 | | (30) ~ (e3 = e2)
% 135.84/20.00 | |
% 135.84/20.00 | | REDUCE: (24), (27) imply:
% 135.84/20.00 | | (31) ~ (e3 = e1)
% 135.84/20.00 | |
% 135.84/20.00 | | REDUCE: (10), (27) imply:
% 135.84/20.00 | | (32) ~ (e3 = e0)
% 135.84/20.00 | |
% 135.84/20.00 | | REDUCE: (16), (27) imply:
% 135.84/20.00 | | (33) op(e3, e3) = e3
% 135.84/20.00 | |
% 135.84/20.00 | | BETA: splitting (14) gives:
% 135.84/20.00 | |
% 135.84/20.00 | | Case 1:
% 135.84/20.00 | | |
% 135.84/20.00 | | | (34) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~
% 135.84/20.00 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.84/20.00 | | | op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = all_56_3 &
% 135.84/20.00 | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 135.84/20.00 | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.84/20.00 | | | $i(all_56_27)) | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5
% 135.84/20.00 | | | = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.84/20.00 | | | (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1,
% 135.84/20.00 | | | e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.84/20.00 | | | all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.84/20.00 | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0
% 135.84/20.00 | | | & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~
% 135.84/20.00 | | | (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.84/20.00 | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15
% 135.84/20.00 | | | & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7)
% 135.84/20.00 | | | & $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 =
% 135.84/20.00 | | | e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) &
% 135.84/20.00 | | | ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1
% 135.84/20.00 | | | & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) =
% 135.84/20.00 | | | all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) &
% 135.84/20.00 | | | $i(all_56_9) & $i(all_56_17) & $i(all_56_25))
% 135.84/20.00 | | |
% 135.84/20.00 | | | BETA: splitting (34) gives:
% 135.84/20.00 | | |
% 135.84/20.00 | | | Case 1:
% 135.84/20.00 | | | |
% 135.84/20.00 | | | | (35) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~
% 135.84/20.00 | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.84/20.00 | | | | op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = all_56_3 &
% 135.84/20.00 | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 135.84/20.00 | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.84/20.00 | | | | $i(all_56_27)) | (all_56_1 = e1 & all_56_17 = e3 & ~
% 135.84/20.00 | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 135.84/20.00 | | | | ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 &
% 135.84/20.00 | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.84/20.00 | | | | all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.84/20.00 | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 135.84/20.00 | | | |
% 135.84/20.00 | | | | REF_CLOSE: (5), (30), (31), (33), (35) are inconsistent by sub-proof
% 135.84/20.00 | | | | #623.
% 135.84/20.00 | | | |
% 135.84/20.00 | | | Case 2:
% 135.84/20.00 | | | |
% 135.84/20.00 | | | | (36) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~
% 135.84/20.00 | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.84/20.00 | | | | op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = all_56_7 &
% 135.84/20.00 | | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 135.84/20.00 | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 135.84/20.00 | | | | $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~
% 135.84/20.00 | | | | (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 135.84/20.00 | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) =
% 135.84/20.00 | | | | all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.84/20.00 | | | | op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) &
% 135.84/20.00 | | | | $i(all_56_9) & $i(all_56_17) & $i(all_56_25))
% 135.84/20.00 | | | |
% 135.84/20.00 | | | | REF_CLOSE: (5), (19), (29), (33), (36) are inconsistent by sub-proof
% 135.84/20.00 | | | | #553.
% 135.84/20.00 | | | |
% 135.84/20.00 | | | End of split
% 135.84/20.00 | | |
% 135.84/20.00 | | Case 2:
% 135.84/20.00 | | |
% 135.84/20.00 | | | (37) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~
% 135.84/20.00 | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 135.84/20.00 | | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) =
% 135.84/20.00 | | | all_56_17 & op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 135.84/20.00 | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.84/20.00 | | | $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5
% 135.84/20.00 | | | = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.84/20.00 | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1,
% 135.84/20.00 | | | e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.84/20.00 | | | all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.84/20.00 | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 135.84/20.00 | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~
% 135.84/20.00 | | | (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 135.84/20.00 | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15
% 135.84/20.00 | | | & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7)
% 135.84/20.00 | | | & $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_13 =
% 135.84/20.00 | | | e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 135.84/20.00 | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.84/20.00 | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 135.84/20.00 | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 &
% 135.84/20.00 | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.84/20.00 | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 135.84/20.00 | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) &
% 135.84/20.00 | | | ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.84/20.00 | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.84/20.00 | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) &
% 135.84/20.00 | | | $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 135.84/20.00 | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.84/20.00 | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2,
% 135.84/20.00 | | | e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.84/20.00 | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.84/20.00 | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.84/20.00 | | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~
% 135.84/20.00 | | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 135.84/20.00 | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 135.84/20.00 | | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1)
% 135.84/20.00 | | | = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 135.84/20.00 | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 135.84/20.00 | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0)
% 135.84/20.00 | | | & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1,
% 135.84/20.00 | | | e1) = all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0
% 135.84/20.00 | | | & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.84/20.00 | | | $i(all_56_29))))
% 135.84/20.00 | | |
% 135.84/20.00 | | | BETA: splitting (37) gives:
% 135.84/20.00 | | |
% 135.84/20.00 | | | Case 1:
% 135.84/20.00 | | | |
% 135.84/20.00 | | | | (38) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~
% 135.84/20.00 | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 135.84/20.00 | | | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) =
% 135.84/20.00 | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 135.84/20.00 | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.84/20.00 | | | | $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~
% 135.84/20.00 | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 135.84/20.00 | | | | ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 &
% 135.84/20.00 | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.84/20.00 | | | | all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.84/20.00 | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 135.84/20.00 | | | |
% 135.84/20.00 | | | | REF_CLOSE: (5), (8), (12), (17), (30), (38) are inconsistent by
% 135.84/20.00 | | | | sub-proof #108.
% 135.84/20.00 | | | |
% 135.84/20.00 | | | Case 2:
% 135.84/20.00 | | | |
% 135.84/20.00 | | | | (39) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 135.84/20.00 | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.84/20.00 | | | | op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 &
% 135.84/20.00 | | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 135.84/20.00 | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 135.84/20.00 | | | | $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~
% 135.84/20.00 | | | | (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 135.84/20.00 | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 135.84/20.00 | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 135.84/20.00 | | | | op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 135.84/20.00 | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 135.84/20.00 | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 &
% 135.84/20.00 | | | | ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 135.84/20.00 | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.84/20.00 | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.84/20.00 | | | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) &
% 135.84/20.00 | | | | $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 135.84/20.00 | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11
% 135.84/20.00 | | | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.84/20.00 | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 135.84/20.00 | | | | e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) =
% 135.84/20.00 | | | | e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.84/20.00 | | | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~
% 135.84/20.00 | | | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 135.84/20.00 | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 135.84/20.00 | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 135.84/20.00 | | | | op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 135.84/20.00 | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 & ~
% 135.84/20.00 | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.84/20.00 | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 135.84/20.00 | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1,
% 135.84/20.00 | | | | e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 135.84/20.00 | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))))
% 135.84/20.00 | | | |
% 135.84/20.00 | | | | BETA: splitting (39) gives:
% 135.84/20.00 | | | |
% 135.84/20.00 | | | | Case 1:
% 135.84/20.00 | | | | |
% 135.84/20.00 | | | | | (40) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 135.84/20.00 | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.84/20.00 | | | | | op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 &
% 135.84/20.00 | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 135.84/20.00 | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 135.84/20.00 | | | | | $i(all_56_31)
% 135.84/20.00 | | | | |
% 135.84/20.00 | | | | | ALPHA: (40) implies:
% 135.84/20.00 | | | | | (41) op(e2, e2) = e0
% 135.84/20.00 | | | | |
% 135.84/20.00 | | | | | REF_CLOSE: (5), (6), (32), (41) are inconsistent by sub-proof #641.
% 135.84/20.00 | | | | |
% 135.84/20.00 | | | | Case 2:
% 135.84/20.00 | | | | |
% 135.84/20.00 | | | | | (42) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 135.84/20.00 | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0)
% 135.84/20.00 | | | | | & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 135.84/20.00 | | | | | e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1
% 135.84/20.00 | | | | | & op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 135.84/20.00 | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = all_56_31 &
% 135.84/20.00 | | | | | $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~
% 135.84/20.00 | | | | | (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 135.84/20.00 | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.84/20.00 | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.84/20.00 | | | | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) &
% 135.84/20.00 | | | | | $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 135.84/20.00 | | | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 135.84/20.00 | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 =
% 135.84/20.00 | | | | | e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.84/20.00 | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 135.84/20.00 | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 135.84/20.00 | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 &
% 135.84/20.00 | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 135.84/20.00 | | | | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.84/20.00 | | | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 135.84/20.00 | | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) =
% 135.84/20.00 | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 135.84/20.00 | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 & ~
% 135.84/20.00 | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.84/20.00 | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 135.84/20.00 | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1,
% 135.84/20.00 | | | | | e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 135.84/20.00 | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))))
% 135.84/20.00 | | | | |
% 135.84/20.00 | | | | | BETA: splitting (42) gives:
% 135.84/20.00 | | | | |
% 135.84/20.00 | | | | | Case 1:
% 135.84/20.00 | | | | | |
% 135.84/20.00 | | | | | | (43) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 135.84/20.00 | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0)
% 135.84/20.00 | | | | | | & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 135.84/20.00 | | | | | | e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1
% 135.84/20.00 | | | | | | & op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 135.84/20.00 | | | | | | $i(all_56_19) & $i(all_56_27)
% 135.84/20.00 | | | | | |
% 135.84/20.00 | | | | | | ALPHA: (43) implies:
% 135.84/20.00 | | | | | | (44) ~ (all_56_19 = e1)
% 135.84/20.00 | | | | | | (45) op(e2, e1) = all_56_19
% 135.84/20.00 | | | | | |
% 135.84/20.00 | | | | | | REF_CLOSE: (1), (5), (44), (45) are inconsistent by sub-proof #106.
% 135.84/20.00 | | | | | |
% 135.84/20.00 | | | | | Case 2:
% 135.84/20.00 | | | | | |
% 135.84/20.00 | | | | | | (46) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 135.84/20.00 | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2)
% 135.84/20.00 | | | | | | & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3)
% 135.84/20.00 | | | | | | = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) =
% 135.84/20.00 | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 135.84/20.00 | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.84/20.00 | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~
% 135.84/20.00 | | | | | | (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.84/20.00 | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.84/20.00 | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 135.84/20.00 | | | | | | e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) &
% 135.84/20.00 | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.84/20.00 | | | | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.84/20.00 | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 =
% 135.84/20.00 | | | | | | e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 135.84/20.00 | | | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) =
% 135.84/20.00 | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 135.84/20.00 | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 & ~
% 135.84/20.00 | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 135.84/20.00 | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 135.84/20.00 | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1,
% 135.84/20.00 | | | | | | e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 135.84/20.00 | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)))
% 135.84/20.00 | | | | | |
% 135.84/20.00 | | | | | | ALPHA: (46) implies:
% 135.84/20.00 | | | | | | (47) op(e0, e0) = all_56_31
% 135.84/20.00 | | | | | | (48) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 135.84/20.00 | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 =
% 135.84/20.00 | | | | | | e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 &
% 135.84/20.00 | | | | | | op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 135.84/20.00 | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 135.84/20.00 | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~
% 135.84/20.00 | | | | | | (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.84/20.00 | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 135.84/20.00 | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 135.84/20.00 | | | | | | e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) &
% 135.84/20.00 | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.84/20.00 | | | | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.84/20.00 | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 =
% 135.84/20.00 | | | | | | e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 135.84/20.00 | | | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23
% 135.84/20.00 | | | | | | & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 135.84/20.00 | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 135.84/20.00 | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 =
% 135.84/20.00 | | | | | | e0) & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 135.84/20.00 | | | | | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & op(e0,
% 135.84/20.00 | | | | | | e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 135.84/20.00 | | | | | | & $i(all_56_29))
% 135.84/20.00 | | | | | |
% 135.84/20.00 | | | | | | REF_CLOSE: (1), (3), (4), (5), (7), (13), (15), (18), (20), (22),
% 135.84/20.00 | | | | | | (25), (28), (33), (47), (48) are inconsistent by
% 135.84/20.00 | | | | | | sub-proof #105.
% 135.84/20.00 | | | | | |
% 135.84/20.00 | | | | | End of split
% 135.84/20.00 | | | | |
% 135.84/20.00 | | | | End of split
% 135.84/20.00 | | | |
% 135.84/20.00 | | | End of split
% 135.84/20.00 | | |
% 135.84/20.00 | | End of split
% 135.84/20.00 | |
% 135.84/20.00 | Case 2:
% 135.84/20.00 | |
% 135.84/20.00 | | (49) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 135.84/20.00 | |
% 135.84/20.00 | | REF_CLOSE: (2), (10), (21), (24), (49) are inconsistent by sub-proof #777.
% 135.84/20.00 | |
% 135.84/20.00 | End of split
% 135.84/20.00 |
% 135.84/20.00 End of proof
% 135.84/20.00
% 135.84/20.00 Sub-proof #105 shows that the following formulas are inconsistent:
% 135.84/20.00 ----------------------------------------------------------------
% 135.84/20.00 (1) op(e2, e1) = e1
% 135.84/20.00 (2) op(e0, e0) = all_4_2
% 135.84/20.00 (3) op(e1, e1) = all_6_2
% 135.84/20.00 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.84/20.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.84/20.00 (5) all_54_2 = all_52_8
% 135.84/20.00 (6) ~ (all_4_2 = e1)
% 135.84/20.00 (7) ~ (all_52_8 = all_6_2)
% 135.84/20.00 (8) ~ (all_52_8 = e2)
% 135.84/20.00 (9) op(e3, e3) = e3
% 135.84/20.00 (10) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 135.84/20.00 (11) op(e3, e1) = all_52_8
% 135.84/20.00 (12) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 135.84/20.00 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.84/20.00 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0)
% 135.84/20.00 = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 135.84/20.00 $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~
% 135.84/20.00 (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 135.84/20.00 (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.84/20.00 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.84/20.00 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 135.84/20.00 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 135.84/20.00 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 135.84/20.00 op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 135.84/20.00 op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 135.84/20.00 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13
% 135.84/20.00 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 135.84/20.00 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1,
% 135.84/20.00 e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.84/20.00 $i(all_56_21) & $i(all_56_29))
% 135.84/20.00 (13) ~ (all_52_8 = e1)
% 135.84/20.00 (14) op(e0, e0) = all_56_31
% 135.84/20.00 (15) ~ (all_52_8 = e3)
% 135.84/20.00
% 135.84/20.00 Begin of proof
% 135.84/20.00 |
% 135.84/20.00 | BETA: splitting (12) gives:
% 135.84/20.00 |
% 135.84/20.00 | Case 1:
% 135.84/20.00 | |
% 135.84/20.00 | | (16) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 135.84/20.00 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.84/20.00 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.84/20.00 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9)
% 135.84/20.00 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 135.84/20.00 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 135.84/20.00 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 135.84/20.00 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 135.84/20.00 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.84/20.00 | | $i(all_56_27))
% 135.84/20.00 | |
% 135.84/20.00 | | BETA: splitting (16) gives:
% 135.84/20.00 | |
% 135.84/20.00 | | Case 1:
% 135.84/20.00 | | |
% 135.84/20.00 | | | (17) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 135.84/20.00 | | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.84/20.00 | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.84/20.00 | | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9)
% 135.84/20.00 | | | & $i(all_56_17) & $i(all_56_25)
% 135.84/20.00 | | |
% 135.84/20.00 | | | ALPHA: (17) implies:
% 135.84/20.00 | | | (18) ~ (all_56_1 = e3)
% 135.84/20.00 | | | (19) op(e3, e3) = all_56_1
% 135.84/20.00 | | |
% 135.84/20.00 | | | REF_CLOSE: (4), (9), (18), (19) are inconsistent by sub-proof #766.
% 135.84/20.00 | | |
% 135.84/20.00 | | Case 2:
% 135.84/20.00 | | |
% 135.84/20.00 | | | (20) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 135.84/20.00 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.84/20.00 | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.84/20.00 | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.84/20.00 | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)
% 135.84/20.00 | | |
% 135.84/20.00 | | | ALPHA: (20) implies:
% 135.84/20.00 | | | (21) ~ (all_56_19 = e1)
% 135.84/20.00 | | | (22) op(e2, e1) = all_56_19
% 135.84/20.00 | | |
% 135.84/20.00 | | | REF_CLOSE: (1), (4), (21), (22) are inconsistent by sub-proof #106.
% 135.84/20.00 | | |
% 135.84/20.00 | | End of split
% 135.84/20.00 | |
% 135.84/20.00 | Case 2:
% 135.84/20.00 | |
% 135.84/20.00 | | (23) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.84/20.00 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.84/20.00 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.84/20.00 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 135.84/20.00 | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 135.84/20.00 | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 135.84/20.00 | | ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.84/20.00 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 135.84/20.00 | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.84/20.00 | | $i(all_56_29))
% 135.84/20.00 | |
% 135.84/20.00 | | BETA: splitting (23) gives:
% 135.84/20.00 | |
% 135.84/20.00 | | Case 1:
% 135.84/20.00 | | |
% 135.84/20.00 | | | (24) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.84/20.00 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.84/20.00 | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 135.84/20.00 | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 135.84/20.00 | | | $i(all_56_15) & $i(all_56_23)
% 135.84/20.00 | | |
% 135.84/20.00 | | | ALPHA: (24) implies:
% 135.84/20.00 | | | (25) op(e1, e1) = e0
% 135.84/20.00 | | |
% 135.84/20.00 | | | BETA: splitting (10) gives:
% 135.84/20.00 | | |
% 135.84/20.00 | | | Case 1:
% 135.84/20.00 | | | |
% 135.84/20.00 | | | | (26) all_54_2 = e3
% 135.84/20.00 | | | |
% 135.84/20.00 | | | | COMBINE_EQS: (5), (26) imply:
% 135.84/20.00 | | | | (27) all_52_8 = e3
% 135.84/20.00 | | | |
% 135.84/20.00 | | | | REDUCE: (15), (27) imply:
% 135.84/20.00 | | | | (28) $false
% 135.84/20.00 | | | |
% 135.84/20.00 | | | | CLOSE: (28) is inconsistent.
% 135.84/20.00 | | | |
% 135.84/20.00 | | | Case 2:
% 135.84/20.00 | | | |
% 135.84/20.00 | | | | (29) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 135.84/20.00 | | | |
% 135.84/20.00 | | | | BETA: splitting (29) gives:
% 135.84/20.00 | | | |
% 135.84/20.00 | | | | Case 1:
% 135.84/20.00 | | | | |
% 135.84/20.00 | | | | | (30) all_54_2 = e2
% 135.84/20.00 | | | | |
% 135.84/20.00 | | | | | COMBINE_EQS: (5), (30) imply:
% 135.84/20.00 | | | | | (31) all_52_8 = e2
% 135.84/20.00 | | | | |
% 135.84/20.00 | | | | | REDUCE: (8), (31) imply:
% 135.84/20.00 | | | | | (32) $false
% 135.84/20.00 | | | | |
% 135.84/20.00 | | | | | CLOSE: (32) is inconsistent.
% 135.84/20.00 | | | | |
% 135.84/20.00 | | | | Case 2:
% 135.84/20.00 | | | | |
% 135.84/20.00 | | | | | (33) all_54_2 = e1 | all_54_2 = e0
% 135.84/20.00 | | | | |
% 135.84/20.00 | | | | | BETA: splitting (33) gives:
% 135.84/20.00 | | | | |
% 135.84/20.00 | | | | | Case 1:
% 135.84/20.00 | | | | | |
% 135.84/20.00 | | | | | | (34) all_54_2 = e1
% 135.84/20.00 | | | | | |
% 135.84/20.00 | | | | | | COMBINE_EQS: (5), (34) imply:
% 135.84/20.00 | | | | | | (35) all_52_8 = e1
% 135.84/20.00 | | | | | |
% 135.84/20.00 | | | | | | REDUCE: (13), (35) imply:
% 135.84/20.00 | | | | | | (36) $false
% 135.84/20.00 | | | | | |
% 135.84/20.00 | | | | | | CLOSE: (36) is inconsistent.
% 135.84/20.00 | | | | | |
% 135.84/20.00 | | | | | Case 2:
% 135.84/20.00 | | | | | |
% 135.84/20.00 | | | | | | (37) all_54_2 = e0
% 135.84/20.00 | | | | | |
% 135.84/20.00 | | | | | | COMBINE_EQS: (5), (37) imply:
% 135.84/20.00 | | | | | | (38) all_52_8 = e0
% 135.84/20.00 | | | | | |
% 135.84/20.00 | | | | | | REDUCE: (11), (38) imply:
% 135.84/20.00 | | | | | | (39) op(e3, e1) = e0
% 135.84/20.00 | | | | | |
% 135.84/20.01 | | | | | | REF_CLOSE: (3), (4), (7), (11), (25), (39) are inconsistent by
% 135.84/20.01 | | | | | | sub-proof #619.
% 135.84/20.01 | | | | | |
% 135.84/20.01 | | | | | End of split
% 135.84/20.01 | | | | |
% 135.84/20.01 | | | | End of split
% 135.84/20.01 | | | |
% 135.84/20.01 | | | End of split
% 135.84/20.01 | | |
% 135.84/20.01 | | Case 2:
% 135.84/20.01 | | |
% 135.84/20.01 | | | (40) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 135.84/20.01 | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 135.84/20.01 | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.84/20.01 | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.84/20.01 | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 135.84/20.01 | | |
% 135.84/20.01 | | | ALPHA: (40) implies:
% 135.84/20.01 | | | (41) all_56_31 = e1
% 135.84/20.01 | | |
% 135.84/20.01 | | | REDUCE: (14), (41) imply:
% 135.84/20.01 | | | (42) op(e0, e0) = e1
% 135.84/20.01 | | |
% 135.84/20.01 | | | REF_CLOSE: (2), (4), (6), (42) are inconsistent by sub-proof #354.
% 135.84/20.01 | | |
% 135.84/20.01 | | End of split
% 135.84/20.01 | |
% 135.84/20.01 | End of split
% 135.84/20.01 |
% 135.84/20.01 End of proof
% 135.84/20.01
% 135.84/20.01 Sub-proof #106 shows that the following formulas are inconsistent:
% 135.84/20.01 ----------------------------------------------------------------
% 135.84/20.01 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.84/20.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.84/20.01 (2) op(e2, e1) = all_56_19
% 135.84/20.01 (3) op(e2, e1) = e1
% 135.84/20.01 (4) ~ (all_56_19 = e1)
% 135.84/20.01
% 135.84/20.01 Begin of proof
% 135.84/20.01 |
% 135.84/20.01 | GROUND_INST: instantiating (1) with e1, all_56_19, e1, e2, simplifying with
% 135.84/20.01 | (2), (3) gives:
% 135.84/20.01 | (5) all_56_19 = e1
% 135.84/20.01 |
% 135.84/20.01 | REDUCE: (4), (5) imply:
% 135.84/20.01 | (6) $false
% 135.84/20.01 |
% 135.84/20.01 | CLOSE: (6) is inconsistent.
% 135.84/20.01 |
% 135.84/20.01 End of proof
% 135.84/20.01
% 135.84/20.01 Sub-proof #107 shows that the following formulas are inconsistent:
% 135.84/20.01 ----------------------------------------------------------------
% 135.84/20.01 (1) all_57_15 = e2 & op(e0, e0) = e2
% 135.84/20.01 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.84/20.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.84/20.01 (3) op(e0, e0) = all_4_2
% 135.84/20.01 (4) ~ (all_4_2 = e2)
% 135.84/20.01
% 135.84/20.01 Begin of proof
% 135.84/20.01 |
% 135.84/20.01 | ALPHA: (1) implies:
% 135.84/20.01 | (5) op(e0, e0) = e2
% 135.84/20.01 |
% 135.84/20.01 | GROUND_INST: instantiating (2) with all_4_2, e2, e0, e0, simplifying with (3),
% 135.84/20.01 | (5) gives:
% 135.84/20.01 | (6) all_4_2 = e2
% 135.84/20.01 |
% 135.84/20.01 | REDUCE: (4), (6) imply:
% 135.84/20.01 | (7) $false
% 135.84/20.01 |
% 135.84/20.01 | CLOSE: (7) is inconsistent.
% 135.84/20.01 |
% 135.84/20.01 End of proof
% 135.84/20.01
% 135.84/20.01 Sub-proof #108 shows that the following formulas are inconsistent:
% 135.84/20.01 ----------------------------------------------------------------
% 135.84/20.01 (1) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2)
% 135.84/20.01 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.84/20.01 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25
% 135.84/20.01 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.84/20.01 $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~
% 135.84/20.01 (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.84/20.01 (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 135.84/20.01 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.84/20.01 = all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.84/20.01 $i(all_56_29))
% 135.84/20.01 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.84/20.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.84/20.01 (3) ~ (e3 = e2)
% 135.84/20.01 (4) op(e1, e1) = e2
% 135.84/20.01 (5) ~ (all_52_9 = e2)
% 135.84/20.01 (6) op(e2, e1) = all_52_9
% 135.84/20.01
% 135.84/20.01 Begin of proof
% 135.84/20.01 |
% 135.84/20.01 | BETA: splitting (1) gives:
% 135.84/20.01 |
% 135.84/20.01 | Case 1:
% 135.84/20.01 | |
% 135.84/20.01 | | (7) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 135.84/20.01 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.84/20.01 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.84/20.01 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1)
% 135.84/20.01 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)
% 135.84/20.01 | |
% 135.84/20.01 | | ALPHA: (7) implies:
% 135.84/20.01 | | (8) op(e1, e1) = e3
% 135.84/20.01 | |
% 135.84/20.01 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #109.
% 135.84/20.01 | |
% 135.84/20.01 | Case 2:
% 135.84/20.01 | |
% 135.84/20.01 | | (9) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13
% 135.84/20.01 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1
% 135.84/20.01 | | & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 135.84/20.01 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.84/20.01 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 135.84/20.01 | |
% 135.84/20.01 | | ALPHA: (9) implies:
% 135.84/20.01 | | (10) op(e2, e1) = e2
% 135.84/20.01 | |
% 135.84/20.01 | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #770.
% 135.84/20.01 | |
% 135.84/20.01 | End of split
% 135.84/20.01 |
% 135.84/20.01 End of proof
% 135.84/20.01
% 135.84/20.01 Sub-proof #109 shows that the following formulas are inconsistent:
% 135.84/20.01 ----------------------------------------------------------------
% 135.84/20.01 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.84/20.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.84/20.01 (2) op(e1, e1) = e3
% 135.84/20.01 (3) op(e1, e1) = e2
% 135.84/20.01 (4) ~ (e3 = e2)
% 135.84/20.01
% 135.84/20.01 Begin of proof
% 135.84/20.01 |
% 135.98/20.01 | GROUND_INST: instantiating (1) with e2, e3, e1, e1, simplifying with (2), (3)
% 135.98/20.01 | gives:
% 135.98/20.01 | (5) e3 = e2
% 135.98/20.01 |
% 135.98/20.01 | REDUCE: (4), (5) imply:
% 135.98/20.01 | (6) $false
% 135.98/20.01 |
% 135.98/20.01 | CLOSE: (6) is inconsistent.
% 135.98/20.01 |
% 135.98/20.01 End of proof
% 135.98/20.01
% 135.98/20.01 Sub-proof #110 shows that the following formulas are inconsistent:
% 135.98/20.01 ----------------------------------------------------------------
% 135.98/20.01 (1) op(e2, e2) = all_8_2
% 135.98/20.01 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.98/20.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.98/20.01 (3) ~ (e3 = e2)
% 135.98/20.01 (4) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 135.98/20.01 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.98/20.01 op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 135.98/20.01 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.98/20.01 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 &
% 135.98/20.01 all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~
% 135.98/20.01 (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3,
% 135.98/20.01 e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.98/20.01 op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.98/20.01 $i(all_56_17) & $i(all_56_25))
% 135.98/20.01 (5) op(e3, e0) = all_52_12
% 135.98/20.01 (6) ~ (all_8_2 = e3)
% 135.98/20.01 (7) op(e3, e0) = e2
% 135.98/20.01
% 135.98/20.01 Begin of proof
% 135.98/20.01 |
% 135.98/20.01 | BETA: splitting (4) gives:
% 135.98/20.01 |
% 135.98/20.01 | Case 1:
% 135.98/20.01 | |
% 135.98/20.01 | | (8) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 135.98/20.01 | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.98/20.01 | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 135.98/20.01 | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.98/20.01 | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)
% 135.98/20.01 | |
% 135.98/20.01 | | ALPHA: (8) implies:
% 135.98/20.01 | | (9) op(e3, e0) = e3
% 135.98/20.01 | |
% 135.98/20.01 | | REF_CLOSE: (2), (3), (5), (7), (9) are inconsistent by sub-proof #111.
% 135.98/20.01 | |
% 135.98/20.01 | Case 2:
% 135.98/20.01 | |
% 135.98/20.01 | | (10) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 135.98/20.01 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.98/20.01 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.98/20.01 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1)
% 135.98/20.01 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)
% 135.98/20.01 | |
% 135.98/20.01 | | ALPHA: (10) implies:
% 135.98/20.01 | | (11) op(e2, e2) = e3
% 135.98/20.01 | |
% 135.98/20.01 | | REF_CLOSE: (1), (2), (6), (11) are inconsistent by sub-proof #228.
% 135.98/20.01 | |
% 135.98/20.01 | End of split
% 135.98/20.01 |
% 135.98/20.01 End of proof
% 135.98/20.01
% 135.98/20.01 Sub-proof #111 shows that the following formulas are inconsistent:
% 135.98/20.01 ----------------------------------------------------------------
% 135.98/20.01 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.98/20.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.98/20.01 (2) ~ (e3 = e2)
% 135.98/20.01 (3) op(e3, e0) = e3
% 135.98/20.01 (4) op(e3, e0) = all_52_12
% 135.98/20.01 (5) op(e3, e0) = e2
% 135.98/20.01
% 135.98/20.01 Begin of proof
% 135.98/20.01 |
% 135.98/20.01 | GROUND_INST: instantiating (1) with all_52_12, e2, e0, e3, simplifying with
% 135.98/20.01 | (4), (5) gives:
% 135.98/20.01 | (6) all_52_12 = e2
% 135.98/20.01 |
% 135.98/20.01 | GROUND_INST: instantiating (1) with all_52_12, e3, e0, e3, simplifying with
% 135.98/20.01 | (3), (4) gives:
% 135.98/20.01 | (7) all_52_12 = e3
% 135.98/20.01 |
% 135.98/20.01 | COMBINE_EQS: (6), (7) imply:
% 135.98/20.01 | (8) e3 = e2
% 135.98/20.01 |
% 135.98/20.01 | SIMP: (8) implies:
% 135.98/20.01 | (9) e3 = e2
% 135.98/20.01 |
% 135.98/20.01 | REDUCE: (2), (9) imply:
% 135.98/20.01 | (10) $false
% 135.98/20.01 |
% 135.98/20.01 | CLOSE: (10) is inconsistent.
% 135.98/20.01 |
% 135.98/20.01 End of proof
% 135.98/20.01
% 135.98/20.01 Sub-proof #112 shows that the following formulas are inconsistent:
% 135.98/20.01 ----------------------------------------------------------------
% 135.98/20.01 (1) op(e2, e0) = all_52_13
% 135.98/20.01 (2) ~ (all_52_13 = e1)
% 135.98/20.01 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.98/20.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.98/20.01 (4) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 135.98/20.01 (5) op(e2, e1) = all_52_9
% 135.98/20.01 (6) ~ (all_52_9 = e1)
% 135.98/20.01
% 135.98/20.01 Begin of proof
% 135.98/20.01 |
% 135.98/20.01 | BETA: splitting (4) gives:
% 135.98/20.01 |
% 135.98/20.01 | Case 1:
% 135.98/20.01 | |
% 135.98/20.01 | | (7) all_57_5 = e1 & op(e2, e1) = e1
% 135.98/20.01 | |
% 135.98/20.01 | | REF_CLOSE: (3), (5), (6), (7) are inconsistent by sub-proof #161.
% 135.98/20.01 | |
% 135.98/20.01 | Case 2:
% 135.98/20.01 | |
% 135.98/20.01 | | (8) all_57_10 = e1 & op(e2, e0) = e1
% 135.98/20.01 | |
% 135.98/20.01 | | ALPHA: (8) implies:
% 135.98/20.01 | | (9) op(e2, e0) = e1
% 135.98/20.01 | |
% 135.98/20.01 | | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #180.
% 135.98/20.01 | |
% 135.98/20.01 | End of split
% 135.98/20.01 |
% 135.98/20.01 End of proof
% 135.98/20.01
% 135.98/20.01 Sub-proof #113 shows that the following formulas are inconsistent:
% 135.98/20.01 ----------------------------------------------------------------
% 135.98/20.01 (1) ~ (all_20_1 = e1) & op(e2, e2) = all_20_1 & $i(all_20_1)
% 135.98/20.01 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.98/20.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.98/20.01 (3) op(e2, e2) = e1
% 135.98/20.01
% 135.98/20.01 Begin of proof
% 135.98/20.01 |
% 135.98/20.01 | ALPHA: (1) implies:
% 135.98/20.01 | (4) ~ (all_20_1 = e1)
% 135.98/20.01 | (5) op(e2, e2) = all_20_1
% 135.98/20.01 |
% 135.98/20.01 | GROUND_INST: instantiating (2) with e1, all_20_1, e2, e2, simplifying with
% 135.98/20.01 | (3), (5) gives:
% 135.98/20.01 | (6) all_20_1 = e1
% 135.98/20.01 |
% 135.98/20.01 | REDUCE: (4), (6) imply:
% 135.98/20.01 | (7) $false
% 135.98/20.01 |
% 135.98/20.01 | CLOSE: (7) is inconsistent.
% 135.98/20.01 |
% 135.98/20.01 End of proof
% 135.98/20.01
% 135.98/20.01 Sub-proof #114 shows that the following formulas are inconsistent:
% 135.98/20.01 ----------------------------------------------------------------
% 135.98/20.01 (1) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.98/20.01 e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 &
% 135.98/20.01 op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1,
% 135.98/20.01 e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13)
% 135.98/20.01 & $i(all_56_21) & $i(all_56_29)
% 135.98/20.01 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.98/20.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.98/20.01 (3) op(e2, e1) = e3
% 135.98/20.01 (4) ~ (e3 = e2)
% 135.98/20.01
% 135.98/20.01 Begin of proof
% 135.98/20.01 |
% 135.98/20.01 | ALPHA: (1) implies:
% 135.98/20.01 | (5) op(e2, e1) = e2
% 135.98/20.01 |
% 135.98/20.01 | GROUND_INST: instantiating (2) with e3, e2, e1, e2, simplifying with (3), (5)
% 135.98/20.01 | gives:
% 135.98/20.01 | (6) e3 = e2
% 135.98/20.01 |
% 135.98/20.01 | REDUCE: (4), (6) imply:
% 135.98/20.01 | (7) $false
% 135.98/20.01 |
% 135.98/20.01 | CLOSE: (7) is inconsistent.
% 135.98/20.01 |
% 135.98/20.01 End of proof
% 135.98/20.01
% 135.98/20.01 Sub-proof #115 shows that the following formulas are inconsistent:
% 135.98/20.01 ----------------------------------------------------------------
% 135.98/20.01 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.98/20.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.98/20.01 (2) op(e2, e2) = e1
% 135.98/20.01 (3) op(e0, e3) = e3
% 135.98/20.01 (4) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 135.98/20.01 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.98/20.01 op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 135.98/20.01 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.98/20.01 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 &
% 135.98/20.01 all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~
% 135.98/20.01 (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3,
% 135.98/20.01 e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 135.98/20.01 op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.98/20.01 $i(all_56_17) & $i(all_56_25))
% 135.98/20.01 (5) ~ (e3 = e1)
% 135.98/20.01
% 135.98/20.01 Begin of proof
% 135.98/20.01 |
% 135.98/20.01 | BETA: splitting (4) gives:
% 135.98/20.01 |
% 135.98/20.01 | Case 1:
% 135.98/20.01 | |
% 135.98/20.01 | | (6) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 135.98/20.01 | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 135.98/20.01 | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 135.98/20.01 | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 135.98/20.01 | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)
% 135.98/20.01 | |
% 135.98/20.01 | | ALPHA: (6) implies:
% 135.98/20.01 | | (7) ~ (all_56_7 = e3)
% 135.98/20.01 | | (8) op(e0, e3) = all_56_7
% 135.98/20.01 | |
% 135.98/20.01 | | REF_CLOSE: (1), (3), (7), (8) are inconsistent by sub-proof #209.
% 135.98/20.01 | |
% 135.98/20.01 | Case 2:
% 135.98/20.01 | |
% 135.98/20.01 | | (9) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 135.98/20.01 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.98/20.01 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.98/20.01 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1)
% 135.98/20.01 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)
% 135.98/20.01 | |
% 135.98/20.01 | | ALPHA: (9) implies:
% 135.98/20.01 | | (10) op(e2, e2) = e3
% 135.98/20.01 | |
% 135.98/20.01 | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #325.
% 135.98/20.01 | |
% 135.98/20.01 | End of split
% 135.98/20.01 |
% 135.98/20.01 End of proof
% 135.98/20.01
% 135.98/20.01 Sub-proof #116 shows that the following formulas are inconsistent:
% 135.98/20.01 ----------------------------------------------------------------
% 135.98/20.01 (1) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2)
% 135.98/20.01 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3,
% 135.98/20.01 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 135.98/20.01 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.98/20.01 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 135.98/20.01 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.98/20.01 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) =
% 135.98/20.01 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.98/20.01 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 135.98/20.01 $i(all_56_21) & $i(all_56_29))
% 135.98/20.01 (2) ~ (all_52_4 = e0)
% 135.98/20.01 (3) ~ (e2 = e0)
% 135.98/20.01 (4) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 135.98/20.01 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 135.98/20.01 (5) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 135.98/20.01 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 135.98/20.01 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.98/20.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.98/20.01 (7) ~ (e2 = e1)
% 135.98/20.01 (8) ~ (e3 = e0)
% 135.98/20.01 (9) ~ (e3 = e2)
% 135.98/20.01 (10) all_57_2 = e2
% 135.98/20.01 (11) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 135.98/20.01 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 135.98/20.01 (12) all_57_12 = e3
% 135.98/20.01 (13) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 135.98/20.01 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 135.98/20.01 (14) op(e3, e2) = all_52_4
% 135.98/20.01 (15) all_57_9 = e1
% 135.98/20.01 (16) ~ (e3 = e1)
% 135.98/20.01 (17) ~ (e1 = e0)
% 135.98/20.01 (18) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 135.98/20.01 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 135.98/20.01
% 135.98/20.01 Begin of proof
% 135.98/20.01 |
% 135.98/20.01 | BETA: splitting (1) gives:
% 135.98/20.01 |
% 135.98/20.01 | Case 1:
% 135.98/20.01 | |
% 135.98/20.01 | | (19) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.98/20.01 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2
% 135.98/20.01 | | & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 135.98/20.01 | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 135.98/20.01 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)
% 135.98/20.01 | |
% 135.98/20.01 | | ALPHA: (19) implies:
% 135.98/20.01 | | (20) op(e3, e3) = e2
% 135.98/20.01 | |
% 135.98/20.01 | | REF_CLOSE: (3), (5), (6), (7), (8), (10), (12), (13), (16), (17), (20) are
% 135.98/20.01 | | inconsistent by sub-proof #489.
% 135.98/20.01 | |
% 135.98/20.01 | Case 2:
% 135.98/20.01 | |
% 135.98/20.01 | | (21) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13
% 135.98/20.01 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) =
% 135.98/20.01 | | e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 135.98/20.01 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 135.98/20.01 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 135.98/20.01 | |
% 135.98/20.01 | | ALPHA: (21) implies:
% 135.98/20.01 | | (22) op(e3, e3) = e1
% 135.98/20.01 | |
% 135.98/20.01 | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (11), (14), (15), (16), (17),
% 135.98/20.01 | | (18), (22) are inconsistent by sub-proof #686.
% 135.98/20.01 | |
% 135.98/20.01 | End of split
% 135.98/20.01 |
% 135.98/20.01 End of proof
% 135.98/20.01
% 135.98/20.01 Sub-proof #117 shows that the following formulas are inconsistent:
% 135.98/20.01 ----------------------------------------------------------------
% 135.98/20.01 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.98/20.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.98/20.01 (2) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1)
% 135.98/20.01 (3) op(e3, e2) = all_52_4
% 135.98/20.01 (4) op(e3, e3) = e0
% 135.98/20.01 (5) ~ (e1 = e0)
% 135.98/20.01 (6) ~ (all_52_4 = e1)
% 135.98/20.01
% 135.98/20.01 Begin of proof
% 135.98/20.01 |
% 135.98/20.01 | BETA: splitting (2) gives:
% 135.98/20.01 |
% 135.98/20.01 | Case 1:
% 135.98/20.01 | |
% 135.98/20.01 | | (7) all_57_0 = e1 & op(e3, e3) = e1
% 135.98/20.01 | |
% 135.98/20.01 | | ALPHA: (7) implies:
% 135.98/20.01 | | (8) op(e3, e3) = e1
% 135.98/20.01 | |
% 135.98/20.01 | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #717.
% 135.98/20.01 | |
% 135.98/20.01 | Case 2:
% 135.98/20.01 | |
% 135.98/20.01 | | (9) all_57_1 = e1 & op(e3, e2) = e1
% 135.98/20.01 | |
% 135.98/20.01 | | REF_CLOSE: (1), (3), (6), (9) are inconsistent by sub-proof #684.
% 135.98/20.01 | |
% 135.98/20.01 | End of split
% 135.98/20.01 |
% 135.98/20.01 End of proof
% 135.98/20.01
% 135.98/20.01 Sub-proof #118 shows that the following formulas are inconsistent:
% 135.98/20.01 ----------------------------------------------------------------
% 135.98/20.01 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.98/20.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.98/20.01 (2) ~ (all_52_1 = e1)
% 135.98/20.01 (3) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1)
% 135.98/20.01 (4) op(e2, e3) = all_52_1
% 135.98/20.01 (5) op(e3, e3) = e0
% 135.98/20.01 (6) ~ (e1 = e0)
% 135.98/20.01
% 135.98/20.01 Begin of proof
% 135.98/20.01 |
% 135.98/20.01 | BETA: splitting (3) gives:
% 135.98/20.01 |
% 135.98/20.01 | Case 1:
% 135.98/20.01 | |
% 135.98/20.01 | | (7) all_57_0 = e1 & op(e3, e3) = e1
% 135.98/20.01 | |
% 135.98/20.01 | | ALPHA: (7) implies:
% 135.98/20.01 | | (8) op(e3, e3) = e1
% 135.98/20.01 | |
% 135.98/20.01 | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #717.
% 135.98/20.01 | |
% 135.98/20.01 | Case 2:
% 135.98/20.01 | |
% 135.98/20.01 | | (9) all_57_2 = e1 & op(e2, e3) = e1
% 135.98/20.01 | |
% 135.98/20.01 | | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #676.
% 135.98/20.01 | |
% 135.98/20.01 | End of split
% 135.98/20.01 |
% 135.98/20.01 End of proof
% 135.98/20.01
% 135.98/20.01 Sub-proof #119 shows that the following formulas are inconsistent:
% 135.98/20.01 ----------------------------------------------------------------
% 135.98/20.02 (1) all_54_7 = all_20_0
% 135.98/20.02 (2) all_54_7 = e3
% 135.98/20.02 (3) ~ (all_20_0 = e3)
% 135.98/20.02
% 135.98/20.02 Begin of proof
% 135.98/20.02 |
% 135.98/20.02 | COMBINE_EQS: (1), (2) imply:
% 135.98/20.02 | (4) all_20_0 = e3
% 135.98/20.02 |
% 135.98/20.02 | SIMP: (4) implies:
% 135.98/20.02 | (5) all_20_0 = e3
% 135.98/20.02 |
% 135.98/20.02 | REDUCE: (3), (5) imply:
% 135.98/20.02 | (6) $false
% 135.98/20.02 |
% 135.98/20.02 | CLOSE: (6) is inconsistent.
% 135.98/20.02 |
% 135.98/20.02 End of proof
% 135.98/20.02
% 135.98/20.02 Sub-proof #120 shows that the following formulas are inconsistent:
% 135.98/20.02 ----------------------------------------------------------------
% 135.98/20.02 (1) ~ (all_24_0 = e1)
% 135.98/20.02 (2) ~ (all_24_0 = e2)
% 135.98/20.02 (3) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 135.98/20.02 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 135.98/20.02 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.98/20.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.98/20.02 (5) all_54_12 = all_24_0
% 135.98/20.02 (6) op(e0, e1) = all_52_11
% 135.98/20.02 (7) op(e0, e2) = all_52_7
% 135.98/20.02 (8) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 135.98/20.02 (9) ~ (all_52_11 = all_24_0)
% 135.98/20.02 (10) ~ (all_24_0 = e0)
% 135.98/20.02 (11) ~ (all_52_7 = all_24_0)
% 135.98/20.02 (12) op(e0, e0) = e2
% 135.98/20.02 (13) all_57_12 = e1
% 135.98/20.02
% 135.98/20.02 Begin of proof
% 135.98/20.02 |
% 135.98/20.02 | BETA: splitting (8) gives:
% 135.98/20.02 |
% 135.98/20.02 | Case 1:
% 135.98/20.02 | |
% 135.98/20.02 | | (14) all_54_12 = e3
% 135.98/20.02 | |
% 135.98/20.02 | | COMBINE_EQS: (5), (14) imply:
% 135.98/20.02 | | (15) all_24_0 = e3
% 135.98/20.02 | |
% 135.98/20.02 | | SIMP: (15) implies:
% 135.98/20.02 | | (16) all_24_0 = e3
% 135.98/20.02 | |
% 135.98/20.02 | | REDUCE: (11), (16) imply:
% 135.98/20.02 | | (17) ~ (all_52_7 = e3)
% 135.98/20.02 | |
% 135.98/20.02 | | REDUCE: (9), (16) imply:
% 135.98/20.02 | | (18) ~ (all_52_11 = e3)
% 135.98/20.02 | |
% 135.98/20.02 | | REDUCE: (2), (16) imply:
% 135.98/20.02 | | (19) ~ (e3 = e2)
% 135.98/20.02 | |
% 135.98/20.02 | | REDUCE: (1), (16) imply:
% 135.98/20.02 | | (20) ~ (e3 = e1)
% 135.98/20.02 | |
% 135.98/20.02 | | REF_CLOSE: (3), (4), (6), (7), (12), (13), (17), (18), (19), (20) are
% 135.98/20.02 | | inconsistent by sub-proof #123.
% 135.98/20.02 | |
% 135.98/20.02 | Case 2:
% 135.98/20.02 | |
% 135.98/20.02 | | (21) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 135.98/20.02 | |
% 135.98/20.02 | | REF_CLOSE: (1), (2), (5), (10), (21) are inconsistent by sub-proof #205.
% 135.98/20.02 | |
% 135.98/20.02 | End of split
% 135.98/20.02 |
% 135.98/20.02 End of proof
% 135.98/20.02
% 135.98/20.02 Sub-proof #121 shows that the following formulas are inconsistent:
% 135.98/20.02 ----------------------------------------------------------------
% 135.98/20.02 (1) all_54_8 = all_52_2
% 135.98/20.02 (2) all_54_8 = e3
% 135.98/20.02 (3) ~ (all_52_2 = e3)
% 135.98/20.02
% 135.98/20.02 Begin of proof
% 135.98/20.02 |
% 135.98/20.02 | COMBINE_EQS: (1), (2) imply:
% 135.98/20.02 | (4) all_52_2 = e3
% 135.98/20.02 |
% 135.98/20.02 | SIMP: (4) implies:
% 135.98/20.02 | (5) all_52_2 = e3
% 135.98/20.02 |
% 135.98/20.02 | REDUCE: (3), (5) imply:
% 135.98/20.02 | (6) $false
% 135.98/20.02 |
% 135.98/20.02 | CLOSE: (6) is inconsistent.
% 135.98/20.02 |
% 135.98/20.02 End of proof
% 135.98/20.02
% 135.98/20.02 Sub-proof #122 shows that the following formulas are inconsistent:
% 135.98/20.02 ----------------------------------------------------------------
% 135.98/20.02 (1) all_57_13 = e2 & op(e0, e2) = e2
% 135.98/20.02 (2) all_57_13 = e0
% 135.98/20.02 (3) ~ (e2 = e0)
% 135.98/20.02
% 135.98/20.02 Begin of proof
% 135.98/20.02 |
% 135.98/20.02 | ALPHA: (1) implies:
% 135.98/20.02 | (4) all_57_13 = e2
% 135.98/20.02 |
% 135.98/20.02 | COMBINE_EQS: (2), (4) imply:
% 135.98/20.02 | (5) e2 = e0
% 135.98/20.02 |
% 135.98/20.02 | REDUCE: (3), (5) imply:
% 135.98/20.02 | (6) $false
% 135.98/20.02 |
% 135.98/20.02 | CLOSE: (6) is inconsistent.
% 135.98/20.02 |
% 135.98/20.02 End of proof
% 135.98/20.02
% 135.98/20.02 Sub-proof #123 shows that the following formulas are inconsistent:
% 135.98/20.02 ----------------------------------------------------------------
% 135.98/20.02 (1) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 135.98/20.02 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 135.98/20.02 (2) ~ (all_52_7 = e3)
% 135.98/20.02 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.98/20.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.98/20.02 (4) ~ (e3 = e2)
% 135.98/20.02 (5) op(e0, e1) = all_52_11
% 135.98/20.02 (6) op(e0, e2) = all_52_7
% 135.98/20.02 (7) ~ (all_52_11 = e3)
% 135.98/20.02 (8) op(e0, e0) = e2
% 135.98/20.02 (9) ~ (e3 = e1)
% 135.98/20.02 (10) all_57_12 = e1
% 135.98/20.02
% 135.98/20.02 Begin of proof
% 135.98/20.02 |
% 135.98/20.02 | BETA: splitting (1) gives:
% 135.98/20.02 |
% 135.98/20.02 | Case 1:
% 135.98/20.02 | |
% 135.98/20.02 | | (11) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 135.98/20.02 | | e3)
% 135.98/20.02 | |
% 135.98/20.02 | | BETA: splitting (11) gives:
% 135.98/20.02 | |
% 135.98/20.02 | | Case 1:
% 135.98/20.02 | | |
% 135.98/20.02 | | | (12) all_57_12 = e3 & op(e0, e3) = e3
% 135.98/20.02 | | |
% 135.98/20.02 | | | REF_CLOSE: (9), (10), (12) are inconsistent by sub-proof #394.
% 135.98/20.02 | | |
% 135.98/20.02 | | Case 2:
% 135.98/20.02 | | |
% 135.98/20.02 | | | (13) all_57_13 = e3 & op(e0, e2) = e3
% 135.98/20.02 | | |
% 135.98/20.02 | | | REF_CLOSE: (2), (3), (6), (13) are inconsistent by sub-proof #556.
% 135.98/20.02 | | |
% 135.98/20.02 | | End of split
% 135.98/20.02 | |
% 135.98/20.02 | Case 2:
% 135.98/20.02 | |
% 135.98/20.02 | | (14) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 135.98/20.02 | | e3)
% 135.98/20.02 | |
% 135.98/20.02 | | REF_CLOSE: (3), (4), (5), (7), (8), (14) are inconsistent by sub-proof #459.
% 135.98/20.02 | |
% 135.98/20.02 | End of split
% 135.98/20.02 |
% 135.98/20.02 End of proof
% 135.98/20.02
% 135.98/20.02 Sub-proof #124 shows that the following formulas are inconsistent:
% 135.98/20.02 ----------------------------------------------------------------
% 135.98/20.02 (1) op(e1, e1) = all_6_2
% 135.98/20.02 (2) ~ (all_6_2 = e3)
% 135.98/20.02 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.98/20.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.98/20.02 (4) all_54_10 = all_6_2
% 135.98/20.02 (5) ~ (all_6_2 = e2)
% 135.98/20.02 (6) ~ (all_6_2 = e0)
% 135.98/20.02 (7) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 135.98/20.02 (8) ~ (all_56_21 = e1)
% 135.98/20.02 (9) op(e1, e1) = all_56_21
% 135.98/20.02
% 135.98/20.02 Begin of proof
% 135.98/20.02 |
% 135.98/20.02 | BETA: splitting (7) gives:
% 135.98/20.02 |
% 135.98/20.02 | Case 1:
% 135.98/20.02 | |
% 135.98/20.02 | | (10) all_54_10 = e3
% 135.98/20.02 | |
% 135.98/20.02 | | REF_CLOSE: (2), (4), (10) are inconsistent by sub-proof #742.
% 135.98/20.02 | |
% 135.98/20.02 | Case 2:
% 135.98/20.02 | |
% 135.98/20.02 | | (11) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 135.98/20.02 | |
% 135.98/20.02 | | BETA: splitting (11) gives:
% 135.98/20.02 | |
% 135.98/20.02 | | Case 1:
% 135.98/20.02 | | |
% 135.98/20.02 | | | (12) all_54_10 = e2
% 135.98/20.02 | | |
% 135.98/20.02 | | | REF_CLOSE: (4), (5), (12) are inconsistent by sub-proof #741.
% 135.98/20.02 | | |
% 135.98/20.02 | | Case 2:
% 135.98/20.02 | | |
% 135.98/20.02 | | | (13) all_54_10 = e1 | all_54_10 = e0
% 135.98/20.02 | | |
% 135.98/20.02 | | | BETA: splitting (13) gives:
% 135.98/20.02 | | |
% 135.98/20.02 | | | Case 1:
% 135.98/20.02 | | | |
% 135.98/20.02 | | | | (14) all_54_10 = e1
% 135.98/20.02 | | | |
% 135.98/20.02 | | | | COMBINE_EQS: (4), (14) imply:
% 135.98/20.02 | | | | (15) all_6_2 = e1
% 135.98/20.02 | | | |
% 135.98/20.02 | | | | SIMP: (15) implies:
% 135.98/20.02 | | | | (16) all_6_2 = e1
% 135.98/20.02 | | | |
% 135.98/20.02 | | | | REDUCE: (1), (16) imply:
% 135.98/20.02 | | | | (17) op(e1, e1) = e1
% 135.98/20.02 | | | |
% 135.98/20.02 | | | | REF_CLOSE: (3), (8), (9), (17) are inconsistent by sub-proof #510.
% 135.98/20.02 | | | |
% 135.98/20.02 | | | Case 2:
% 135.98/20.02 | | | |
% 135.98/20.02 | | | | (18) all_54_10 = e0
% 135.98/20.02 | | | |
% 135.98/20.02 | | | | REF_CLOSE: (4), (6), (18) are inconsistent by sub-proof #506.
% 135.98/20.02 | | | |
% 135.98/20.02 | | | End of split
% 135.98/20.02 | | |
% 135.98/20.02 | | End of split
% 135.98/20.02 | |
% 135.98/20.02 | End of split
% 135.98/20.02 |
% 135.98/20.02 End of proof
% 135.98/20.02
% 135.98/20.02 Sub-proof #125 shows that the following formulas are inconsistent:
% 135.98/20.02 ----------------------------------------------------------------
% 135.98/20.02 (1) ~ (all_38_1 = e1) & op(e2, e2) = all_38_1 & $i(all_38_1)
% 135.98/20.02 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.98/20.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.98/20.02 (3) op(e2, e2) = e1
% 135.98/20.02
% 135.98/20.02 Begin of proof
% 135.98/20.02 |
% 135.98/20.02 | ALPHA: (1) implies:
% 135.98/20.02 | (4) ~ (all_38_1 = e1)
% 135.98/20.02 | (5) op(e2, e2) = all_38_1
% 135.98/20.02 |
% 135.98/20.02 | GROUND_INST: instantiating (2) with e1, all_38_1, e2, e2, simplifying with
% 135.98/20.02 | (3), (5) gives:
% 135.98/20.02 | (6) all_38_1 = e1
% 135.98/20.02 |
% 135.98/20.02 | REDUCE: (4), (6) imply:
% 135.98/20.02 | (7) $false
% 135.98/20.02 |
% 135.98/20.02 | CLOSE: (7) is inconsistent.
% 135.98/20.02 |
% 135.98/20.02 End of proof
% 135.98/20.02
% 135.98/20.02 Sub-proof #126 shows that the following formulas are inconsistent:
% 135.98/20.02 ----------------------------------------------------------------
% 135.98/20.02 (1) ~ (all_38_0 = e1)
% 135.98/20.02 (2) ~ (all_38_0 = e2)
% 135.98/20.02 (3) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 135.98/20.02 (4) ~ (all_38_0 = e0)
% 135.98/20.02 (5) all_54_4 = all_38_0
% 135.98/20.02
% 135.98/20.02 Begin of proof
% 135.98/20.02 |
% 135.98/20.02 | BETA: splitting (3) gives:
% 135.98/20.02 |
% 135.98/20.02 | Case 1:
% 135.98/20.02 | |
% 135.98/20.02 | | (6) all_54_4 = e2
% 135.98/20.02 | |
% 135.98/20.02 | | COMBINE_EQS: (5), (6) imply:
% 135.98/20.02 | | (7) all_38_0 = e2
% 135.98/20.02 | |
% 135.98/20.02 | | SIMP: (7) implies:
% 135.98/20.02 | | (8) all_38_0 = e2
% 135.98/20.02 | |
% 135.98/20.02 | | REDUCE: (2), (8) imply:
% 135.98/20.02 | | (9) $false
% 135.98/20.02 | |
% 135.98/20.02 | | CLOSE: (9) is inconsistent.
% 135.98/20.02 | |
% 135.98/20.02 | Case 2:
% 135.98/20.02 | |
% 135.98/20.02 | | (10) all_54_4 = e1 | all_54_4 = e0
% 135.98/20.02 | |
% 135.98/20.02 | | BETA: splitting (10) gives:
% 135.98/20.02 | |
% 135.98/20.02 | | Case 1:
% 135.98/20.02 | | |
% 135.98/20.02 | | | (11) all_54_4 = e1
% 135.98/20.02 | | |
% 135.98/20.02 | | | COMBINE_EQS: (5), (11) imply:
% 135.98/20.02 | | | (12) all_38_0 = e1
% 135.98/20.02 | | |
% 135.98/20.02 | | | SIMP: (12) implies:
% 135.98/20.02 | | | (13) all_38_0 = e1
% 135.98/20.02 | | |
% 135.98/20.02 | | | REDUCE: (1), (13) imply:
% 135.98/20.02 | | | (14) $false
% 135.98/20.02 | | |
% 135.98/20.02 | | | CLOSE: (14) is inconsistent.
% 135.98/20.02 | | |
% 135.98/20.02 | | Case 2:
% 135.98/20.02 | | |
% 135.98/20.02 | | | (15) all_54_4 = e0
% 135.98/20.02 | | |
% 135.98/20.02 | | | COMBINE_EQS: (5), (15) imply:
% 135.98/20.02 | | | (16) all_38_0 = e0
% 135.98/20.02 | | |
% 135.98/20.02 | | | SIMP: (16) implies:
% 135.98/20.02 | | | (17) all_38_0 = e0
% 135.98/20.02 | | |
% 135.98/20.02 | | | REDUCE: (4), (17) imply:
% 135.98/20.02 | | | (18) $false
% 135.98/20.02 | | |
% 135.98/20.02 | | | CLOSE: (18) is inconsistent.
% 135.98/20.02 | | |
% 135.98/20.02 | | End of split
% 135.98/20.02 | |
% 135.98/20.02 | End of split
% 135.98/20.02 |
% 135.98/20.02 End of proof
% 135.98/20.02
% 135.98/20.02 Sub-proof #127 shows that the following formulas are inconsistent:
% 135.98/20.02 ----------------------------------------------------------------
% 135.98/20.02 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.98/20.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.98/20.02 (2) ~ (e2 = e1)
% 135.98/20.02 (3) all_57_3 = e1
% 135.98/20.02 (4) ~ (all_52_1 = e2)
% 135.98/20.02 (5) op(e2, e3) = all_52_1
% 135.98/20.02 (6) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 135.98/20.02
% 135.98/20.02 Begin of proof
% 135.98/20.02 |
% 135.98/20.02 | BETA: splitting (6) gives:
% 135.98/20.02 |
% 135.98/20.02 | Case 1:
% 135.98/20.02 | |
% 135.98/20.02 | | (7) all_57_2 = e2 & op(e2, e3) = e2
% 135.98/20.02 | |
% 135.98/20.02 | | ALPHA: (7) implies:
% 135.98/20.02 | | (8) op(e2, e3) = e2
% 135.98/20.02 | |
% 135.98/20.02 | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #779.
% 135.98/20.02 | |
% 135.98/20.02 | Case 2:
% 135.98/20.02 | |
% 135.98/20.02 | | (9) all_57_3 = e2 & op(e2, e2) = e2
% 135.98/20.02 | |
% 135.98/20.02 | | ALPHA: (9) implies:
% 135.98/20.02 | | (10) all_57_3 = e2
% 135.98/20.02 | |
% 135.98/20.02 | | REF_CLOSE: (2), (3), (10) are inconsistent by sub-proof #728.
% 135.98/20.02 | |
% 135.98/20.02 | End of split
% 135.98/20.02 |
% 135.98/20.02 End of proof
% 135.98/20.02
% 135.98/20.02 Sub-proof #128 shows that the following formulas are inconsistent:
% 135.98/20.02 ----------------------------------------------------------------
% 135.98/20.02 (1) ~ (all_8_1 = e3) & op(e1, e1) = all_8_1 & $i(all_8_1)
% 135.98/20.02 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.98/20.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.98/20.02 (3) op(e1, e1) = e3
% 135.98/20.02
% 135.98/20.02 Begin of proof
% 135.98/20.02 |
% 135.98/20.02 | ALPHA: (1) implies:
% 135.98/20.02 | (4) ~ (all_8_1 = e3)
% 135.98/20.02 | (5) op(e1, e1) = all_8_1
% 135.98/20.02 |
% 135.98/20.02 | GROUND_INST: instantiating (2) with e3, all_8_1, e1, e1, simplifying with (3),
% 135.98/20.02 | (5) gives:
% 135.98/20.02 | (6) all_8_1 = e3
% 135.98/20.02 |
% 135.98/20.02 | REDUCE: (4), (6) imply:
% 135.98/20.02 | (7) $false
% 135.98/20.02 |
% 135.98/20.02 | CLOSE: (7) is inconsistent.
% 135.98/20.02 |
% 135.98/20.02 End of proof
% 135.98/20.02
% 135.98/20.02 Sub-proof #129 shows that the following formulas are inconsistent:
% 135.98/20.02 ----------------------------------------------------------------
% 135.98/20.02 (1) all_57_11 = e0 & op(e1, e0) = e0
% 135.98/20.02 (2) all_57_11 = e3
% 135.98/20.02 (3) ~ (e3 = e0)
% 135.98/20.02
% 135.98/20.02 Begin of proof
% 135.98/20.02 |
% 135.98/20.02 | ALPHA: (1) implies:
% 135.98/20.02 | (4) all_57_11 = e0
% 135.98/20.02 |
% 135.98/20.02 | COMBINE_EQS: (2), (4) imply:
% 135.98/20.02 | (5) e3 = e0
% 135.98/20.02 |
% 135.98/20.02 | REDUCE: (3), (5) imply:
% 135.98/20.02 | (6) $false
% 135.98/20.02 |
% 135.98/20.02 | CLOSE: (6) is inconsistent.
% 135.98/20.02 |
% 135.98/20.02 End of proof
% 135.98/20.02
% 135.98/20.02 Sub-proof #130 shows that the following formulas are inconsistent:
% 135.98/20.02 ----------------------------------------------------------------
% 135.98/20.02 (1) all_57_6 = e1 & op(e1, e3) = e1
% 135.98/20.02 (2) all_57_6 = e0
% 135.98/20.02 (3) ~ (e1 = e0)
% 135.98/20.02
% 135.98/20.02 Begin of proof
% 135.98/20.02 |
% 135.98/20.02 | ALPHA: (1) implies:
% 135.98/20.02 | (4) all_57_6 = e1
% 135.98/20.02 |
% 135.98/20.02 | COMBINE_EQS: (2), (4) imply:
% 135.98/20.02 | (5) e1 = e0
% 135.98/20.02 |
% 135.98/20.02 | REDUCE: (3), (5) imply:
% 135.98/20.02 | (6) $false
% 135.98/20.02 |
% 135.98/20.02 | CLOSE: (6) is inconsistent.
% 135.98/20.02 |
% 135.98/20.02 End of proof
% 135.98/20.02
% 135.98/20.02 Sub-proof #131 shows that the following formulas are inconsistent:
% 135.98/20.02 ----------------------------------------------------------------
% 135.98/20.02 (1) op(e1, e1) = all_6_2
% 135.98/20.02 (2) op(e1, e2) = e2
% 135.98/20.02 (3) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2)
% 135.98/20.02 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.98/20.02 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25
% 135.98/20.02 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.98/20.02 $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~
% 135.98/20.02 (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.98/20.02 (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 135.98/20.02 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.98/20.02 = all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.98/20.02 $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3)
% 135.98/20.02 & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.98/20.02 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2)
% 135.98/20.02 = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 &
% 135.98/20.02 $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 135.98/20.02 (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.98/20.02 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.98/20.02 all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0)
% 135.98/20.02 = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 135.98/20.02 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 135.98/20.02 all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~
% 135.98/20.02 (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 135.98/20.02 (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 &
% 135.98/20.02 op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 135.98/20.02 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 135.98/20.02 (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11
% 135.98/20.02 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 135.98/20.02 all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 135.98/20.02 e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 135.98/20.02 & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1
% 135.98/20.02 & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 135.98/20.02 ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3)
% 135.98/20.02 = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.98/20.02 $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 &
% 135.98/20.02 all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.98/20.02 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 135.98/20.02 op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 135.98/20.02 all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.98/20.02 $i(all_56_21) & $i(all_56_29))))
% 135.98/20.02 (4) op(e3, e1) = e1
% 135.98/20.02 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.98/20.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.98/20.02 (6) ~ (e3 = e0)
% 135.98/20.02 (7) op(e2, e2) = e1
% 135.98/20.02 (8) op(e1, e1) = e3
% 135.98/20.02 (9) ~ (all_6_2 = e2)
% 135.98/20.02 (10) op(e2, e3) = e3
% 135.98/20.02 (11) ~ (e1 = e0)
% 135.98/20.02
% 135.98/20.02 Begin of proof
% 135.98/20.02 |
% 135.98/20.02 | BETA: splitting (3) gives:
% 135.98/20.02 |
% 135.98/20.02 | Case 1:
% 135.98/20.02 | |
% 135.98/20.02 | | (12) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 135.98/20.02 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.98/20.02 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.98/20.02 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 135.98/20.02 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 135.98/20.02 | | (all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 135.98/20.02 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 135.98/20.02 | | op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1,
% 135.98/20.02 | | e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 135.98/20.02 | | all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.98/20.02 | | $i(all_56_29))
% 135.98/20.02 | |
% 135.98/20.02 | | REF_CLOSE: (2), (4), (5), (12) are inconsistent by sub-proof #132.
% 135.98/20.02 | |
% 135.98/20.02 | Case 2:
% 135.98/20.02 | |
% 135.98/20.02 | | (13) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 135.98/20.02 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.98/20.02 | | op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 135.98/20.02 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 135.98/20.02 | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 135.98/20.02 | | $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 135.98/20.02 | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 135.98/20.02 | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 135.98/20.02 | | e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 135.98/20.02 | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.98/20.02 | | $i(all_56_27)) | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.98/20.02 | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 135.98/20.02 | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 135.98/20.02 | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) =
% 135.98/20.02 | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 135.98/20.02 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 135.98/20.02 | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 135.98/20.02 | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.98/20.02 | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.98/20.02 | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.98/20.02 | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27))
% 135.98/20.02 | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.98/20.02 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.98/20.02 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 135.98/20.02 | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7)
% 135.98/20.02 | | & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.98/20.02 | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.98/20.02 | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5
% 135.98/20.02 | | & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.98/20.02 | | = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.98/20.02 | | $i(all_56_21) & $i(all_56_29))))
% 135.98/20.02 | |
% 135.98/20.02 | | BETA: splitting (13) gives:
% 135.98/20.02 | |
% 135.98/20.02 | | Case 1:
% 135.98/20.02 | | |
% 135.98/20.02 | | | (14) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 135.98/20.02 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.98/20.02 | | | op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 135.98/20.02 | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 135.98/20.02 | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 135.98/20.02 | | | $i(all_56_31)
% 135.98/20.02 | | |
% 135.98/20.02 | | | ALPHA: (14) implies:
% 135.98/20.02 | | | (15) op(e2, e2) = e0
% 135.98/20.02 | | |
% 135.98/20.02 | | | REF_CLOSE: (5), (7), (11), (15) are inconsistent by sub-proof #675.
% 135.98/20.02 | | |
% 135.98/20.02 | | Case 2:
% 135.98/20.02 | | |
% 135.98/20.02 | | | (16) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 135.98/20.02 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.98/20.02 | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.98/20.02 | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 135.98/20.02 | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.98/20.02 | | | $i(all_56_27)) | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 135.98/20.02 | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 135.98/20.02 | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0)
% 135.98/20.02 | | | & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 135.98/20.02 | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 135.98/20.02 | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25))
% 135.98/20.02 | | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 135.98/20.02 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0)
% 135.98/20.02 | | | & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 135.98/20.02 | | | e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0
% 135.98/20.02 | | | & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.98/20.02 | | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~
% 135.98/20.02 | | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 135.98/20.02 | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 135.98/20.02 | | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1)
% 135.98/20.02 | | | = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 135.98/20.02 | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 135.98/20.02 | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0)
% 135.98/20.02 | | | & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1,
% 135.98/20.02 | | | e1) = all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0
% 135.98/20.02 | | | & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.98/20.02 | | | $i(all_56_29))))
% 135.98/20.02 | | |
% 135.98/20.02 | | | BETA: splitting (16) gives:
% 135.98/20.02 | | |
% 135.98/20.02 | | | Case 1:
% 135.98/20.02 | | | |
% 135.98/20.02 | | | | (17) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 135.98/20.02 | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.98/20.02 | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.98/20.02 | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 135.98/20.02 | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.98/20.02 | | | | $i(all_56_27)
% 135.98/20.02 | | | |
% 135.98/20.02 | | | | ALPHA: (17) implies:
% 135.98/20.02 | | | | (18) op(e1, e1) = e2
% 135.98/20.02 | | | |
% 135.98/20.02 | | | | REF_CLOSE: (1), (5), (9), (18) are inconsistent by sub-proof #767.
% 135.98/20.02 | | | |
% 135.98/20.02 | | | Case 2:
% 135.98/20.02 | | | |
% 135.98/20.02 | | | | (19) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 135.98/20.02 | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) &
% 135.98/20.02 | | | | ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.98/20.02 | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 135.98/20.02 | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) &
% 135.98/20.02 | | | | $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 135.98/20.02 | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 135.98/20.02 | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2,
% 135.98/20.02 | | | | e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.98/20.02 | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.98/20.02 | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.98/20.02 | | | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~
% 135.98/20.02 | | | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 135.98/20.02 | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 135.98/20.02 | | | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1)
% 135.98/20.02 | | | | = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 135.98/20.02 | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 135.98/20.02 | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0)
% 135.98/20.02 | | | | & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1,
% 135.98/20.02 | | | | e1) = all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0
% 135.98/20.02 | | | | & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.98/20.02 | | | | $i(all_56_29)))
% 135.98/20.02 | | | |
% 135.98/20.02 | | | | ALPHA: (19) implies:
% 135.98/20.02 | | | | (20) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 135.98/20.02 | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 135.98/20.02 | | | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) =
% 135.98/20.02 | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 135.98/20.02 | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 135.98/20.02 | | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 135.98/20.02 | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 135.98/20.02 | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 135.98/20.02 | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 135.98/20.02 | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27))
% 135.98/20.02 | | | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.98/20.02 | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 135.98/20.02 | | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 135.98/20.02 | | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7)
% 135.98/20.02 | | | | & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 135.98/20.02 | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 135.98/20.02 | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5
% 135.98/20.02 | | | | & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.98/20.02 | | | | = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 135.98/20.02 | | | | $i(all_56_21) & $i(all_56_29))
% 135.98/20.02 | | | |
% 135.98/20.02 | | | | BETA: splitting (20) gives:
% 135.98/20.02 | | | |
% 135.98/20.02 | | | | Case 1:
% 135.98/20.02 | | | | |
% 135.98/20.02 | | | | | (21) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 135.98/20.02 | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0)
% 135.98/20.02 | | | | | & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 135.98/20.02 | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 135.98/20.02 | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25))
% 135.98/20.02 | | | | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 135.98/20.02 | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0)
% 135.98/20.02 | | | | | & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 135.98/20.02 | | | | | e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0
% 135.98/20.02 | | | | | & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 135.98/20.02 | | | | | $i(all_56_27))
% 135.98/20.02 | | | | |
% 135.98/20.02 | | | | | REF_CLOSE: (4), (5), (10), (21) are inconsistent by sub-proof #346.
% 135.98/20.02 | | | | |
% 135.98/20.02 | | | | Case 2:
% 135.98/20.02 | | | | |
% 135.98/20.02 | | | | | (22) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.98/20.02 | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0)
% 135.98/20.02 | | | | | & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7
% 135.98/20.02 | | | | | & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.98/20.02 | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 =
% 135.98/20.02 | | | | | e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 135.98/20.02 | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1,
% 135.98/20.02 | | | | | e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 135.98/20.02 | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 135.98/20.02 | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.98/20.02 | | | | | $i(all_56_29))
% 135.98/20.02 | | | | |
% 135.98/20.02 | | | | | BETA: splitting (22) gives:
% 135.98/20.02 | | | | |
% 135.98/20.02 | | | | | Case 1:
% 135.98/20.02 | | | | | |
% 135.98/20.03 | | | | | | (23) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 135.98/20.03 | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0)
% 135.98/20.03 | | | | | | & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7
% 135.98/20.03 | | | | | | & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 135.98/20.03 | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)
% 135.98/20.03 | | | | | |
% 135.98/20.03 | | | | | | ALPHA: (23) implies:
% 135.98/20.03 | | | | | | (24) op(e1, e1) = e0
% 135.98/20.03 | | | | | |
% 135.98/20.03 | | | | | | REF_CLOSE: (5), (6), (8), (24) are inconsistent by sub-proof #753.
% 135.98/20.03 | | | | | |
% 135.98/20.03 | | | | | Case 2:
% 135.98/20.03 | | | | | |
% 135.98/20.03 | | | | | | (25) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 135.98/20.03 | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0)
% 135.98/20.03 | | | | | | & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1,
% 135.98/20.03 | | | | | | e1) = all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0
% 135.98/20.03 | | | | | | & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.98/20.03 | | | | | | $i(all_56_29)
% 135.98/20.03 | | | | | |
% 135.98/20.03 | | | | | | ALPHA: (25) implies:
% 135.98/20.03 | | | | | | (26) ~ (all_56_13 = e2)
% 135.98/20.03 | | | | | | (27) op(e1, e2) = all_56_13
% 135.98/20.03 | | | | | |
% 135.98/20.03 | | | | | | REF_CLOSE: (2), (5), (26), (27) are inconsistent by sub-proof #165.
% 135.98/20.03 | | | | | |
% 135.98/20.03 | | | | | End of split
% 135.98/20.03 | | | | |
% 135.98/20.03 | | | | End of split
% 135.98/20.03 | | | |
% 135.98/20.03 | | | End of split
% 135.98/20.03 | | |
% 135.98/20.03 | | End of split
% 135.98/20.03 | |
% 135.98/20.03 | End of split
% 135.98/20.03 |
% 135.98/20.03 End of proof
% 135.98/20.03
% 135.98/20.03 Sub-proof #132 shows that the following formulas are inconsistent:
% 135.98/20.03 ----------------------------------------------------------------
% 135.98/20.03 (1) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2)
% 135.98/20.03 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 135.98/20.03 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25
% 135.98/20.03 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 135.98/20.03 $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~
% 135.98/20.03 (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 135.98/20.03 (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 135.98/20.03 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 135.98/20.03 = all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 135.98/20.03 $i(all_56_29))
% 135.98/20.03 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.98/20.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.98/20.03 (3) op(e3, e1) = e1
% 135.98/20.03 (4) op(e1, e2) = e2
% 135.98/20.03
% 135.98/20.03 Begin of proof
% 135.98/20.03 |
% 135.98/20.03 | BETA: splitting (1) gives:
% 135.98/20.03 |
% 135.98/20.03 | Case 1:
% 135.98/20.03 | |
% 135.98/20.03 | | (5) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 135.98/20.03 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 135.98/20.03 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 135.98/20.03 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1)
% 135.98/20.03 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)
% 135.98/20.03 | |
% 135.98/20.03 | | ALPHA: (5) implies:
% 135.98/20.03 | | (6) ~ (all_56_17 = e1)
% 135.98/20.03 | | (7) op(e3, e1) = all_56_17
% 135.98/20.03 | |
% 135.98/20.03 | | REF_CLOSE: (2), (3), (6), (7) are inconsistent by sub-proof #349.
% 135.98/20.03 | |
% 135.98/20.03 | Case 2:
% 135.98/20.03 | |
% 135.98/20.03 | | (8) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13
% 135.98/20.03 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1
% 135.98/20.03 | | & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 135.98/20.03 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 135.98/20.03 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 135.98/20.03 | |
% 135.98/20.03 | | ALPHA: (8) implies:
% 135.98/20.03 | | (9) ~ (all_56_13 = e2)
% 135.98/20.03 | | (10) op(e1, e2) = all_56_13
% 135.98/20.03 | |
% 135.98/20.03 | | REF_CLOSE: (2), (4), (9), (10) are inconsistent by sub-proof #165.
% 135.98/20.03 | |
% 135.98/20.03 | End of split
% 135.98/20.03 |
% 135.98/20.03 End of proof
% 135.98/20.03
% 135.98/20.03 Sub-proof #133 shows that the following formulas are inconsistent:
% 135.98/20.03 ----------------------------------------------------------------
% 135.98/20.03 (1) ~ (e2 = e0)
% 135.98/20.03 (2) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 135.98/20.03 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 135.98/20.03 (3) ~ (e2 = e1)
% 135.98/20.03 (4) ~ (e3 = e0)
% 135.98/20.03 (5) all_57_0 = e2
% 135.98/20.03 (6) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 135.98/20.03 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 135.98/20.03 (7) all_57_2 = e3
% 135.98/20.03 (8) ~ (e3 = e1)
% 135.98/20.03 (9) ~ (e1 = e0)
% 135.98/20.03 (10) all_57_12 = e2
% 135.98/20.03
% 135.98/20.03 Begin of proof
% 135.98/20.03 |
% 135.98/20.03 | BETA: splitting (6) gives:
% 135.98/20.03 |
% 135.98/20.03 | Case 1:
% 135.98/20.03 | |
% 135.98/20.03 | | (11) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 135.98/20.03 | | e0)
% 135.98/20.03 | |
% 135.98/20.03 | | BETA: splitting (11) gives:
% 135.98/20.03 | |
% 135.98/20.03 | | Case 1:
% 135.98/20.03 | | |
% 135.98/20.03 | | | (12) all_57_0 = e0 & op(e3, e3) = e0
% 135.98/20.03 | | |
% 135.98/20.03 | | | ALPHA: (12) implies:
% 135.98/20.03 | | | (13) all_57_0 = e0
% 135.98/20.03 | | |
% 135.98/20.03 | | | COMBINE_EQS: (5), (13) imply:
% 135.98/20.03 | | | (14) e2 = e0
% 135.98/20.03 | | |
% 135.98/20.03 | | | REDUCE: (1), (14) imply:
% 135.98/20.03 | | | (15) $false
% 135.98/20.03 | | |
% 135.98/20.03 | | | CLOSE: (15) is inconsistent.
% 135.98/20.03 | | |
% 135.98/20.03 | | Case 2:
% 135.98/20.03 | | |
% 135.98/20.03 | | | (16) all_57_2 = e0 & op(e2, e3) = e0
% 135.98/20.03 | | |
% 135.98/20.03 | | | REF_CLOSE: (4), (7), (16) are inconsistent by sub-proof #521.
% 135.98/20.03 | | |
% 135.98/20.03 | | End of split
% 135.98/20.03 | |
% 135.98/20.03 | Case 2:
% 135.98/20.03 | |
% 135.98/20.03 | | (17) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 135.98/20.03 | | e0)
% 135.98/20.03 | |
% 135.98/20.03 | | BETA: splitting (17) gives:
% 135.98/20.03 | |
% 135.98/20.03 | | Case 1:
% 135.98/20.03 | | |
% 135.98/20.03 | | | (18) all_57_6 = e0 & op(e1, e3) = e0
% 135.98/20.03 | | |
% 135.98/20.03 | | | ALPHA: (18) implies:
% 135.98/20.03 | | | (19) all_57_6 = e0
% 135.98/20.03 | | |
% 135.98/20.03 | | | REF_CLOSE: (2), (3), (5), (7), (8), (9), (10), (19) are inconsistent by
% 135.98/20.03 | | | sub-proof #416.
% 135.98/20.03 | | |
% 135.98/20.03 | | Case 2:
% 135.98/20.03 | | |
% 135.98/20.03 | | | (20) all_57_12 = e0 & op(e0, e3) = e0
% 135.98/20.03 | | |
% 135.98/20.03 | | | REF_CLOSE: (1), (10), (20) are inconsistent by sub-proof #578.
% 135.98/20.03 | | |
% 135.98/20.03 | | End of split
% 135.98/20.03 | |
% 135.98/20.03 | End of split
% 135.98/20.03 |
% 135.98/20.03 End of proof
% 135.98/20.03
% 135.98/20.03 Sub-proof #134 shows that the following formulas are inconsistent:
% 135.98/20.03 ----------------------------------------------------------------
% 135.98/20.03 (1) op(e3, e3) = e2
% 135.98/20.03 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.98/20.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 135.98/20.03 (3) ~ (e2 = e1)
% 135.98/20.03 (4) ( ~ (all_44_0 = e1) & op(e3, e0) = all_44_0 & $i(all_44_0)) | ( ~
% 135.98/20.03 (all_44_1 = e2) & op(e3, e3) = all_44_1 & $i(all_44_1))
% 135.98/20.03 (5) op(e3, e2) = all_52_4
% 135.98/20.03 (6) all_57_4 = e3
% 135.98/20.03 (7) ~ (e3 = e1)
% 135.98/20.03 (8) ~ (all_52_4 = e1)
% 135.98/20.03 (9) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 135.98/20.03 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 135.98/20.03
% 135.98/20.03 Begin of proof
% 135.98/20.03 |
% 135.98/20.03 | BETA: splitting (9) gives:
% 135.98/20.03 |
% 135.98/20.03 | Case 1:
% 135.98/20.03 | |
% 135.98/20.03 | | (10) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 135.98/20.03 | | e1)
% 135.98/20.03 | |
% 135.98/20.03 | | REF_CLOSE: (1), (2), (3), (5), (8), (10) are inconsistent by sub-proof #378.
% 135.98/20.03 | |
% 135.98/20.03 | Case 2:
% 135.98/20.03 | |
% 135.98/20.03 | | (11) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 135.98/20.03 | | e1)
% 135.98/20.03 | |
% 135.98/20.03 | | BETA: splitting (11) gives:
% 135.98/20.03 | |
% 135.98/20.03 | | Case 1:
% 135.98/20.03 | | |
% 135.98/20.03 | | | (12) all_57_4 = e1 & op(e3, e1) = e1
% 135.98/20.03 | | |
% 135.98/20.03 | | | REF_CLOSE: (6), (7), (12) are inconsistent by sub-proof #382.
% 135.98/20.03 | | |
% 135.98/20.03 | | Case 2:
% 135.98/20.03 | | |
% 135.98/20.03 | | | (13) all_57_9 = e1 & op(e3, e0) = e1
% 135.98/20.03 | | |
% 135.98/20.03 | | | ALPHA: (13) implies:
% 135.98/20.03 | | | (14) op(e3, e0) = e1
% 135.98/20.03 | | |
% 135.98/20.03 | | | BETA: splitting (4) gives:
% 135.98/20.03 | | |
% 135.98/20.03 | | | Case 1:
% 135.98/20.03 | | | |
% 135.98/20.03 | | | | (15) ~ (all_44_0 = e1) & op(e3, e0) = all_44_0 & $i(all_44_0)
% 135.98/20.03 | | | |
% 135.98/20.03 | | | | ALPHA: (15) implies:
% 135.98/20.03 | | | | (16) ~ (all_44_0 = e1)
% 135.98/20.03 | | | | (17) op(e3, e0) = all_44_0
% 135.98/20.03 | | | |
% 135.98/20.03 | | | | REF_CLOSE: (2), (14), (16), (17) are inconsistent by sub-proof #432.
% 135.98/20.03 | | | |
% 135.98/20.03 | | | Case 2:
% 135.98/20.03 | | | |
% 135.98/20.03 | | | | (18) ~ (all_44_1 = e2) & op(e3, e3) = all_44_1 & $i(all_44_1)
% 135.98/20.03 | | | |
% 135.98/20.03 | | | | REF_CLOSE: (1), (2), (18) are inconsistent by sub-proof #431.
% 135.98/20.03 | | | |
% 135.98/20.03 | | | End of split
% 135.98/20.03 | | |
% 135.98/20.03 | | End of split
% 135.98/20.03 | |
% 135.98/20.03 | End of split
% 135.98/20.03 |
% 135.98/20.03 End of proof
% 135.98/20.03
% 135.98/20.03 Sub-proof #135 shows that the following formulas are inconsistent:
% 135.98/20.03 ----------------------------------------------------------------
% 135.98/20.03 (1) op(e0, e0) = e0
% 135.98/20.03 (2) op(e1, e1) = all_6_2
% 135.98/20.03 (3) ~ (all_52_9 = all_6_2)
% 135.98/20.03 (4) ~ (all_52_13 = e0)
% 135.98/20.03 (5) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 135.98/20.03 (6) ~ (e2 = e0)
% 136.03/20.03 (7) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2)
% 136.03/20.03 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 136.03/20.03 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25
% 136.03/20.03 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 136.03/20.03 $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~
% 136.03/20.03 (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 136.03/20.03 (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 136.03/20.03 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 136.03/20.03 = all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.03/20.03 $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3)
% 136.03/20.03 & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.03/20.03 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2)
% 136.03/20.03 = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 &
% 136.03/20.03 $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 136.03/20.03 (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 136.03/20.03 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 136.03/20.03 all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0)
% 136.03/20.03 = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 136.03/20.03 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 136.03/20.03 all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~
% 136.03/20.03 (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 136.03/20.03 (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 &
% 136.03/20.03 op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 136.03/20.03 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.03/20.03 (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11
% 136.03/20.03 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 136.03/20.03 all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 136.03/20.03 e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 136.03/20.03 & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1
% 136.03/20.03 & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 136.03/20.03 ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3)
% 136.03/20.03 = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 136.03/20.03 $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 &
% 136.03/20.03 all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.03/20.03 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 136.03/20.03 op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 136.03/20.03 all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 136.03/20.03 $i(all_56_21) & $i(all_56_29))))
% 136.03/20.03 (8) ~ (all_52_13 = e1)
% 136.03/20.03 (9) ~ (all_6_2 = e3)
% 136.03/20.03 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.03 (11) ~ (e3 = e0)
% 136.03/20.03 (12) ~ (all_52_13 = all_52_14)
% 136.03/20.03 (13) op(e2, e2) = e1
% 136.03/20.03 (14) all_48_2 = e1
% 136.03/20.03 (15) all_54_10 = all_6_2
% 136.03/20.03 (16) ~ (all_6_2 = e2)
% 136.03/20.03 (17) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e3) & op(e1, e2) = all_48_0 &
% 136.03/20.03 $i(all_48_0)) | ( ~ (all_48_1 = e0) & op(e1, e1) = all_48_1 &
% 136.03/20.03 $i(all_48_1))
% 136.03/20.03 (18) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 136.03/20.03 (19) op(e2, e1) = all_52_9
% 136.03/20.03 (20) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 136.03/20.03 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 136.03/20.03 (21) all_54_7 = all_52_13
% 136.03/20.03 (22) ~ (e1 = e0)
% 136.03/20.03 (23) ~ (all_52_9 = all_52_13)
% 136.03/20.03 (24) op(e1, e0) = all_52_14
% 136.03/20.03
% 136.03/20.03 Begin of proof
% 136.03/20.03 |
% 136.03/20.03 | BETA: splitting (7) gives:
% 136.03/20.03 |
% 136.03/20.03 | Case 1:
% 136.03/20.03 | |
% 136.03/20.03 | | (25) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 136.03/20.03 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.03/20.03 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.03/20.03 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 136.03/20.03 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.03/20.03 | | (all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 136.03/20.03 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 136.03/20.03 | | op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1,
% 136.03/20.03 | | e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 136.03/20.03 | | all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.03/20.03 | | $i(all_56_29))
% 136.03/20.03 | |
% 136.03/20.03 | | BETA: splitting (25) gives:
% 136.03/20.03 | |
% 136.03/20.03 | | Case 1:
% 136.03/20.03 | | |
% 136.03/20.03 | | | (26) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 136.03/20.03 | | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.03/20.03 | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.03/20.03 | | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 136.03/20.03 | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)
% 136.03/20.03 | | |
% 136.03/20.03 | | | ALPHA: (26) implies:
% 136.03/20.03 | | | (27) op(e1, e1) = e3
% 136.03/20.03 | | |
% 136.03/20.03 | | | REF_CLOSE: (2), (9), (10), (27) are inconsistent by sub-proof #771.
% 136.03/20.03 | | |
% 136.03/20.03 | | Case 2:
% 136.03/20.03 | | |
% 136.03/20.03 | | | (28) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 136.03/20.03 | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 136.03/20.03 | | | op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1,
% 136.03/20.03 | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 136.03/20.03 | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.03/20.03 | | | $i(all_56_29)
% 136.03/20.03 | | |
% 136.03/20.03 | | | ALPHA: (28) implies:
% 136.03/20.03 | | | (29) ~ (all_56_21 = e1)
% 136.03/20.03 | | | (30) ~ (all_56_5 = e3)
% 136.03/20.03 | | | (31) op(e1, e0) = all_56_29
% 136.03/20.03 | | | (32) op(e1, e1) = all_56_21
% 136.03/20.03 | | | (33) op(e1, e3) = all_56_5
% 136.03/20.03 | | | (34) op(e2, e1) = e2
% 136.03/20.03 | | |
% 136.03/20.03 | | | REF_CLOSE: (2), (3), (4), (5), (8), (9), (10), (12), (14), (15), (17),
% 136.03/20.03 | | | (18), (19), (20), (21), (23), (24), (29), (30), (31), (32),
% 136.03/20.03 | | | (33), (34) are inconsistent by sub-proof #185.
% 136.03/20.03 | | |
% 136.03/20.03 | | End of split
% 136.03/20.03 | |
% 136.03/20.03 | Case 2:
% 136.03/20.03 | |
% 136.03/20.03 | | (35) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 136.03/20.03 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.03/20.03 | | op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 136.03/20.03 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 136.03/20.03 | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 136.03/20.03 | | $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 136.03/20.03 | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 136.03/20.03 | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 136.03/20.03 | | e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 136.03/20.03 | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 136.03/20.03 | | $i(all_56_27)) | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 136.03/20.03 | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 136.03/20.03 | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 136.03/20.03 | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) =
% 136.03/20.03 | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 136.03/20.03 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.03/20.03 | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 136.03/20.03 | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.03/20.03 | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.03/20.03 | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.03/20.03 | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27))
% 136.03/20.03 | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.03/20.03 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.03/20.03 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 136.03/20.03 | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7)
% 136.03/20.03 | | & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 136.03/20.03 | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.03/20.03 | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5
% 136.03/20.03 | | & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 136.03/20.03 | | = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 136.03/20.03 | | $i(all_56_21) & $i(all_56_29))))
% 136.03/20.03 | |
% 136.03/20.03 | | REF_CLOSE: (1), (2), (6), (10), (11), (13), (16), (22), (35) are
% 136.03/20.03 | | inconsistent by sub-proof #184.
% 136.03/20.03 | |
% 136.03/20.03 | End of split
% 136.03/20.03 |
% 136.03/20.03 End of proof
% 136.03/20.03
% 136.03/20.03 Sub-proof #136 shows that the following formulas are inconsistent:
% 136.03/20.03 ----------------------------------------------------------------
% 136.03/20.03 (1) op(e3, e3) = e2
% 136.03/20.03 (2) ~ (e2 = e0)
% 136.03/20.03 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.03 (4) op(e2, e2) = e1
% 136.03/20.03 (5) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.03/20.03 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 136.03/20.03 op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.03/20.03 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.03/20.03 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 &
% 136.03/20.03 all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~
% 136.03/20.03 (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3,
% 136.03/20.03 e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 136.03/20.03 op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 136.03/20.03 $i(all_56_17) & $i(all_56_25))
% 136.03/20.03 (6) ~ (e3 = e1)
% 136.03/20.03
% 136.03/20.03 Begin of proof
% 136.03/20.03 |
% 136.03/20.03 | BETA: splitting (5) gives:
% 136.03/20.03 |
% 136.03/20.03 | Case 1:
% 136.03/20.03 | |
% 136.03/20.03 | | (7) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.03/20.03 | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 136.03/20.03 | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.03/20.03 | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.03/20.03 | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)
% 136.03/20.03 | |
% 136.03/20.03 | | ALPHA: (7) implies:
% 136.03/20.03 | | (8) op(e3, e3) = e0
% 136.03/20.03 | |
% 136.03/20.03 | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #495.
% 136.03/20.03 | |
% 136.03/20.03 | Case 2:
% 136.03/20.03 | |
% 136.03/20.03 | | (9) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.03/20.03 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.03/20.03 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.03/20.03 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1)
% 136.03/20.03 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)
% 136.03/20.03 | |
% 136.03/20.03 | | ALPHA: (9) implies:
% 136.03/20.03 | | (10) op(e2, e2) = e3
% 136.03/20.03 | |
% 136.03/20.03 | | REF_CLOSE: (3), (4), (6), (10) are inconsistent by sub-proof #325.
% 136.03/20.03 | |
% 136.03/20.03 | End of split
% 136.03/20.03 |
% 136.03/20.03 End of proof
% 136.03/20.03
% 136.03/20.03 Sub-proof #137 shows that the following formulas are inconsistent:
% 136.03/20.03 ----------------------------------------------------------------
% 136.03/20.03 (1) all_57_12 = e0
% 136.03/20.03 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.03 (3) ~ (all_52_2 = e1)
% 136.03/20.03 (4) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 136.03/20.03 (5) op(e1, e3) = all_52_2
% 136.03/20.03 (6) ~ (e1 = e0)
% 136.03/20.03
% 136.03/20.03 Begin of proof
% 136.03/20.03 |
% 136.03/20.03 | BETA: splitting (4) gives:
% 136.03/20.03 |
% 136.03/20.03 | Case 1:
% 136.03/20.03 | |
% 136.03/20.03 | | (7) all_57_6 = e1 & op(e1, e3) = e1
% 136.03/20.03 | |
% 136.03/20.03 | | ALPHA: (7) implies:
% 136.03/20.03 | | (8) op(e1, e3) = e1
% 136.03/20.03 | |
% 136.03/20.03 | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #725.
% 136.03/20.03 | |
% 136.03/20.03 | Case 2:
% 136.03/20.03 | |
% 136.03/20.03 | | (9) all_57_12 = e1 & op(e0, e3) = e1
% 136.03/20.03 | |
% 136.03/20.03 | | REF_CLOSE: (1), (6), (9) are inconsistent by sub-proof #405.
% 136.03/20.03 | |
% 136.03/20.03 | End of split
% 136.03/20.03 |
% 136.03/20.03 End of proof
% 136.03/20.03
% 136.03/20.03 Sub-proof #138 shows that the following formulas are inconsistent:
% 136.03/20.03 ----------------------------------------------------------------
% 136.03/20.03 (1) op(e1, e1) = all_6_2
% 136.03/20.03 (2) ~ (all_40_2 = e0) | ( ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 &
% 136.03/20.03 $i(all_40_0)) | ( ~ (all_40_1 = e2) & op(e0, e0) = all_40_1 &
% 136.03/20.03 $i(all_40_1))
% 136.03/20.03 (3) ~ (all_52_11 = e2)
% 136.03/20.03 (4) all_57_5 = e2
% 136.03/20.03 (5) all_40_2 = all_6_2
% 136.03/20.03 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.03 (7) ~ (e2 = e1)
% 136.03/20.03 (8) ~ (e3 = e2)
% 136.03/20.03 (9) ~ (all_52_11 = all_6_2)
% 136.03/20.03 (10) op(e0, e1) = all_52_11
% 136.03/20.03 (11) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 136.03/20.03 (12) ~ (all_6_2 = e2)
% 136.03/20.03 (13) op(e2, e0) = e0
% 136.03/20.03 (14) op(e0, e0) = e2
% 136.03/20.03 (15) all_57_2 = e3
% 136.03/20.03 (16) all_54_14 = all_52_11
% 136.03/20.03 (17) ~ (e3 = e1)
% 136.03/20.03 (18) ~ (e1 = e0)
% 136.03/20.03 (19) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 136.03/20.03 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 136.03/20.03 (20) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.03/20.03 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 136.03/20.03 op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.03/20.03 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.03/20.03 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 &
% 136.03/20.03 all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~
% 136.03/20.03 (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 136.03/20.03 op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 136.03/20.03 all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 136.03/20.03 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 136.03/20.03 all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~
% 136.03/20.03 (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 136.03/20.03 (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 &
% 136.03/20.03 op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0
% 136.03/20.03 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.03/20.03 (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 136.03/20.03 (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.03/20.03 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.03/20.03 all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.03/20.03 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.03/20.03 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.03/20.03 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.03/20.03 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 136.03/20.03 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 136.03/20.03 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 136.03/20.03 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 136.03/20.03 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 136.03/20.03 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 136.03/20.03 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.03/20.03 $i(all_56_29))))
% 136.03/20.03
% 136.03/20.03 Begin of proof
% 136.03/20.03 |
% 136.03/20.03 | BETA: splitting (20) gives:
% 136.03/20.03 |
% 136.03/20.03 | Case 1:
% 136.03/20.03 | |
% 136.03/20.03 | | (21) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ (all_56_15
% 136.03/20.03 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e2, e2) =
% 136.03/20.03 | | e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 136.03/20.03 | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 &
% 136.03/20.03 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31)
% 136.03/20.03 | |
% 136.03/20.03 | | ALPHA: (21) implies:
% 136.03/20.03 | | (22) op(e2, e2) = e0
% 136.03/20.03 | |
% 136.03/20.03 | | REF_CLOSE: (4), (6), (7), (13), (15), (17), (18), (19), (22) are
% 136.03/20.03 | | inconsistent by sub-proof #452.
% 136.03/20.03 | |
% 136.03/20.03 | Case 2:
% 136.03/20.03 | |
% 136.03/20.03 | | (23) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 136.03/20.03 | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.03/20.03 | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.03/20.03 | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1)
% 136.03/20.03 | | = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 136.03/20.03 | | $i(all_56_27)) | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 136.03/20.03 | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 136.03/20.03 | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 136.03/20.03 | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) =
% 136.03/20.03 | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 136.03/20.03 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.03/20.03 | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 136.03/20.03 | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.03/20.03 | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.03/20.03 | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.03/20.03 | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27))
% 136.03/20.03 | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.03/20.03 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.03/20.03 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 136.03/20.03 | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7)
% 136.03/20.03 | | & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 136.03/20.03 | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.03/20.03 | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5
% 136.03/20.03 | | & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 136.03/20.03 | | = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 136.03/20.03 | | $i(all_56_21) & $i(all_56_29))))
% 136.03/20.03 | |
% 136.03/20.03 | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 136.03/20.03 | | (14), (16), (23) are inconsistent by sub-proof #266.
% 136.03/20.03 | |
% 136.03/20.03 | End of split
% 136.03/20.03 |
% 136.03/20.03 End of proof
% 136.03/20.03
% 136.03/20.03 Sub-proof #139 shows that the following formulas are inconsistent:
% 136.03/20.03 ----------------------------------------------------------------
% 136.03/20.03 (1) all_57_6 = e0
% 136.03/20.03 (2) ~ (e2 = e0)
% 136.03/20.03 (3) all_57_12 = e0
% 136.03/20.03 (4) op(e3, e3) = e1
% 136.03/20.03 (5) ~ (all_56_5 = e3)
% 136.03/20.03 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.03 (7) ~ (e2 = e1)
% 136.03/20.03 (8) ~ (e3 = e0)
% 136.03/20.03 (9) ~ (e3 = e2)
% 136.03/20.03 (10) op(e1, e3) = all_56_5
% 136.03/20.03 (11) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 136.03/20.03 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 136.03/20.03 (12) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 136.03/20.03 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 136.03/20.03 (13) ~ (e3 = e1)
% 136.03/20.03
% 136.03/20.03 Begin of proof
% 136.03/20.03 |
% 136.03/20.03 | BETA: splitting (12) gives:
% 136.03/20.03 |
% 136.03/20.03 | Case 1:
% 136.03/20.03 | |
% 136.03/20.03 | | (14) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) =
% 136.03/20.03 | | e2)
% 136.03/20.03 | |
% 136.03/20.03 | | BETA: splitting (14) gives:
% 136.03/20.03 | |
% 136.03/20.03 | | Case 1:
% 136.03/20.03 | | |
% 136.03/20.03 | | | (15) all_57_0 = e2 & op(e3, e3) = e2
% 136.03/20.03 | | |
% 136.03/20.03 | | | ALPHA: (15) implies:
% 136.03/20.03 | | | (16) op(e3, e3) = e2
% 136.03/20.03 | | |
% 136.03/20.03 | | | REF_CLOSE: (4), (6), (7), (16) are inconsistent by sub-proof #743.
% 136.03/20.04 | | |
% 136.03/20.04 | | Case 2:
% 136.03/20.04 | | |
% 136.03/20.04 | | | (17) all_57_2 = e2 & op(e2, e3) = e2
% 136.03/20.04 | | |
% 136.03/20.04 | | | ALPHA: (17) implies:
% 136.03/20.04 | | | (18) all_57_2 = e2
% 136.03/20.04 | | |
% 136.03/20.04 | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (10), (11), (13), (18) are
% 136.03/20.04 | | | inconsistent by sub-proof #144.
% 136.03/20.04 | | |
% 136.03/20.04 | | End of split
% 136.03/20.04 | |
% 136.03/20.04 | Case 2:
% 136.03/20.04 | |
% 136.03/20.04 | | (19) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) =
% 136.03/20.04 | | e2)
% 136.03/20.04 | |
% 136.03/20.04 | | REF_CLOSE: (1), (2), (3), (19) are inconsistent by sub-proof #140.
% 136.03/20.04 | |
% 136.03/20.04 | End of split
% 136.03/20.04 |
% 136.03/20.04 End of proof
% 136.03/20.04
% 136.03/20.04 Sub-proof #140 shows that the following formulas are inconsistent:
% 136.03/20.04 ----------------------------------------------------------------
% 136.03/20.04 (1) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 136.03/20.04 (2) all_57_6 = e0
% 136.03/20.04 (3) ~ (e2 = e0)
% 136.03/20.04 (4) all_57_12 = e0
% 136.03/20.04
% 136.03/20.04 Begin of proof
% 136.03/20.04 |
% 136.03/20.04 | BETA: splitting (1) gives:
% 136.03/20.04 |
% 136.03/20.04 | Case 1:
% 136.03/20.04 | |
% 136.03/20.04 | | (5) all_57_6 = e2 & op(e1, e3) = e2
% 136.03/20.04 | |
% 136.03/20.04 | | ALPHA: (5) implies:
% 136.03/20.04 | | (6) all_57_6 = e2
% 136.03/20.04 | |
% 136.03/20.04 | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #586.
% 136.03/20.04 | |
% 136.03/20.04 | Case 2:
% 136.03/20.04 | |
% 136.03/20.04 | | (7) all_57_12 = e2 & op(e0, e3) = e2
% 136.03/20.04 | |
% 136.03/20.04 | | ALPHA: (7) implies:
% 136.03/20.04 | | (8) all_57_12 = e2
% 136.03/20.04 | |
% 136.03/20.04 | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #682.
% 136.03/20.04 | |
% 136.03/20.04 | End of split
% 136.03/20.04 |
% 136.03/20.04 End of proof
% 136.03/20.04
% 136.03/20.04 Sub-proof #141 shows that the following formulas are inconsistent:
% 136.03/20.04 ----------------------------------------------------------------
% 136.03/20.04 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.04 (2) ~ (e2 = e1)
% 136.03/20.04 (3) all_57_3 = e1
% 136.03/20.04 (4) ~ (all_52_1 = e2)
% 136.03/20.04 (5) op(e2, e3) = all_52_1
% 136.03/20.04 (6) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 136.03/20.04
% 136.03/20.04 Begin of proof
% 136.03/20.04 |
% 136.03/20.04 | BETA: splitting (6) gives:
% 136.03/20.04 |
% 136.03/20.04 | Case 1:
% 136.03/20.04 | |
% 136.03/20.04 | | (7) all_57_2 = e2 & op(e2, e3) = e2
% 136.03/20.04 | |
% 136.03/20.04 | | ALPHA: (7) implies:
% 136.03/20.04 | | (8) op(e2, e3) = e2
% 136.03/20.04 | |
% 136.03/20.04 | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #779.
% 136.03/20.04 | |
% 136.03/20.04 | Case 2:
% 136.03/20.04 | |
% 136.03/20.04 | | (9) all_57_3 = e2 & op(e2, e2) = e2
% 136.03/20.04 | |
% 136.03/20.04 | | ALPHA: (9) implies:
% 136.03/20.04 | | (10) all_57_3 = e2
% 136.03/20.04 | |
% 136.03/20.04 | | COMBINE_EQS: (3), (10) imply:
% 136.03/20.04 | | (11) e2 = e1
% 136.03/20.04 | |
% 136.03/20.04 | | REDUCE: (2), (11) imply:
% 136.03/20.04 | | (12) $false
% 136.03/20.04 | |
% 136.03/20.04 | | CLOSE: (12) is inconsistent.
% 136.03/20.04 | |
% 136.03/20.04 | End of split
% 136.03/20.04 |
% 136.03/20.04 End of proof
% 136.03/20.04
% 136.03/20.04 Sub-proof #142 shows that the following formulas are inconsistent:
% 136.03/20.04 ----------------------------------------------------------------
% 136.03/20.04 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.04 (2) ~ (all_52_1 = e0)
% 136.03/20.04 (3) ~ (all_10_2 = e0)
% 136.03/20.04 (4) op(e3, e3) = all_10_2
% 136.03/20.04 (5) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0)
% 136.03/20.04 (6) op(e2, e3) = all_52_1
% 136.03/20.04
% 136.03/20.04 Begin of proof
% 136.03/20.04 |
% 136.03/20.04 | BETA: splitting (5) gives:
% 136.03/20.04 |
% 136.03/20.04 | Case 1:
% 136.03/20.04 | |
% 136.03/20.04 | | (7) all_57_0 = e0 & op(e3, e3) = e0
% 136.03/20.04 | |
% 136.03/20.04 | | ALPHA: (7) implies:
% 136.03/20.04 | | (8) op(e3, e3) = e0
% 136.03/20.04 | |
% 136.03/20.04 | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #534.
% 136.03/20.04 | |
% 136.03/20.04 | Case 2:
% 136.03/20.04 | |
% 136.03/20.04 | | (9) all_57_2 = e0 & op(e2, e3) = e0
% 136.03/20.04 | |
% 136.03/20.04 | | REF_CLOSE: (1), (2), (6), (9) are inconsistent by sub-proof #225.
% 136.03/20.04 | |
% 136.03/20.04 | End of split
% 136.03/20.04 |
% 136.03/20.04 End of proof
% 136.03/20.04
% 136.03/20.04 Sub-proof #143 shows that the following formulas are inconsistent:
% 136.03/20.04 ----------------------------------------------------------------
% 136.03/20.04 (1) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2)
% 136.03/20.04 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 136.03/20.04 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25
% 136.03/20.04 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 136.03/20.04 $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~
% 136.03/20.04 (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 136.03/20.04 (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 136.03/20.04 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 136.03/20.04 = all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.03/20.04 $i(all_56_29))
% 136.03/20.04 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.04 (3) ~ (e3 = e0)
% 136.03/20.04 (4) ~ (all_52_9 = e2)
% 136.03/20.04 (5) op(e1, e1) = e0
% 136.03/20.04 (6) op(e2, e1) = all_52_9
% 136.03/20.04
% 136.03/20.04 Begin of proof
% 136.03/20.04 |
% 136.03/20.04 | BETA: splitting (1) gives:
% 136.03/20.04 |
% 136.03/20.04 | Case 1:
% 136.03/20.04 | |
% 136.03/20.04 | | (7) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.03/20.04 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.03/20.04 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.03/20.04 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1)
% 136.03/20.04 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)
% 136.03/20.04 | |
% 136.03/20.04 | | ALPHA: (7) implies:
% 136.03/20.04 | | (8) op(e1, e1) = e3
% 136.03/20.04 | |
% 136.03/20.04 | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #753.
% 136.03/20.04 | |
% 136.03/20.04 | Case 2:
% 136.03/20.04 | |
% 136.03/20.04 | | (9) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13
% 136.03/20.04 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1
% 136.03/20.04 | | & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 136.03/20.04 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 136.03/20.04 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 136.03/20.04 | |
% 136.03/20.04 | | ALPHA: (9) implies:
% 136.03/20.04 | | (10) op(e2, e1) = e2
% 136.03/20.04 | |
% 136.03/20.04 | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #770.
% 136.03/20.04 | |
% 136.03/20.04 | End of split
% 136.03/20.04 |
% 136.03/20.04 End of proof
% 136.03/20.04
% 136.03/20.04 Sub-proof #144 shows that the following formulas are inconsistent:
% 136.03/20.04 ----------------------------------------------------------------
% 136.03/20.04 (1) all_57_12 = e0
% 136.03/20.04 (2) op(e3, e3) = e1
% 136.03/20.04 (3) ~ (all_56_5 = e3)
% 136.03/20.04 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.04 (5) ~ (e3 = e0)
% 136.03/20.04 (6) ~ (e3 = e2)
% 136.03/20.04 (7) op(e1, e3) = all_56_5
% 136.03/20.04 (8) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 136.03/20.04 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 136.03/20.04 (9) all_57_2 = e2
% 136.03/20.04 (10) ~ (e3 = e1)
% 136.03/20.04
% 136.03/20.04 Begin of proof
% 136.03/20.04 |
% 136.03/20.04 | BETA: splitting (8) gives:
% 136.03/20.04 |
% 136.03/20.04 | Case 1:
% 136.03/20.04 | |
% 136.03/20.04 | | (11) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 136.03/20.04 | | e3)
% 136.03/20.04 | |
% 136.03/20.04 | | REF_CLOSE: (2), (4), (6), (9), (10), (11) are inconsistent by sub-proof
% 136.03/20.04 | | #589.
% 136.03/20.04 | |
% 136.03/20.04 | Case 2:
% 136.03/20.04 | |
% 136.03/20.04 | | (12) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 136.03/20.04 | | e3)
% 136.03/20.04 | |
% 136.03/20.04 | | BETA: splitting (12) gives:
% 136.03/20.04 | |
% 136.03/20.04 | | Case 1:
% 136.03/20.04 | | |
% 136.03/20.04 | | | (13) all_57_6 = e3 & op(e1, e3) = e3
% 136.03/20.04 | | |
% 136.03/20.04 | | | ALPHA: (13) implies:
% 136.03/20.04 | | | (14) op(e1, e3) = e3
% 136.03/20.04 | | |
% 136.03/20.04 | | | REF_CLOSE: (3), (4), (7), (14) are inconsistent by sub-proof #724.
% 136.03/20.04 | | |
% 136.03/20.04 | | Case 2:
% 136.03/20.04 | | |
% 136.03/20.04 | | | (15) all_57_12 = e3 & op(e0, e3) = e3
% 136.03/20.04 | | |
% 136.03/20.04 | | | ALPHA: (15) implies:
% 136.03/20.04 | | | (16) all_57_12 = e3
% 136.03/20.04 | | |
% 136.03/20.04 | | | REF_CLOSE: (1), (5), (16) are inconsistent by sub-proof #492.
% 136.03/20.04 | | |
% 136.03/20.04 | | End of split
% 136.03/20.04 | |
% 136.03/20.04 | End of split
% 136.03/20.04 |
% 136.03/20.04 End of proof
% 136.03/20.04
% 136.03/20.04 Sub-proof #145 shows that the following formulas are inconsistent:
% 136.03/20.04 ----------------------------------------------------------------
% 136.03/20.04 (1) ~ (all_52_14 = e3)
% 136.03/20.04 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.04 (3) ~ (e3 = e0)
% 136.03/20.04 (4) ~ (all_52_1 = e0)
% 136.03/20.04 (5) all_57_9 = e3
% 136.03/20.04 (6) ~ (e3 = e2)
% 136.03/20.04 (7) op(e2, e2) = e1
% 136.03/20.04 (8) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 136.03/20.04 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 136.03/20.04 (9) op(e2, e1) = all_52_9
% 136.03/20.04 (10) op(e0, e0) = e2
% 136.03/20.04 (11) op(e2, e3) = all_52_1
% 136.03/20.04 (12) e3 = e1
% 136.03/20.04 (13) ~ (all_52_9 = e0)
% 136.03/20.04 (14) ~ (e3 = e1)
% 136.03/20.04 (15) ~ (e1 = e0)
% 136.03/20.04 (16) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 136.03/20.04 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 136.03/20.04 (17) op(e1, e0) = all_52_14
% 136.03/20.04
% 136.03/20.04 Begin of proof
% 136.03/20.04 |
% 136.03/20.04 | SIMP: (12) implies:
% 136.03/20.04 | (18) e3 = e1
% 136.03/20.04 |
% 136.03/20.04 | COMBINE_EQS: (5), (18) imply:
% 136.03/20.04 | (19) all_57_9 = e1
% 136.03/20.04 |
% 136.03/20.04 | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (13), (14),
% 136.03/20.04 | (15), (16), (17), (19) are inconsistent by sub-proof #150.
% 136.03/20.04 |
% 136.03/20.04 End of proof
% 136.03/20.04
% 136.03/20.04 Sub-proof #146 shows that the following formulas are inconsistent:
% 136.03/20.04 ----------------------------------------------------------------
% 136.03/20.04 (1) op(e1, e1) = all_6_2
% 136.03/20.04 (2) ~ (e2 = e0)
% 136.03/20.04 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.04 (4) ~ (e2 = e1)
% 136.03/20.04 (5) ~ (e3 = e0)
% 136.03/20.04 (6) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 136.03/20.04 (7) all_57_9 = e3
% 136.03/20.04 (8) ~ (all_6_2 = e2)
% 136.03/20.04 (9) op(e0, e0) = e2
% 136.03/20.04 (10) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 136.03/20.04 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 136.03/20.04 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 136.03/20.04 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 136.03/20.04 (11) ~ (e3 = e1)
% 136.03/20.04 (12) ~ (e1 = e0)
% 136.03/20.04 (13) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 136.03/20.04 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 136.03/20.04
% 136.03/20.04 Begin of proof
% 136.03/20.04 |
% 136.03/20.04 | BETA: splitting (6) gives:
% 136.03/20.04 |
% 136.03/20.04 | Case 1:
% 136.03/20.04 | |
% 136.03/20.04 | | (14) all_57_8 = e2 & op(e1, e1) = e2
% 136.03/20.04 | |
% 136.03/20.04 | | ALPHA: (14) implies:
% 136.03/20.04 | | (15) op(e1, e1) = e2
% 136.03/20.04 | |
% 136.03/20.04 | | REF_CLOSE: (1), (3), (8), (15) are inconsistent by sub-proof #767.
% 136.03/20.04 | |
% 136.03/20.04 | Case 2:
% 136.03/20.04 | |
% 136.03/20.04 | | (16) all_57_11 = e2 & op(e1, e0) = e2
% 136.03/20.04 | |
% 136.03/20.04 | | ALPHA: (16) implies:
% 136.03/20.04 | | (17) all_57_11 = e2
% 136.03/20.04 | |
% 136.03/20.04 | | REF_CLOSE: (2), (3), (4), (5), (7), (9), (10), (11), (12), (13), (17) are
% 136.03/20.04 | | inconsistent by sub-proof #635.
% 136.03/20.04 | |
% 136.03/20.04 | End of split
% 136.03/20.04 |
% 136.03/20.04 End of proof
% 136.03/20.04
% 136.03/20.04 Sub-proof #147 shows that the following formulas are inconsistent:
% 136.03/20.04 ----------------------------------------------------------------
% 136.03/20.04 (1) all_57_7 = e0 & op(e1, e2) = e0
% 136.03/20.04 (2) all_57_7 = e3
% 136.03/20.04 (3) ~ (e3 = e0)
% 136.03/20.04
% 136.03/20.04 Begin of proof
% 136.03/20.04 |
% 136.03/20.04 | ALPHA: (1) implies:
% 136.03/20.04 | (4) all_57_7 = e0
% 136.03/20.04 |
% 136.03/20.04 | COMBINE_EQS: (2), (4) imply:
% 136.03/20.04 | (5) e3 = e0
% 136.03/20.04 |
% 136.03/20.04 | REDUCE: (3), (5) imply:
% 136.03/20.04 | (6) $false
% 136.03/20.04 |
% 136.03/20.04 | CLOSE: (6) is inconsistent.
% 136.03/20.04 |
% 136.03/20.04 End of proof
% 136.03/20.04
% 136.03/20.04 Sub-proof #148 shows that the following formulas are inconsistent:
% 136.03/20.04 ----------------------------------------------------------------
% 136.03/20.04 (1) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2)
% 136.03/20.04 (2) ~ (e2 = e0)
% 136.03/20.04 (3) op(e3, e3) = e1
% 136.03/20.04 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.04 (5) ~ (e2 = e1)
% 136.03/20.04 (6) all_57_1 = e0
% 136.03/20.04
% 136.03/20.04 Begin of proof
% 136.03/20.04 |
% 136.03/20.04 | BETA: splitting (1) gives:
% 136.03/20.04 |
% 136.03/20.04 | Case 1:
% 136.03/20.04 | |
% 136.03/20.04 | | (7) all_57_0 = e2 & op(e3, e3) = e2
% 136.03/20.04 | |
% 136.03/20.04 | | ALPHA: (7) implies:
% 136.03/20.04 | | (8) op(e3, e3) = e2
% 136.03/20.04 | |
% 136.03/20.04 | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #743.
% 136.03/20.04 | |
% 136.03/20.04 | Case 2:
% 136.03/20.04 | |
% 136.03/20.04 | | (9) all_57_1 = e2 & op(e3, e2) = e2
% 136.03/20.04 | |
% 136.03/20.04 | | REF_CLOSE: (2), (6), (9) are inconsistent by sub-proof #149.
% 136.03/20.04 | |
% 136.03/20.04 | End of split
% 136.03/20.04 |
% 136.03/20.04 End of proof
% 136.03/20.04
% 136.03/20.04 Sub-proof #149 shows that the following formulas are inconsistent:
% 136.03/20.04 ----------------------------------------------------------------
% 136.03/20.04 (1) all_57_1 = e2 & op(e3, e2) = e2
% 136.03/20.04 (2) all_57_1 = e0
% 136.03/20.04 (3) ~ (e2 = e0)
% 136.03/20.04
% 136.03/20.04 Begin of proof
% 136.03/20.04 |
% 136.03/20.04 | ALPHA: (1) implies:
% 136.03/20.04 | (4) all_57_1 = e2
% 136.03/20.04 |
% 136.03/20.04 | COMBINE_EQS: (2), (4) imply:
% 136.03/20.04 | (5) e2 = e0
% 136.03/20.04 |
% 136.03/20.04 | SIMP: (5) implies:
% 136.03/20.04 | (6) e2 = e0
% 136.03/20.04 |
% 136.03/20.04 | REDUCE: (3), (6) imply:
% 136.03/20.04 | (7) $false
% 136.03/20.04 |
% 136.03/20.04 | CLOSE: (7) is inconsistent.
% 136.03/20.04 |
% 136.03/20.04 End of proof
% 136.03/20.04
% 136.03/20.04 Sub-proof #150 shows that the following formulas are inconsistent:
% 136.03/20.04 ----------------------------------------------------------------
% 136.03/20.04 (1) ~ (all_52_14 = e3)
% 136.03/20.04 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.04 (3) ~ (e3 = e0)
% 136.03/20.04 (4) ~ (all_52_1 = e0)
% 136.03/20.04 (5) ~ (e3 = e2)
% 136.03/20.04 (6) op(e2, e2) = e1
% 136.03/20.04 (7) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 136.03/20.04 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 136.03/20.04 (8) op(e2, e1) = all_52_9
% 136.03/20.04 (9) op(e0, e0) = e2
% 136.03/20.04 (10) op(e2, e3) = all_52_1
% 136.03/20.04 (11) all_57_9 = e1
% 136.03/20.04 (12) ~ (all_52_9 = e0)
% 136.03/20.04 (13) ~ (e3 = e1)
% 136.03/20.04 (14) ~ (e1 = e0)
% 136.03/20.04 (15) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 136.03/20.04 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 136.03/20.04 (16) op(e1, e0) = all_52_14
% 136.03/20.04
% 136.03/20.04 Begin of proof
% 136.03/20.04 |
% 136.03/20.04 | BETA: splitting (7) gives:
% 136.03/20.04 |
% 136.03/20.04 | Case 1:
% 136.03/20.04 | |
% 136.03/20.04 | | (17) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 136.03/20.04 | | e3)
% 136.03/20.04 | |
% 136.03/20.04 | | BETA: splitting (17) gives:
% 136.03/20.04 | |
% 136.03/20.04 | | Case 1:
% 136.03/20.04 | | |
% 136.03/20.04 | | | (18) all_57_9 = e3 & op(e3, e0) = e3
% 136.03/20.04 | | |
% 136.03/20.04 | | | ALPHA: (18) implies:
% 136.03/20.04 | | | (19) all_57_9 = e3
% 136.03/20.04 | | |
% 136.03/20.04 | | | REF_CLOSE: (11), (13), (19) are inconsistent by sub-proof #690.
% 136.03/20.04 | | |
% 136.03/20.04 | | Case 2:
% 136.03/20.04 | | |
% 136.03/20.04 | | | (20) all_57_10 = e3 & op(e2, e0) = e3
% 136.03/20.04 | | |
% 136.03/20.04 | | | ALPHA: (20) implies:
% 136.03/20.04 | | | (21) all_57_10 = e3
% 136.03/20.04 | | |
% 136.03/20.04 | | | REF_CLOSE: (2), (3), (4), (6), (8), (10), (12), (14), (15), (21) are
% 136.03/20.04 | | | inconsistent by sub-proof #151.
% 136.03/20.04 | | |
% 136.03/20.04 | | End of split
% 136.03/20.04 | |
% 136.03/20.04 | Case 2:
% 136.03/20.04 | |
% 136.03/20.04 | | (22) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 136.03/20.04 | | e3)
% 136.03/20.04 | |
% 136.03/20.04 | | REF_CLOSE: (1), (2), (5), (9), (16), (22) are inconsistent by sub-proof
% 136.03/20.04 | | #330.
% 136.03/20.04 | |
% 136.03/20.04 | End of split
% 136.03/20.04 |
% 136.03/20.04 End of proof
% 136.03/20.04
% 136.03/20.04 Sub-proof #151 shows that the following formulas are inconsistent:
% 136.03/20.04 ----------------------------------------------------------------
% 136.03/20.04 (1) all_57_10 = e3
% 136.03/20.04 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.04 (3) ~ (e3 = e0)
% 136.03/20.04 (4) ~ (all_52_1 = e0)
% 136.03/20.04 (5) op(e2, e2) = e1
% 136.03/20.04 (6) op(e2, e1) = all_52_9
% 136.03/20.04 (7) op(e2, e3) = all_52_1
% 136.03/20.04 (8) ~ (all_52_9 = e0)
% 136.03/20.04 (9) ~ (e1 = e0)
% 136.03/20.04 (10) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 136.03/20.04 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 136.03/20.04
% 136.03/20.04 Begin of proof
% 136.03/20.04 |
% 136.03/20.04 | BETA: splitting (10) gives:
% 136.03/20.04 |
% 136.03/20.04 | Case 1:
% 136.03/20.04 | |
% 136.03/20.04 | | (11) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 136.03/20.04 | | e0)
% 136.03/20.04 | |
% 136.03/20.04 | | REF_CLOSE: (2), (4), (5), (7), (9), (11) are inconsistent by sub-proof #152.
% 136.03/20.04 | |
% 136.03/20.04 | Case 2:
% 136.03/20.04 | |
% 136.03/20.04 | | (12) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 136.03/20.04 | | e0)
% 136.03/20.04 | |
% 136.03/20.04 | | BETA: splitting (12) gives:
% 136.03/20.04 | |
% 136.03/20.04 | | Case 1:
% 136.03/20.04 | | |
% 136.03/20.04 | | | (13) all_57_5 = e0 & op(e2, e1) = e0
% 136.03/20.04 | | |
% 136.03/20.04 | | | REF_CLOSE: (2), (6), (8), (13) are inconsistent by sub-proof #455.
% 136.03/20.04 | | |
% 136.03/20.04 | | Case 2:
% 136.03/20.04 | | |
% 136.03/20.04 | | | (14) all_57_10 = e0 & op(e2, e0) = e0
% 136.03/20.04 | | |
% 136.03/20.04 | | | ALPHA: (14) implies:
% 136.03/20.04 | | | (15) all_57_10 = e0
% 136.03/20.04 | | |
% 136.03/20.04 | | | REF_CLOSE: (1), (3), (15) are inconsistent by sub-proof #448.
% 136.03/20.04 | | |
% 136.03/20.04 | | End of split
% 136.03/20.04 | |
% 136.03/20.04 | End of split
% 136.03/20.04 |
% 136.03/20.04 End of proof
% 136.03/20.04
% 136.03/20.04 Sub-proof #152 shows that the following formulas are inconsistent:
% 136.03/20.04 ----------------------------------------------------------------
% 136.03/20.04 (1) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 136.03/20.04 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.04 (3) ~ (all_52_1 = e0)
% 136.03/20.04 (4) op(e2, e2) = e1
% 136.03/20.04 (5) op(e2, e3) = all_52_1
% 136.03/20.04 (6) ~ (e1 = e0)
% 136.03/20.04
% 136.03/20.04 Begin of proof
% 136.03/20.04 |
% 136.03/20.04 | BETA: splitting (1) gives:
% 136.03/20.04 |
% 136.03/20.04 | Case 1:
% 136.03/20.04 | |
% 136.03/20.04 | | (7) all_57_2 = e0 & op(e2, e3) = e0
% 136.03/20.04 | |
% 136.03/20.04 | | REF_CLOSE: (2), (3), (5), (7) are inconsistent by sub-proof #225.
% 136.03/20.04 | |
% 136.03/20.04 | Case 2:
% 136.03/20.04 | |
% 136.03/20.04 | | (8) all_57_3 = e0 & op(e2, e2) = e0
% 136.03/20.04 | |
% 136.03/20.04 | | ALPHA: (8) implies:
% 136.03/20.04 | | (9) op(e2, e2) = e0
% 136.03/20.04 | |
% 136.03/20.04 | | REF_CLOSE: (2), (4), (6), (9) are inconsistent by sub-proof #675.
% 136.03/20.04 | |
% 136.03/20.04 | End of split
% 136.03/20.04 |
% 136.03/20.04 End of proof
% 136.03/20.04
% 136.03/20.04 Sub-proof #153 shows that the following formulas are inconsistent:
% 136.03/20.04 ----------------------------------------------------------------
% 136.03/20.04 (1) all_54_4 = e1 | all_54_4 = e0
% 136.03/20.04 (2) all_54_4 = all_52_1
% 136.03/20.04 (3) ~ (all_52_1 = e1)
% 136.03/20.04 (4) ~ (all_52_1 = e0)
% 136.03/20.04
% 136.03/20.04 Begin of proof
% 136.03/20.04 |
% 136.03/20.04 | BETA: splitting (1) gives:
% 136.03/20.04 |
% 136.03/20.04 | Case 1:
% 136.03/20.04 | |
% 136.03/20.04 | | (5) all_54_4 = e1
% 136.03/20.04 | |
% 136.03/20.04 | | COMBINE_EQS: (2), (5) imply:
% 136.03/20.04 | | (6) all_52_1 = e1
% 136.03/20.04 | |
% 136.03/20.04 | | REDUCE: (3), (6) imply:
% 136.03/20.04 | | (7) $false
% 136.03/20.04 | |
% 136.03/20.04 | | CLOSE: (7) is inconsistent.
% 136.03/20.04 | |
% 136.03/20.04 | Case 2:
% 136.03/20.04 | |
% 136.03/20.04 | | (8) all_54_4 = e0
% 136.03/20.04 | |
% 136.03/20.04 | | COMBINE_EQS: (2), (8) imply:
% 136.03/20.04 | | (9) all_52_1 = e0
% 136.03/20.04 | |
% 136.03/20.04 | | REDUCE: (4), (9) imply:
% 136.03/20.04 | | (10) $false
% 136.03/20.04 | |
% 136.03/20.04 | | CLOSE: (10) is inconsistent.
% 136.03/20.04 | |
% 136.03/20.04 | End of split
% 136.03/20.04 |
% 136.03/20.04 End of proof
% 136.03/20.04
% 136.03/20.04 Sub-proof #154 shows that the following formulas are inconsistent:
% 136.03/20.04 ----------------------------------------------------------------
% 136.03/20.04 (1) op(e1, e1) = all_6_2
% 136.03/20.04 (2) ~ (all_40_2 = e0) | ( ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 &
% 136.03/20.04 $i(all_40_0)) | ( ~ (all_40_1 = e2) & op(e0, e0) = all_40_1 &
% 136.03/20.04 $i(all_40_1))
% 136.03/20.04 (3) ~ (all_52_11 = e2)
% 136.03/20.04 (4) all_40_2 = all_6_2
% 136.03/20.04 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.04 (6) ~ (e2 = e1)
% 136.03/20.04 (7) ~ (e3 = e2)
% 136.03/20.04 (8) op(e2, e2) = e1
% 136.03/20.04 (9) ~ (all_52_11 = all_6_2)
% 136.03/20.04 (10) op(e0, e1) = all_52_11
% 136.03/20.04 (11) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 136.03/20.04 (12) ~ (all_6_2 = e2)
% 136.03/20.04 (13) op(e2, e0) = e0
% 136.03/20.04 (14) op(e0, e0) = e2
% 136.03/20.04 (15) all_54_14 = all_52_11
% 136.03/20.04 (16) ~ (e1 = e0)
% 136.03/20.04 (17) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.03/20.04 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 136.03/20.04 op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.03/20.04 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.03/20.04 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 &
% 136.03/20.04 all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~
% 136.03/20.04 (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 136.03/20.04 op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 136.03/20.04 all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 136.03/20.04 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 136.03/20.04 all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~
% 136.03/20.04 (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 136.03/20.04 (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 &
% 136.03/20.04 op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0
% 136.03/20.04 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.03/20.04 (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 136.03/20.04 (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.03/20.04 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.03/20.04 all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.03/20.04 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.03/20.04 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.03/20.04 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.03/20.04 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 136.03/20.04 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 136.03/20.04 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 136.03/20.04 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 136.03/20.04 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 136.03/20.04 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 136.03/20.04 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.03/20.04 $i(all_56_29))))
% 136.03/20.04
% 136.03/20.04 Begin of proof
% 136.03/20.04 |
% 136.03/20.04 | BETA: splitting (17) gives:
% 136.03/20.04 |
% 136.03/20.04 | Case 1:
% 136.03/20.04 | |
% 136.03/20.04 | | (18) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ (all_56_15
% 136.03/20.04 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e2, e2) =
% 136.03/20.04 | | e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 136.03/20.04 | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 &
% 136.03/20.04 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31)
% 136.03/20.04 | |
% 136.03/20.04 | | ALPHA: (18) implies:
% 136.03/20.04 | | (19) op(e2, e2) = e0
% 136.03/20.04 | |
% 136.03/20.04 | | REF_CLOSE: (5), (8), (16), (19) are inconsistent by sub-proof #675.
% 136.03/20.04 | |
% 136.03/20.04 | Case 2:
% 136.03/20.04 | |
% 136.03/20.04 | | (20) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 136.03/20.04 | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.03/20.04 | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.03/20.04 | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1)
% 136.03/20.04 | | = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 136.03/20.04 | | $i(all_56_27)) | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 136.03/20.04 | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 136.03/20.04 | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 136.03/20.04 | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) =
% 136.03/20.04 | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 136.03/20.04 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.03/20.04 | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 136.03/20.04 | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.03/20.04 | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.03/20.04 | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.03/20.04 | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27))
% 136.03/20.04 | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.03/20.04 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.03/20.04 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 136.03/20.04 | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7)
% 136.03/20.04 | | & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 136.03/20.04 | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.03/20.04 | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5
% 136.03/20.04 | | & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 136.03/20.04 | | = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 136.03/20.04 | | $i(all_56_21) & $i(all_56_29))))
% 136.03/20.04 | |
% 136.03/20.04 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 136.03/20.04 | | (14), (15), (20) are inconsistent by sub-proof #266.
% 136.03/20.04 | |
% 136.03/20.04 | End of split
% 136.03/20.04 |
% 136.03/20.04 End of proof
% 136.03/20.04
% 136.03/20.04 Sub-proof #155 shows that the following formulas are inconsistent:
% 136.03/20.04 ----------------------------------------------------------------
% 136.03/20.04 (1) all_54_9 = e1 | all_54_9 = e0
% 136.03/20.04 (2) all_54_9 = all_8_0
% 136.03/20.04 (3) ~ (all_8_0 = e1)
% 136.03/20.04 (4) ~ (all_8_0 = e0)
% 136.03/20.04
% 136.03/20.04 Begin of proof
% 136.03/20.04 |
% 136.03/20.04 | BETA: splitting (1) gives:
% 136.03/20.04 |
% 136.03/20.04 | Case 1:
% 136.03/20.04 | |
% 136.03/20.04 | | (5) all_54_9 = e1
% 136.03/20.04 | |
% 136.03/20.04 | | COMBINE_EQS: (2), (5) imply:
% 136.03/20.04 | | (6) all_8_0 = e1
% 136.03/20.04 | |
% 136.03/20.04 | | REDUCE: (3), (6) imply:
% 136.03/20.04 | | (7) $false
% 136.03/20.04 | |
% 136.03/20.04 | | CLOSE: (7) is inconsistent.
% 136.03/20.04 | |
% 136.03/20.04 | Case 2:
% 136.03/20.04 | |
% 136.03/20.04 | | (8) all_54_9 = e0
% 136.03/20.04 | |
% 136.03/20.04 | | COMBINE_EQS: (2), (8) imply:
% 136.03/20.04 | | (9) all_8_0 = e0
% 136.03/20.04 | |
% 136.03/20.04 | | REDUCE: (4), (9) imply:
% 136.03/20.04 | | (10) $false
% 136.03/20.04 | |
% 136.03/20.04 | | CLOSE: (10) is inconsistent.
% 136.03/20.04 | |
% 136.03/20.04 | End of split
% 136.03/20.04 |
% 136.03/20.04 End of proof
% 136.03/20.04
% 136.03/20.04 Sub-proof #156 shows that the following formulas are inconsistent:
% 136.03/20.04 ----------------------------------------------------------------
% 136.03/20.04 (1) op(e0, e0) = all_4_2
% 136.03/20.04 (2) op(e1, e1) = all_6_2
% 136.03/20.04 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.04 (4) ~ (all_4_2 = e2)
% 136.03/20.04 (5) op(e2, e2) = e1
% 136.03/20.04 (6) ~ (all_6_2 = e2)
% 136.03/20.04 (7) op(e0, e0) = e2
% 136.03/20.04 (8) ~ (e1 = e0)
% 136.03/20.05 (9) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.03/20.05 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 136.03/20.05 op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.03/20.05 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.03/20.05 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 &
% 136.03/20.05 all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~
% 136.03/20.05 (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2,
% 136.03/20.05 e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 136.03/20.05 op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 136.03/20.05 $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = all_56_31 &
% 136.03/20.05 $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) &
% 136.03/20.05 ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 136.03/20.05 op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) =
% 136.03/20.05 all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1)
% 136.03/20.05 & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 &
% 136.03/20.05 all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~
% 136.03/20.05 (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 136.03/20.05 op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 136.03/20.05 all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 136.03/20.05 $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 &
% 136.03/20.05 ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 136.03/20.05 (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 136.03/20.05 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 136.03/20.05 $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 &
% 136.03/20.05 all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.03/20.05 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 136.03/20.05 op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 136.03/20.05 all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 136.03/20.05 $i(all_56_21) & $i(all_56_29))))
% 136.03/20.05
% 136.03/20.05 Begin of proof
% 136.03/20.05 |
% 136.03/20.05 | BETA: splitting (9) gives:
% 136.03/20.05 |
% 136.03/20.05 | Case 1:
% 136.03/20.05 | |
% 136.03/20.05 | | (10) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ (all_56_15
% 136.03/20.05 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e2, e2) =
% 136.03/20.05 | | e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 136.03/20.05 | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 &
% 136.03/20.05 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31)
% 136.03/20.05 | |
% 136.03/20.05 | | ALPHA: (10) implies:
% 136.03/20.05 | | (11) op(e2, e2) = e0
% 136.03/20.05 | |
% 136.03/20.05 | | REF_CLOSE: (3), (5), (8), (11) are inconsistent by sub-proof #675.
% 136.03/20.05 | |
% 136.03/20.05 | Case 2:
% 136.03/20.05 | |
% 136.03/20.05 | | (12) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 136.03/20.05 | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.03/20.05 | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.03/20.05 | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1)
% 136.03/20.05 | | = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 136.03/20.05 | | $i(all_56_27)) | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 136.03/20.05 | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 136.03/20.05 | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 136.03/20.05 | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) =
% 136.03/20.05 | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 136.03/20.05 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.03/20.05 | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 136.03/20.05 | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.03/20.05 | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.03/20.05 | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.03/20.05 | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27))
% 136.03/20.05 | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.03/20.05 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.03/20.05 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 136.03/20.05 | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7)
% 136.03/20.05 | | & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 136.03/20.05 | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.03/20.05 | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5
% 136.03/20.05 | | & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 136.03/20.05 | | = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 136.03/20.05 | | $i(all_56_21) & $i(all_56_29))))
% 136.03/20.05 | |
% 136.03/20.05 | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (12) are inconsistent by sub-proof
% 136.03/20.05 | | #352.
% 136.03/20.05 | |
% 136.03/20.05 | End of split
% 136.03/20.05 |
% 136.03/20.05 End of proof
% 136.03/20.05
% 136.03/20.05 Sub-proof #157 shows that the following formulas are inconsistent:
% 136.03/20.05 ----------------------------------------------------------------
% 136.03/20.05 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.05 (2) op(e2, e2) = e1
% 136.03/20.05 (3) op(e0, e2) = e2
% 136.03/20.05 (4) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.03/20.05 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 136.03/20.05 op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.03/20.05 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.03/20.05 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 &
% 136.03/20.05 all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~
% 136.03/20.05 (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3,
% 136.03/20.05 e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 136.03/20.05 op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 136.03/20.05 $i(all_56_17) & $i(all_56_25))
% 136.03/20.05 (5) ~ (e3 = e1)
% 136.03/20.05
% 136.03/20.05 Begin of proof
% 136.03/20.05 |
% 136.03/20.05 | BETA: splitting (4) gives:
% 136.03/20.05 |
% 136.03/20.05 | Case 1:
% 136.03/20.05 | |
% 136.03/20.05 | | (6) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.03/20.05 | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 136.03/20.05 | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.03/20.05 | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.03/20.05 | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)
% 136.03/20.05 | |
% 136.03/20.05 | | ALPHA: (6) implies:
% 136.03/20.05 | | (7) ~ (all_56_15 = e2)
% 136.03/20.05 | | (8) op(e0, e2) = all_56_15
% 136.03/20.05 | |
% 136.03/20.05 | | REF_CLOSE: (1), (3), (7), (8) are inconsistent by sub-proof #609.
% 136.03/20.05 | |
% 136.03/20.05 | Case 2:
% 136.03/20.05 | |
% 136.03/20.05 | | (9) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.03/20.05 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.03/20.05 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.03/20.05 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1)
% 136.03/20.05 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)
% 136.03/20.05 | |
% 136.03/20.05 | | ALPHA: (9) implies:
% 136.03/20.05 | | (10) op(e2, e2) = e3
% 136.03/20.05 | |
% 136.03/20.05 | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #325.
% 136.03/20.05 | |
% 136.03/20.05 | End of split
% 136.03/20.05 |
% 136.03/20.05 End of proof
% 136.03/20.05
% 136.03/20.05 Sub-proof #158 shows that the following formulas are inconsistent:
% 136.03/20.05 ----------------------------------------------------------------
% 136.03/20.05 (1) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2)
% 136.03/20.05 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3,
% 136.03/20.05 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 136.03/20.05 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 136.03/20.05 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 136.03/20.05 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.03/20.05 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) =
% 136.03/20.05 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.03/20.05 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 136.03/20.05 $i(all_56_21) & $i(all_56_29))
% 136.03/20.05 (2) op(e1, e2) = e2
% 136.03/20.05 (3) op(e3, e3) = e1
% 136.03/20.05 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.05 (5) ~ (e2 = e1)
% 136.03/20.05
% 136.03/20.05 Begin of proof
% 136.03/20.05 |
% 136.03/20.05 | BETA: splitting (1) gives:
% 136.03/20.05 |
% 136.03/20.05 | Case 1:
% 136.03/20.05 | |
% 136.03/20.05 | | (6) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 136.03/20.05 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 136.03/20.05 | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 136.03/20.05 | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 136.03/20.05 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)
% 136.03/20.05 | |
% 136.03/20.05 | | ALPHA: (6) implies:
% 136.03/20.05 | | (7) op(e3, e3) = e2
% 136.03/20.05 | |
% 136.03/20.05 | | REF_CLOSE: (3), (4), (5), (7) are inconsistent by sub-proof #743.
% 136.03/20.05 | |
% 136.03/20.05 | Case 2:
% 136.03/20.05 | |
% 136.03/20.05 | | (8) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 136.03/20.05 | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 136.03/20.05 | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 136.03/20.05 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 136.03/20.05 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 136.03/20.05 | |
% 136.03/20.05 | | ALPHA: (8) implies:
% 136.03/20.05 | | (9) ~ (all_56_13 = e2)
% 136.03/20.05 | | (10) op(e1, e2) = all_56_13
% 136.03/20.05 | |
% 136.03/20.05 | | REF_CLOSE: (2), (4), (9), (10) are inconsistent by sub-proof #165.
% 136.03/20.05 | |
% 136.03/20.05 | End of split
% 136.03/20.05 |
% 136.03/20.05 End of proof
% 136.03/20.05
% 136.03/20.05 Sub-proof #159 shows that the following formulas are inconsistent:
% 136.03/20.05 ----------------------------------------------------------------
% 136.03/20.05 (1) op(e0, e0) = all_4_2
% 136.03/20.05 (2) op(e1, e1) = all_6_2
% 136.03/20.05 (3) op(e1, e2) = e2
% 136.03/20.05 (4) ~ (e2 = e0)
% 136.03/20.05 (5) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2)
% 136.03/20.05 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 136.03/20.05 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25
% 136.03/20.05 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 136.03/20.05 $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~
% 136.03/20.05 (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 136.03/20.05 (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 136.03/20.05 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 136.03/20.05 = all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.03/20.05 $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3)
% 136.03/20.05 & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.03/20.05 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2)
% 136.03/20.05 = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 &
% 136.03/20.05 $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 136.03/20.05 (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 136.03/20.05 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 136.03/20.05 all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0)
% 136.03/20.05 = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 136.03/20.05 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 136.03/20.05 all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~
% 136.03/20.05 (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 136.03/20.05 (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 &
% 136.03/20.05 op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 136.03/20.05 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.03/20.05 (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11
% 136.03/20.05 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 136.03/20.05 all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 136.03/20.05 e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 136.03/20.05 & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1
% 136.03/20.05 & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 136.03/20.05 ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3)
% 136.03/20.05 = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 136.03/20.05 $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 &
% 136.03/20.05 all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.03/20.05 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 136.03/20.05 op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 136.03/20.05 all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 136.03/20.05 $i(all_56_21) & $i(all_56_29))))
% 136.03/20.05 (6) op(e3, e3) = e1
% 136.03/20.05 (7) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 136.03/20.05 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 136.03/20.05 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.05 (9) ~ (e2 = e1)
% 136.03/20.05 (10) ~ (all_4_2 = e2)
% 136.03/20.05 (11) ~ (e3 = e0)
% 136.03/20.05 (12) ~ (all_52_2 = e1)
% 136.03/20.05 (13) op(e2, e2) = e1
% 136.03/20.05 (14) op(e1, e1) = e3
% 136.03/20.05 (15) ~ (all_4_2 = e1)
% 136.03/20.05 (16) ~ (all_6_2 = e2)
% 136.03/20.05 (17) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 136.03/20.05 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 136.03/20.05 (18) ~ (all_52_4 = e2)
% 136.03/20.05 (19) ~ (all_52_3 = e1)
% 136.03/20.05 (20) op(e1, e3) = all_52_2
% 136.03/20.05 (21) op(e3, e2) = all_52_4
% 136.03/20.05 (22) op(e0, e3) = all_52_3
% 136.03/20.05 (23) op(e3, e0) = all_52_12
% 136.03/20.05 (24) op(e3, e1) = all_52_8
% 136.03/20.05 (25) ~ (all_52_3 = all_4_2)
% 136.03/20.05 (26) ~ (e1 = e0)
% 136.03/20.05 (27) ~ (all_34_2 = e3) | ( ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 &
% 136.03/20.05 $i(all_34_0)) | ( ~ (all_34_1 = e1) & op(e3, e3) = all_34_1 &
% 136.03/20.05 $i(all_34_1))
% 136.03/20.05 (28) ~ (all_52_12 = all_4_2)
% 136.03/20.05 (29) all_34_2 = all_4_2
% 136.03/20.05 (30) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 136.03/20.05 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 136.03/20.05 (31) ~ (all_52_8 = e3)
% 136.03/20.05
% 136.03/20.05 Begin of proof
% 136.03/20.05 |
% 136.03/20.05 | BETA: splitting (5) gives:
% 136.03/20.05 |
% 136.03/20.05 | Case 1:
% 136.03/20.05 | |
% 136.03/20.05 | | (32) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 136.03/20.05 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.03/20.05 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.03/20.05 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 136.03/20.05 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.03/20.05 | | (all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 136.03/20.05 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 136.03/20.05 | | op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1,
% 136.03/20.05 | | e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 136.03/20.05 | | all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.03/20.05 | | $i(all_56_29))
% 136.03/20.05 | |
% 136.03/20.05 | | REF_CLOSE: (3), (8), (12), (20), (32) are inconsistent by sub-proof #160.
% 136.03/20.05 | |
% 136.03/20.05 | Case 2:
% 136.03/20.05 | |
% 136.03/20.05 | | (33) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 136.03/20.05 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.03/20.05 | | op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 136.03/20.05 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 136.03/20.05 | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 136.03/20.05 | | $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 136.03/20.05 | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 136.03/20.05 | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 136.03/20.05 | | e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 136.03/20.05 | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 136.03/20.05 | | $i(all_56_27)) | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 136.03/20.05 | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 136.03/20.05 | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 136.03/20.05 | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) =
% 136.03/20.05 | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 136.03/20.05 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.03/20.05 | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 136.03/20.05 | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.03/20.05 | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.03/20.05 | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.03/20.05 | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27))
% 136.03/20.05 | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.03/20.05 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.03/20.05 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 136.03/20.05 | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7)
% 136.03/20.05 | | & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 136.03/20.05 | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.03/20.05 | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5
% 136.03/20.05 | | & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 136.03/20.05 | | = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 136.03/20.05 | | $i(all_56_21) & $i(all_56_29))))
% 136.03/20.05 | |
% 136.03/20.05 | | BETA: splitting (33) gives:
% 136.03/20.05 | |
% 136.03/20.05 | | Case 1:
% 136.03/20.05 | | |
% 136.03/20.05 | | | (34) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 136.03/20.05 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.03/20.05 | | | op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 136.03/20.05 | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 136.03/20.05 | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 136.03/20.05 | | | $i(all_56_31)
% 136.03/20.05 | | |
% 136.03/20.05 | | | ALPHA: (34) implies:
% 136.03/20.05 | | | (35) op(e2, e2) = e0
% 136.03/20.05 | | |
% 136.03/20.05 | | | REF_CLOSE: (8), (13), (26), (35) are inconsistent by sub-proof #675.
% 136.03/20.05 | | |
% 136.03/20.05 | | Case 2:
% 136.03/20.05 | | |
% 136.03/20.05 | | | (36) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 136.03/20.05 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.03/20.05 | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.03/20.05 | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 136.03/20.05 | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 136.03/20.05 | | | $i(all_56_27)) | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 136.03/20.05 | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 136.03/20.05 | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0)
% 136.03/20.05 | | | & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 136.03/20.05 | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 136.03/20.05 | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25))
% 136.03/20.05 | | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 136.03/20.05 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0)
% 136.03/20.05 | | | & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 136.03/20.05 | | | e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0
% 136.03/20.05 | | | & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 136.03/20.05 | | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~
% 136.03/20.05 | | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 136.03/20.05 | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 136.03/20.05 | | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1)
% 136.03/20.05 | | | = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 136.03/20.05 | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 136.03/20.05 | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0)
% 136.03/20.05 | | | & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1,
% 136.03/20.05 | | | e1) = all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0
% 136.03/20.05 | | | & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.03/20.05 | | | $i(all_56_29))))
% 136.03/20.05 | | |
% 136.03/20.05 | | | BETA: splitting (36) gives:
% 136.03/20.05 | | |
% 136.03/20.05 | | | Case 1:
% 136.03/20.05 | | | |
% 136.03/20.05 | | | | (37) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 136.03/20.05 | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.03/20.05 | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.03/20.05 | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 136.03/20.05 | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 136.03/20.05 | | | | $i(all_56_27)
% 136.03/20.05 | | | |
% 136.03/20.05 | | | | ALPHA: (37) implies:
% 136.03/20.05 | | | | (38) op(e1, e1) = e2
% 136.03/20.05 | | | |
% 136.03/20.05 | | | | REF_CLOSE: (2), (8), (16), (38) are inconsistent by sub-proof #767.
% 136.03/20.05 | | | |
% 136.03/20.05 | | | Case 2:
% 136.03/20.05 | | | |
% 136.03/20.05 | | | | (39) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 136.03/20.05 | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) &
% 136.03/20.05 | | | | ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.03/20.05 | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 136.03/20.05 | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) &
% 136.03/20.05 | | | | $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 136.03/20.05 | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 136.03/20.05 | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2,
% 136.03/20.05 | | | | e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.03/20.05 | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.03/20.05 | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 136.03/20.05 | | | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~
% 136.03/20.05 | | | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 136.03/20.05 | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 136.03/20.05 | | | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1)
% 136.03/20.05 | | | | = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 136.03/20.05 | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 136.03/20.05 | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0)
% 136.03/20.05 | | | | & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1,
% 136.03/20.05 | | | | e1) = all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0
% 136.03/20.05 | | | | & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.03/20.05 | | | | $i(all_56_29)))
% 136.03/20.05 | | | |
% 136.03/20.05 | | | | ALPHA: (39) implies:
% 136.03/20.05 | | | | (40) op(e0, e0) = all_56_31
% 136.03/20.05 | | | | (41) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 136.03/20.05 | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 136.03/20.05 | | | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) =
% 136.03/20.05 | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 136.03/20.05 | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.03/20.05 | | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 136.03/20.05 | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.03/20.05 | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.03/20.05 | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.03/20.05 | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27))
% 136.03/20.05 | | | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.03/20.05 | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.03/20.05 | | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 136.03/20.05 | | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7)
% 136.03/20.05 | | | | & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 136.03/20.05 | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.03/20.05 | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5
% 136.03/20.05 | | | | & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 136.03/20.05 | | | | = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 136.03/20.05 | | | | $i(all_56_21) & $i(all_56_29))
% 136.03/20.05 | | | |
% 136.03/20.05 | | | | REF_CLOSE: (1), (4), (6), (7), (8), (9), (10), (11), (14), (15), (17),
% 136.03/20.05 | | | | (18), (19), (21), (22), (23), (24), (25), (27), (28), (29),
% 136.03/20.05 | | | | (30), (31), (40), (41) are inconsistent by sub-proof #548.
% 136.03/20.05 | | | |
% 136.03/20.05 | | | End of split
% 136.03/20.05 | | |
% 136.03/20.05 | | End of split
% 136.03/20.05 | |
% 136.03/20.05 | End of split
% 136.03/20.05 |
% 136.03/20.05 End of proof
% 136.03/20.05
% 136.03/20.05 Sub-proof #160 shows that the following formulas are inconsistent:
% 136.03/20.05 ----------------------------------------------------------------
% 136.03/20.05 (1) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2)
% 136.03/20.05 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 136.03/20.05 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25
% 136.03/20.05 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 136.03/20.05 $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~
% 136.03/20.05 (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 136.03/20.05 (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 136.03/20.05 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 136.03/20.05 = all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.03/20.05 $i(all_56_29))
% 136.03/20.05 (2) op(e1, e2) = e2
% 136.03/20.05 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.05 (4) ~ (all_52_2 = e1)
% 136.03/20.05 (5) op(e1, e3) = all_52_2
% 136.03/20.05
% 136.03/20.05 Begin of proof
% 136.03/20.05 |
% 136.03/20.05 | BETA: splitting (1) gives:
% 136.03/20.05 |
% 136.03/20.05 | Case 1:
% 136.03/20.05 | |
% 136.03/20.05 | | (6) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.03/20.05 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.03/20.05 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.03/20.05 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1)
% 136.03/20.05 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)
% 136.03/20.05 | |
% 136.03/20.05 | | ALPHA: (6) implies:
% 136.03/20.05 | | (7) op(e1, e3) = e1
% 136.03/20.05 | |
% 136.03/20.05 | | REF_CLOSE: (3), (4), (5), (7) are inconsistent by sub-proof #725.
% 136.03/20.05 | |
% 136.03/20.05 | Case 2:
% 136.03/20.05 | |
% 136.03/20.05 | | (8) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13
% 136.03/20.05 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1
% 136.03/20.05 | | & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 136.03/20.05 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 136.03/20.05 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 136.03/20.05 | |
% 136.03/20.05 | | ALPHA: (8) implies:
% 136.03/20.05 | | (9) ~ (all_56_13 = e2)
% 136.03/20.05 | | (10) op(e1, e2) = all_56_13
% 136.03/20.05 | |
% 136.03/20.05 | | REF_CLOSE: (2), (3), (9), (10) are inconsistent by sub-proof #165.
% 136.03/20.05 | |
% 136.03/20.05 | End of split
% 136.03/20.05 |
% 136.03/20.05 End of proof
% 136.03/20.05
% 136.03/20.05 Sub-proof #161 shows that the following formulas are inconsistent:
% 136.03/20.05 ----------------------------------------------------------------
% 136.03/20.05 (1) all_57_5 = e1 & op(e2, e1) = e1
% 136.03/20.05 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.05 (3) op(e2, e1) = all_52_9
% 136.03/20.05 (4) ~ (all_52_9 = e1)
% 136.03/20.05
% 136.03/20.05 Begin of proof
% 136.03/20.05 |
% 136.03/20.05 | ALPHA: (1) implies:
% 136.03/20.05 | (5) op(e2, e1) = e1
% 136.03/20.05 |
% 136.03/20.05 | GROUND_INST: instantiating (2) with all_52_9, e1, e1, e2, simplifying with
% 136.03/20.05 | (3), (5) gives:
% 136.03/20.05 | (6) all_52_9 = e1
% 136.03/20.05 |
% 136.03/20.05 | REDUCE: (4), (6) imply:
% 136.03/20.05 | (7) $false
% 136.03/20.05 |
% 136.03/20.05 | CLOSE: (7) is inconsistent.
% 136.03/20.05 |
% 136.03/20.05 End of proof
% 136.03/20.05
% 136.03/20.05 Sub-proof #162 shows that the following formulas are inconsistent:
% 136.03/20.05 ----------------------------------------------------------------
% 136.03/20.05 (1) ~ (e2 = e0)
% 136.03/20.05 (2) op(e3, e3) = e1
% 136.03/20.05 (3) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 136.03/20.05 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 136.03/20.05 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.05 (5) ~ (e2 = e1)
% 136.03/20.05 (6) ~ (e3 = e0)
% 136.03/20.05 (7) ~ (e3 = e2)
% 136.03/20.05 (8) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 136.03/20.05 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 136.03/20.05 (9) ~ (all_52_4 = e2)
% 136.03/20.05 (10) op(e3, e2) = all_52_4
% 136.03/20.05 (11) all_57_4 = e1
% 136.03/20.05 (12) op(e3, e1) = all_52_8
% 136.03/20.05 (13) ~ (e3 = e1)
% 136.03/20.05 (14) ~ (e1 = e0)
% 136.03/20.05 (15) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 136.03/20.05 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 136.03/20.05 (16) ~ (all_52_8 = e3)
% 136.03/20.05
% 136.03/20.05 Begin of proof
% 136.03/20.05 |
% 136.03/20.05 | BETA: splitting (8) gives:
% 136.03/20.05 |
% 136.03/20.05 | Case 1:
% 136.03/20.05 | |
% 136.03/20.05 | | (17) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) =
% 136.03/20.05 | | e2)
% 136.03/20.05 | |
% 136.03/20.05 | | BETA: splitting (17) gives:
% 136.03/20.05 | |
% 136.03/20.05 | | Case 1:
% 136.03/20.05 | | |
% 136.03/20.05 | | | (18) all_57_0 = e2 & op(e3, e3) = e2
% 136.03/20.05 | | |
% 136.03/20.05 | | | ALPHA: (18) implies:
% 136.03/20.05 | | | (19) op(e3, e3) = e2
% 136.03/20.05 | | |
% 136.03/20.05 | | | REF_CLOSE: (2), (4), (5), (19) are inconsistent by sub-proof #743.
% 136.03/20.05 | | |
% 136.03/20.05 | | Case 2:
% 136.03/20.05 | | |
% 136.03/20.05 | | | (20) all_57_1 = e2 & op(e3, e2) = e2
% 136.03/20.05 | | |
% 136.03/20.05 | | | REF_CLOSE: (4), (9), (10), (20) are inconsistent by sub-proof #396.
% 136.03/20.05 | | |
% 136.03/20.05 | | End of split
% 136.03/20.05 | |
% 136.03/20.05 | Case 2:
% 136.03/20.05 | |
% 136.03/20.05 | | (21) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) =
% 136.03/20.05 | | e2)
% 136.03/20.05 | |
% 136.03/20.05 | | BETA: splitting (21) gives:
% 136.03/20.05 | |
% 136.03/20.05 | | Case 1:
% 136.03/20.05 | | |
% 136.03/20.05 | | | (22) all_57_4 = e2 & op(e3, e1) = e2
% 136.03/20.05 | | |
% 136.03/20.05 | | | ALPHA: (22) implies:
% 136.03/20.05 | | | (23) all_57_4 = e2
% 136.03/20.05 | | |
% 136.03/20.05 | | | REF_CLOSE: (5), (11), (23) are inconsistent by sub-proof #669.
% 136.03/20.05 | | |
% 136.03/20.05 | | Case 2:
% 136.03/20.05 | | |
% 136.03/20.05 | | | (24) all_57_9 = e2 & op(e3, e0) = e2
% 136.03/20.05 | | |
% 136.03/20.05 | | | ALPHA: (24) implies:
% 136.03/20.05 | | | (25) all_57_9 = e2
% 136.03/20.05 | | |
% 136.03/20.05 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (11), (12), (13), (14),
% 136.03/20.05 | | | (15), (16), (25) are inconsistent by sub-proof #163.
% 136.03/20.05 | | |
% 136.03/20.05 | | End of split
% 136.03/20.05 | |
% 136.03/20.05 | End of split
% 136.03/20.05 |
% 136.03/20.05 End of proof
% 136.03/20.05
% 136.03/20.05 Sub-proof #163 shows that the following formulas are inconsistent:
% 136.03/20.05 ----------------------------------------------------------------
% 136.03/20.05 (1) ~ (e2 = e0)
% 136.03/20.05 (2) op(e3, e3) = e1
% 136.03/20.05 (3) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 136.03/20.05 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 136.03/20.05 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.05 (5) ~ (e2 = e1)
% 136.03/20.05 (6) ~ (e3 = e0)
% 136.03/20.05 (7) ~ (e3 = e2)
% 136.03/20.05 (8) all_57_9 = e2
% 136.03/20.06 (9) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 136.03/20.06 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 136.03/20.06 (10) all_57_4 = e1
% 136.03/20.06 (11) op(e3, e1) = all_52_8
% 136.03/20.06 (12) ~ (e3 = e1)
% 136.03/20.06 (13) ~ (e1 = e0)
% 136.03/20.06 (14) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 136.03/20.06 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 136.03/20.06 (15) ~ (all_52_8 = e3)
% 136.03/20.06
% 136.03/20.06 Begin of proof
% 136.03/20.06 |
% 136.03/20.06 | BETA: splitting (14) gives:
% 136.03/20.06 |
% 136.03/20.06 | Case 1:
% 136.03/20.06 | |
% 136.03/20.06 | | (16) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 136.03/20.06 | | e3)
% 136.03/20.06 | |
% 136.03/20.06 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (12), (13), (14),
% 136.03/20.06 | | (16) are inconsistent by sub-proof #164.
% 136.03/20.06 | |
% 136.03/20.06 | Case 2:
% 136.03/20.06 | |
% 136.03/20.06 | | (17) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 136.03/20.06 | | e3)
% 136.03/20.06 | |
% 136.03/20.06 | | BETA: splitting (17) gives:
% 136.03/20.06 | |
% 136.03/20.06 | | Case 1:
% 136.03/20.06 | | |
% 136.03/20.06 | | | (18) all_57_4 = e3 & op(e3, e1) = e3
% 136.03/20.06 | | |
% 136.03/20.06 | | | ALPHA: (18) implies:
% 136.03/20.06 | | | (19) op(e3, e1) = e3
% 136.03/20.06 | | |
% 136.03/20.06 | | | REF_CLOSE: (4), (11), (15), (19) are inconsistent by sub-proof #705.
% 136.03/20.06 | | |
% 136.03/20.06 | | Case 2:
% 136.03/20.06 | | |
% 136.03/20.06 | | | (20) all_57_9 = e3 & op(e3, e0) = e3
% 136.03/20.06 | | |
% 136.03/20.06 | | | ALPHA: (20) implies:
% 136.03/20.06 | | | (21) all_57_9 = e3
% 136.03/20.06 | | |
% 136.03/20.06 | | | COMBINE_EQS: (8), (21) imply:
% 136.03/20.06 | | | (22) e3 = e2
% 136.03/20.06 | | |
% 136.03/20.06 | | | SIMP: (22) implies:
% 136.03/20.06 | | | (23) e3 = e2
% 136.03/20.06 | | |
% 136.03/20.06 | | | REDUCE: (7), (23) imply:
% 136.03/20.06 | | | (24) $false
% 136.03/20.06 | | |
% 136.03/20.06 | | | CLOSE: (24) is inconsistent.
% 136.03/20.06 | | |
% 136.03/20.06 | | End of split
% 136.03/20.06 | |
% 136.03/20.06 | End of split
% 136.03/20.06 |
% 136.03/20.06 End of proof
% 136.03/20.06
% 136.03/20.06 Sub-proof #164 shows that the following formulas are inconsistent:
% 136.03/20.06 ----------------------------------------------------------------
% 136.03/20.06 (1) ~ (e2 = e0)
% 136.03/20.06 (2) op(e3, e3) = e1
% 136.03/20.06 (3) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 136.03/20.06 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 136.03/20.06 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.06 (5) ~ (e2 = e1)
% 136.03/20.06 (6) ~ (e3 = e0)
% 136.03/20.06 (7) ~ (e3 = e2)
% 136.03/20.06 (8) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3)
% 136.03/20.06 (9) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 136.03/20.06 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 136.03/20.06 (10) all_57_4 = e1
% 136.03/20.06 (11) ~ (e3 = e1)
% 136.03/20.06 (12) ~ (e1 = e0)
% 136.03/20.06 (13) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 136.03/20.06 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 136.03/20.06
% 136.03/20.06 Begin of proof
% 136.03/20.06 |
% 136.03/20.06 | BETA: splitting (8) gives:
% 136.03/20.06 |
% 136.03/20.06 | Case 1:
% 136.03/20.06 | |
% 136.03/20.06 | | (14) all_57_0 = e3 & op(e3, e3) = e3
% 136.03/20.06 | |
% 136.03/20.06 | | ALPHA: (14) implies:
% 136.03/20.06 | | (15) op(e3, e3) = e3
% 136.03/20.06 | |
% 136.03/20.06 | | REF_CLOSE: (2), (4), (11), (15) are inconsistent by sub-proof #775.
% 136.03/20.06 | |
% 136.03/20.06 | Case 2:
% 136.03/20.06 | |
% 136.03/20.06 | | (16) all_57_1 = e3 & op(e3, e2) = e3
% 136.03/20.06 | |
% 136.03/20.06 | | ALPHA: (16) implies:
% 136.03/20.06 | | (17) all_57_1 = e3
% 136.03/20.06 | |
% 136.03/20.06 | | BETA: splitting (3) gives:
% 136.03/20.06 | |
% 136.03/20.06 | | Case 1:
% 136.03/20.06 | | |
% 136.03/20.06 | | | (18) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 136.03/20.06 | | | e0)
% 136.03/20.06 | | |
% 136.03/20.06 | | | REF_CLOSE: (2), (4), (6), (12), (17), (18) are inconsistent by sub-proof
% 136.03/20.06 | | | #648.
% 136.03/20.06 | | |
% 136.03/20.06 | | Case 2:
% 136.03/20.06 | | |
% 136.03/20.06 | | | (19) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 136.03/20.06 | | | e0)
% 136.03/20.06 | | |
% 136.03/20.06 | | | BETA: splitting (19) gives:
% 136.03/20.06 | | |
% 136.03/20.06 | | | Case 1:
% 136.03/20.06 | | | |
% 136.03/20.06 | | | | (20) all_57_4 = e0 & op(e3, e1) = e0
% 136.03/20.06 | | | |
% 136.03/20.06 | | | | REF_CLOSE: (10), (12), (20) are inconsistent by sub-proof #672.
% 136.03/20.06 | | | |
% 136.03/20.06 | | | Case 2:
% 136.03/20.06 | | | |
% 136.03/20.06 | | | | (21) all_57_9 = e0 & op(e3, e0) = e0
% 136.03/20.06 | | | |
% 136.03/20.06 | | | | ALPHA: (21) implies:
% 136.03/20.06 | | | | (22) all_57_9 = e0
% 136.03/20.06 | | | |
% 136.03/20.06 | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11), (13), (22) are
% 136.03/20.06 | | | | inconsistent by sub-proof #668.
% 136.03/20.06 | | | |
% 136.03/20.06 | | | End of split
% 136.03/20.06 | | |
% 136.03/20.06 | | End of split
% 136.03/20.06 | |
% 136.03/20.06 | End of split
% 136.03/20.06 |
% 136.03/20.06 End of proof
% 136.03/20.06
% 136.03/20.06 Sub-proof #165 shows that the following formulas are inconsistent:
% 136.03/20.06 ----------------------------------------------------------------
% 136.03/20.06 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.06 (2) op(e1, e2) = all_56_13
% 136.03/20.06 (3) op(e1, e2) = e2
% 136.03/20.06 (4) ~ (all_56_13 = e2)
% 136.03/20.06
% 136.03/20.06 Begin of proof
% 136.03/20.06 |
% 136.03/20.06 | GROUND_INST: instantiating (1) with e2, all_56_13, e2, e1, simplifying with
% 136.03/20.06 | (2), (3) gives:
% 136.03/20.06 | (5) all_56_13 = e2
% 136.03/20.06 |
% 136.03/20.06 | REDUCE: (4), (5) imply:
% 136.03/20.06 | (6) $false
% 136.03/20.06 |
% 136.03/20.06 | CLOSE: (6) is inconsistent.
% 136.03/20.06 |
% 136.03/20.06 End of proof
% 136.03/20.06
% 136.03/20.06 Sub-proof #166 shows that the following formulas are inconsistent:
% 136.03/20.06 ----------------------------------------------------------------
% 136.03/20.06 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.06 (2) op(e2, e2) = e1
% 136.03/20.06 (3) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 136.03/20.06 (4) ~ (all_52_1 = e3)
% 136.03/20.06 (5) op(e2, e3) = all_52_1
% 136.03/20.06 (6) ~ (e3 = e1)
% 136.03/20.06
% 136.03/20.06 Begin of proof
% 136.03/20.06 |
% 136.03/20.06 | BETA: splitting (3) gives:
% 136.03/20.06 |
% 136.03/20.06 | Case 1:
% 136.03/20.06 | |
% 136.03/20.06 | | (7) all_57_2 = e3 & op(e2, e3) = e3
% 136.03/20.06 | |
% 136.03/20.06 | | ALPHA: (7) implies:
% 136.03/20.06 | | (8) op(e2, e3) = e3
% 136.03/20.06 | |
% 136.03/20.06 | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #763.
% 136.03/20.06 | |
% 136.03/20.06 | Case 2:
% 136.03/20.06 | |
% 136.03/20.06 | | (9) all_57_3 = e3 & op(e2, e2) = e3
% 136.03/20.06 | |
% 136.03/20.06 | | ALPHA: (9) implies:
% 136.03/20.06 | | (10) op(e2, e2) = e3
% 136.03/20.06 | |
% 136.03/20.06 | | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #325.
% 136.03/20.06 | |
% 136.03/20.06 | End of split
% 136.03/20.06 |
% 136.03/20.06 End of proof
% 136.03/20.06
% 136.03/20.06 Sub-proof #167 shows that the following formulas are inconsistent:
% 136.03/20.06 ----------------------------------------------------------------
% 136.03/20.06 (1) all_57_11 = e3
% 136.03/20.06 (2) all_57_11 = e1
% 136.03/20.06 (3) ~ (e3 = e1)
% 136.03/20.06
% 136.03/20.06 Begin of proof
% 136.03/20.06 |
% 136.03/20.06 | COMBINE_EQS: (1), (2) imply:
% 136.03/20.06 | (4) e3 = e1
% 136.03/20.06 |
% 136.03/20.06 | SIMP: (4) implies:
% 136.03/20.06 | (5) e3 = e1
% 136.03/20.06 |
% 136.03/20.06 | REDUCE: (3), (5) imply:
% 136.03/20.06 | (6) $false
% 136.03/20.06 |
% 136.03/20.06 | CLOSE: (6) is inconsistent.
% 136.03/20.06 |
% 136.03/20.06 End of proof
% 136.03/20.06
% 136.03/20.06 Sub-proof #168 shows that the following formulas are inconsistent:
% 136.03/20.06 ----------------------------------------------------------------
% 136.03/20.06 (1) all_54_9 = e1 | all_54_9 = e0
% 136.03/20.06 (2) all_54_9 = all_52_6
% 136.03/20.06 (3) ~ (all_52_6 = e1)
% 136.03/20.06 (4) ~ (all_52_6 = e0)
% 136.03/20.06
% 136.03/20.06 Begin of proof
% 136.03/20.06 |
% 136.03/20.06 | BETA: splitting (1) gives:
% 136.03/20.06 |
% 136.03/20.06 | Case 1:
% 136.03/20.06 | |
% 136.03/20.06 | | (5) all_54_9 = e1
% 136.03/20.06 | |
% 136.03/20.06 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #169.
% 136.03/20.06 | |
% 136.03/20.06 | Case 2:
% 136.03/20.06 | |
% 136.03/20.06 | | (6) all_54_9 = e0
% 136.03/20.06 | |
% 136.03/20.06 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #568.
% 136.03/20.06 | |
% 136.03/20.06 | End of split
% 136.03/20.06 |
% 136.03/20.06 End of proof
% 136.03/20.06
% 136.03/20.06 Sub-proof #169 shows that the following formulas are inconsistent:
% 136.03/20.06 ----------------------------------------------------------------
% 136.03/20.06 (1) all_54_9 = all_52_6
% 136.03/20.06 (2) all_54_9 = e1
% 136.03/20.06 (3) ~ (all_52_6 = e1)
% 136.03/20.06
% 136.03/20.06 Begin of proof
% 136.03/20.06 |
% 136.03/20.06 | COMBINE_EQS: (1), (2) imply:
% 136.03/20.06 | (4) all_52_6 = e1
% 136.03/20.06 |
% 136.03/20.06 | SIMP: (4) implies:
% 136.03/20.06 | (5) all_52_6 = e1
% 136.03/20.06 |
% 136.03/20.06 | REDUCE: (3), (5) imply:
% 136.03/20.06 | (6) $false
% 136.03/20.06 |
% 136.03/20.06 | CLOSE: (6) is inconsistent.
% 136.03/20.06 |
% 136.03/20.06 End of proof
% 136.03/20.06
% 136.03/20.06 Sub-proof #170 shows that the following formulas are inconsistent:
% 136.03/20.06 ----------------------------------------------------------------
% 136.03/20.06 (1) ~ (e2 = e0)
% 136.03/20.06 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.06 (3) ~ (all_52_6 = e0)
% 136.03/20.06 (4) op(e1, e2) = all_52_6
% 136.03/20.06 (5) all_57_13 = e2
% 136.03/20.06 (6) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 136.03/20.06
% 136.03/20.06 Begin of proof
% 136.03/20.06 |
% 136.03/20.06 | BETA: splitting (6) gives:
% 136.03/20.06 |
% 136.03/20.06 | Case 1:
% 136.03/20.06 | |
% 136.03/20.06 | | (7) all_57_7 = e0 & op(e1, e2) = e0
% 136.03/20.06 | |
% 136.03/20.06 | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #505.
% 136.03/20.06 | |
% 136.03/20.06 | Case 2:
% 136.03/20.06 | |
% 136.03/20.06 | | (8) all_57_13 = e0 & op(e0, e2) = e0
% 136.03/20.06 | |
% 136.03/20.06 | | ALPHA: (8) implies:
% 136.03/20.06 | | (9) all_57_13 = e0
% 136.03/20.06 | |
% 136.03/20.06 | | REF_CLOSE: (1), (5), (9) are inconsistent by sub-proof #404.
% 136.03/20.06 | |
% 136.03/20.06 | End of split
% 136.03/20.06 |
% 136.03/20.06 End of proof
% 136.03/20.06
% 136.03/20.06 Sub-proof #171 shows that the following formulas are inconsistent:
% 136.03/20.06 ----------------------------------------------------------------
% 136.03/20.06 (1) op(e1, e1) = all_6_2
% 136.03/20.06 (2) all_57_7 = e3 & op(e1, e2) = e3
% 136.03/20.06 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.06 (4) ~ (e2 = e1)
% 136.03/20.06 (5) ~ (e3 = e2)
% 136.03/20.06 (6) op(e1, e0) = e1
% 136.03/20.06 (7) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 136.03/20.06 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 136.03/20.06 (8) ~ (all_6_2 = e2)
% 136.03/20.06 (9) op(e1, e3) = all_50_0
% 136.03/20.06 (10) ~ (all_50_0 = e2)
% 136.03/20.06
% 136.03/20.06 Begin of proof
% 136.03/20.06 |
% 136.03/20.06 | ALPHA: (2) implies:
% 136.03/20.06 | (11) all_57_7 = e3
% 136.03/20.06 |
% 136.03/20.06 | BETA: splitting (7) gives:
% 136.03/20.06 |
% 136.03/20.06 | Case 1:
% 136.03/20.06 | |
% 136.03/20.06 | | (12) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) =
% 136.03/20.06 | | e2)
% 136.03/20.06 | |
% 136.03/20.06 | | BETA: splitting (12) gives:
% 136.03/20.06 | |
% 136.03/20.06 | | Case 1:
% 136.03/20.06 | | |
% 136.03/20.06 | | | (13) all_57_6 = e2 & op(e1, e3) = e2
% 136.03/20.06 | | |
% 136.03/20.06 | | | ALPHA: (13) implies:
% 136.03/20.06 | | | (14) op(e1, e3) = e2
% 136.03/20.06 | | |
% 136.03/20.06 | | | REF_CLOSE: (3), (9), (10), (14) are inconsistent by sub-proof #735.
% 136.03/20.06 | | |
% 136.03/20.06 | | Case 2:
% 136.03/20.06 | | |
% 136.03/20.06 | | | (15) all_57_7 = e2 & op(e1, e2) = e2
% 136.03/20.06 | | |
% 136.03/20.06 | | | REF_CLOSE: (5), (11), (15) are inconsistent by sub-proof #385.
% 136.03/20.06 | | |
% 136.03/20.06 | | End of split
% 136.03/20.06 | |
% 136.03/20.06 | Case 2:
% 136.03/20.06 | |
% 136.03/20.06 | | (16) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) =
% 136.03/20.06 | | e2)
% 136.03/20.06 | |
% 136.03/20.06 | | REF_CLOSE: (1), (3), (4), (6), (8), (16) are inconsistent by sub-proof #172.
% 136.03/20.06 | |
% 136.03/20.06 | End of split
% 136.03/20.06 |
% 136.03/20.06 End of proof
% 136.03/20.06
% 136.03/20.06 Sub-proof #172 shows that the following formulas are inconsistent:
% 136.03/20.06 ----------------------------------------------------------------
% 136.03/20.06 (1) op(e1, e1) = all_6_2
% 136.03/20.06 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.06 (3) ~ (e2 = e1)
% 136.03/20.06 (4) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 136.03/20.06 (5) op(e1, e0) = e1
% 136.03/20.06 (6) ~ (all_6_2 = e2)
% 136.03/20.06
% 136.03/20.06 Begin of proof
% 136.03/20.06 |
% 136.03/20.06 | BETA: splitting (4) gives:
% 136.03/20.06 |
% 136.03/20.06 | Case 1:
% 136.03/20.06 | |
% 136.03/20.06 | | (7) all_57_8 = e2 & op(e1, e1) = e2
% 136.03/20.06 | |
% 136.03/20.06 | | ALPHA: (7) implies:
% 136.03/20.06 | | (8) op(e1, e1) = e2
% 136.03/20.06 | |
% 136.03/20.06 | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #767.
% 136.03/20.06 | |
% 136.03/20.06 | Case 2:
% 136.03/20.06 | |
% 136.03/20.06 | | (9) all_57_11 = e2 & op(e1, e0) = e2
% 136.03/20.06 | |
% 136.03/20.06 | | ALPHA: (9) implies:
% 136.03/20.06 | | (10) op(e1, e0) = e2
% 136.03/20.06 | |
% 136.03/20.06 | | REF_CLOSE: (2), (3), (5), (10) are inconsistent by sub-proof #720.
% 136.03/20.06 | |
% 136.03/20.06 | End of split
% 136.03/20.06 |
% 136.03/20.06 End of proof
% 136.03/20.06
% 136.03/20.06 Sub-proof #173 shows that the following formulas are inconsistent:
% 136.03/20.06 ----------------------------------------------------------------
% 136.03/20.06 (1) ~ (e2 = e0)
% 136.03/20.06 (2) op(e3, e3) = e1
% 136.03/20.06 (3) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 136.03/20.06 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 136.03/20.06 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.06 (5) ~ (e2 = e1)
% 136.03/20.06 (6) ~ (all_56_25 = e0)
% 136.03/20.06 (7) ~ (all_52_3 = e3)
% 136.03/20.06 (8) op(e2, e2) = e1
% 136.03/20.06 (9) op(e3, e3) = all_56_1
% 136.03/20.06 (10) op(e3, e0) = all_56_25
% 136.03/20.06 (11) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 136.03/20.06 (12) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 136.03/20.06 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 136.03/20.06 (13) ( ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 & $i(all_34_0)) | ( ~
% 136.03/20.06 (all_34_1 = e1) & op(e3, e3) = all_34_1 & $i(all_34_1))
% 136.03/20.06 (14) ~ (all_52_4 = e2)
% 136.03/20.06 (15) ~ (all_52_3 = e1)
% 136.03/20.06 (16) op(e3, e2) = all_52_4
% 136.03/20.06 (17) op(e0, e3) = all_52_3
% 136.03/20.06 (18) op(e3, e0) = all_52_12
% 136.03/20.06 (19) op(e3, e2) = all_56_9
% 136.03/20.06 (20) op(e0, e3) = e0
% 136.03/20.06 (21) ~ (e3 = e1)
% 136.03/20.06
% 136.03/20.06 Begin of proof
% 136.03/20.06 |
% 136.03/20.06 | BETA: splitting (11) gives:
% 136.03/20.06 |
% 136.03/20.06 | Case 1:
% 136.03/20.06 | |
% 136.03/20.06 | | (22) all_57_1 = e3 & op(e3, e2) = e3
% 136.03/20.06 | |
% 136.03/20.06 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (12), (13), (14),
% 136.03/20.06 | | (15), (16), (17), (18), (19), (20), (22) are inconsistent by
% 136.03/20.06 | | sub-proof #549.
% 136.03/20.06 | |
% 136.03/20.06 | Case 2:
% 136.03/20.06 | |
% 136.03/20.06 | | (23) all_57_3 = e3 & op(e2, e2) = e3
% 136.03/20.06 | |
% 136.03/20.06 | | ALPHA: (23) implies:
% 136.03/20.06 | | (24) op(e2, e2) = e3
% 136.03/20.06 | |
% 136.03/20.06 | | REF_CLOSE: (4), (8), (21), (24) are inconsistent by sub-proof #325.
% 136.03/20.06 | |
% 136.03/20.06 | End of split
% 136.03/20.06 |
% 136.03/20.06 End of proof
% 136.03/20.06
% 136.03/20.06 Sub-proof #174 shows that the following formulas are inconsistent:
% 136.03/20.06 ----------------------------------------------------------------
% 136.03/20.06 (1) op(e3, e3) = e1
% 136.03/20.06 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.06 (3) ~ (e2 = e1)
% 136.03/20.06 (4) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2)
% 136.03/20.06 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3,
% 136.03/20.06 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 136.03/20.06 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 136.03/20.06 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 136.03/20.06 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.03/20.06 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) =
% 136.03/20.06 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.03/20.06 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 136.03/20.06 $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~
% 136.03/20.06 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 136.03/20.06 (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) =
% 136.03/20.06 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 136.03/20.06 = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 136.03/20.06 $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) &
% 136.03/20.06 ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3,
% 136.03/20.06 e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 136.03/20.06 op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 136.03/20.06 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25))
% 136.03/20.06 (5) op(e2, e2) = e1
% 136.03/20.06 (6) ~ (e3 = e1)
% 136.03/20.06 (7) ~ (e1 = e0)
% 136.03/20.06 (8) op(e1, e3) = e3
% 136.03/20.06
% 136.03/20.06 Begin of proof
% 136.03/20.06 |
% 136.03/20.06 | BETA: splitting (4) gives:
% 136.03/20.06 |
% 136.03/20.06 | Case 1:
% 136.03/20.06 | |
% 136.03/20.06 | | (9) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 136.03/20.06 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2
% 136.03/20.06 | | & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11
% 136.03/20.06 | | & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 136.03/20.06 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 136.03/20.06 | | all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.03/20.06 | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 136.03/20.06 | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 136.03/20.06 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 136.03/20.06 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 136.03/20.06 | |
% 136.03/20.06 | | BETA: splitting (9) gives:
% 136.03/20.06 | |
% 136.03/20.06 | | Case 1:
% 136.03/20.06 | | |
% 136.03/20.06 | | | (10) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11
% 136.03/20.06 | | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) =
% 136.03/20.06 | | | e2 & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 136.03/20.06 | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 136.03/20.06 | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)
% 136.03/20.06 | | |
% 136.03/20.06 | | | ALPHA: (10) implies:
% 136.03/20.06 | | | (11) op(e3, e3) = e2
% 136.03/20.06 | | |
% 136.03/20.06 | | | REF_CLOSE: (1), (2), (3), (11) are inconsistent by sub-proof #743.
% 136.03/20.06 | | |
% 136.03/20.06 | | Case 2:
% 136.03/20.06 | | |
% 136.03/20.06 | | | (12) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~
% 136.03/20.06 | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 136.03/20.06 | | | op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 136.03/20.06 | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 136.03/20.06 | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.03/20.06 | | | $i(all_56_29)
% 136.03/20.06 | | |
% 136.03/20.06 | | | ALPHA: (12) implies:
% 136.03/20.06 | | | (13) ~ (all_56_5 = e3)
% 136.03/20.06 | | | (14) op(e1, e3) = all_56_5
% 136.03/20.06 | | |
% 136.03/20.06 | | | REF_CLOSE: (2), (8), (13), (14) are inconsistent by sub-proof #724.
% 136.03/20.06 | | |
% 136.03/20.06 | | End of split
% 136.03/20.06 | |
% 136.03/20.06 | Case 2:
% 136.03/20.06 | |
% 136.03/20.06 | | (15) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15
% 136.03/20.06 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) =
% 136.03/20.06 | | e0 & op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 136.03/20.06 | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 &
% 136.03/20.06 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 136.03/20.06 | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 136.03/20.06 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.03/20.06 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.03/20.06 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 136.03/20.06 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25))
% 136.03/20.06 | |
% 136.03/20.06 | | REF_CLOSE: (1), (2), (5), (6), (7), (15) are inconsistent by sub-proof #175.
% 136.03/20.06 | |
% 136.03/20.06 | End of split
% 136.03/20.06 |
% 136.03/20.06 End of proof
% 136.03/20.06
% 136.03/20.06 Sub-proof #175 shows that the following formulas are inconsistent:
% 136.03/20.06 ----------------------------------------------------------------
% 136.03/20.06 (1) op(e3, e3) = e1
% 136.03/20.06 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.06 (3) op(e2, e2) = e1
% 136.03/20.06 (4) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.03/20.06 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 136.03/20.06 op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.03/20.06 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.03/20.06 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 &
% 136.03/20.06 all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~
% 136.03/20.06 (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3,
% 136.03/20.06 e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 136.03/20.06 op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 136.03/20.06 $i(all_56_17) & $i(all_56_25))
% 136.03/20.06 (5) ~ (e3 = e1)
% 136.03/20.06 (6) ~ (e1 = e0)
% 136.03/20.06
% 136.03/20.06 Begin of proof
% 136.03/20.06 |
% 136.03/20.06 | BETA: splitting (4) gives:
% 136.03/20.06 |
% 136.03/20.06 | Case 1:
% 136.03/20.06 | |
% 136.03/20.06 | | (7) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.03/20.06 | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 136.03/20.06 | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.03/20.06 | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.03/20.06 | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)
% 136.03/20.06 | |
% 136.03/20.06 | | ALPHA: (7) implies:
% 136.03/20.06 | | (8) op(e3, e3) = e0
% 136.03/20.06 | |
% 136.03/20.06 | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #717.
% 136.03/20.06 | |
% 136.03/20.06 | Case 2:
% 136.03/20.06 | |
% 136.03/20.06 | | (9) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.03/20.06 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.03/20.06 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.03/20.06 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1)
% 136.03/20.06 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)
% 136.03/20.06 | |
% 136.03/20.06 | | ALPHA: (9) implies:
% 136.03/20.06 | | (10) op(e2, e2) = e3
% 136.03/20.06 | |
% 136.03/20.06 | | REF_CLOSE: (2), (3), (5), (10) are inconsistent by sub-proof #325.
% 136.03/20.06 | |
% 136.03/20.06 | End of split
% 136.03/20.06 |
% 136.03/20.06 End of proof
% 136.03/20.06
% 136.03/20.06 Sub-proof #176 shows that the following formulas are inconsistent:
% 136.03/20.06 ----------------------------------------------------------------
% 136.03/20.06 (1) all_54_9 = all_48_0
% 136.03/20.06 (2) all_54_9 = e3
% 136.03/20.06 (3) ~ (all_48_0 = e3)
% 136.03/20.06
% 136.03/20.06 Begin of proof
% 136.03/20.06 |
% 136.03/20.06 | COMBINE_EQS: (1), (2) imply:
% 136.03/20.06 | (4) all_48_0 = e3
% 136.03/20.06 |
% 136.03/20.06 | SIMP: (4) implies:
% 136.03/20.06 | (5) all_48_0 = e3
% 136.03/20.06 |
% 136.03/20.06 | REDUCE: (3), (5) imply:
% 136.03/20.06 | (6) $false
% 136.03/20.06 |
% 136.03/20.06 | CLOSE: (6) is inconsistent.
% 136.03/20.06 |
% 136.03/20.06 End of proof
% 136.03/20.06
% 136.03/20.06 Sub-proof #177 shows that the following formulas are inconsistent:
% 136.03/20.06 ----------------------------------------------------------------
% 136.03/20.06 (1) ~ (e2 = e0)
% 136.03/20.06 (2) op(e3, e3) = e1
% 136.03/20.06 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.06 (4) ~ (e2 = e1)
% 136.03/20.06 (5) ~ (e3 = e0)
% 136.03/20.06 (6) ~ (e3 = e2)
% 136.03/20.06 (7) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 136.03/20.06 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 136.03/20.06 (8) op(e0, e2) = all_52_7
% 136.03/20.06 (9) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 136.03/20.06 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 136.03/20.06 (10) ~ (all_52_7 = e1)
% 136.03/20.06 (11) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 136.03/20.06 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 136.03/20.06 (12) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 136.03/20.06 (13) ~ (e3 = e1)
% 136.03/20.06 (14) ~ (e1 = e0)
% 136.03/20.06
% 136.03/20.06 Begin of proof
% 136.03/20.06 |
% 136.03/20.06 | BETA: splitting (12) gives:
% 136.03/20.06 |
% 136.03/20.06 | Case 1:
% 136.03/20.06 | |
% 136.03/20.06 | | (15) all_57_12 = e1 & op(e0, e3) = e1
% 136.03/20.06 | |
% 136.03/20.06 | | ALPHA: (15) implies:
% 136.03/20.06 | | (16) all_57_12 = e1
% 136.03/20.06 | |
% 136.03/20.06 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (11), (13), (14), (16)
% 136.03/20.06 | | are inconsistent by sub-proof #583.
% 136.03/20.06 | |
% 136.03/20.06 | Case 2:
% 136.03/20.06 | |
% 136.03/20.06 | | (17) all_57_13 = e1 & op(e0, e2) = e1
% 136.03/20.06 | |
% 136.03/20.06 | | REF_CLOSE: (3), (8), (10), (17) are inconsistent by sub-proof #178.
% 136.03/20.06 | |
% 136.03/20.06 | End of split
% 136.03/20.06 |
% 136.03/20.06 End of proof
% 136.03/20.06
% 136.03/20.06 Sub-proof #178 shows that the following formulas are inconsistent:
% 136.03/20.06 ----------------------------------------------------------------
% 136.03/20.06 (1) all_57_13 = e1 & op(e0, e2) = e1
% 136.03/20.06 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.06 (3) op(e0, e2) = all_52_7
% 136.03/20.06 (4) ~ (all_52_7 = e1)
% 136.03/20.06
% 136.03/20.06 Begin of proof
% 136.03/20.06 |
% 136.03/20.06 | ALPHA: (1) implies:
% 136.03/20.06 | (5) op(e0, e2) = e1
% 136.03/20.06 |
% 136.03/20.06 | GROUND_INST: instantiating (2) with all_52_7, e1, e2, e0, simplifying with
% 136.03/20.06 | (3), (5) gives:
% 136.03/20.06 | (6) all_52_7 = e1
% 136.03/20.06 |
% 136.03/20.06 | REDUCE: (4), (6) imply:
% 136.03/20.06 | (7) $false
% 136.03/20.06 |
% 136.03/20.06 | CLOSE: (7) is inconsistent.
% 136.03/20.06 |
% 136.03/20.06 End of proof
% 136.03/20.06
% 136.03/20.06 Sub-proof #179 shows that the following formulas are inconsistent:
% 136.03/20.06 ----------------------------------------------------------------
% 136.03/20.06 (1) ~ (all_52_12 = e1)
% 136.03/20.06 (2) op(e2, e0) = all_52_13
% 136.03/20.06 (3) ~ (all_52_13 = e1)
% 136.03/20.06 (4) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 136.03/20.06 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.06 (6) op(e3, e0) = all_52_12
% 136.03/20.06
% 136.03/20.06 Begin of proof
% 136.03/20.06 |
% 136.03/20.06 | BETA: splitting (4) gives:
% 136.03/20.06 |
% 136.03/20.06 | Case 1:
% 136.03/20.06 | |
% 136.03/20.06 | | (7) all_57_9 = e1 & op(e3, e0) = e1
% 136.03/20.06 | |
% 136.03/20.06 | | REF_CLOSE: (1), (5), (6), (7) are inconsistent by sub-proof #181.
% 136.03/20.06 | |
% 136.03/20.06 | Case 2:
% 136.03/20.06 | |
% 136.03/20.06 | | (8) all_57_10 = e1 & op(e2, e0) = e1
% 136.03/20.06 | |
% 136.03/20.06 | | ALPHA: (8) implies:
% 136.03/20.06 | | (9) op(e2, e0) = e1
% 136.03/20.06 | |
% 136.03/20.06 | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #180.
% 136.03/20.06 | |
% 136.03/20.06 | End of split
% 136.03/20.06 |
% 136.03/20.06 End of proof
% 136.03/20.06
% 136.03/20.06 Sub-proof #180 shows that the following formulas are inconsistent:
% 136.03/20.06 ----------------------------------------------------------------
% 136.03/20.06 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.06 (2) op(e2, e0) = all_52_13
% 136.03/20.06 (3) op(e2, e0) = e1
% 136.03/20.06 (4) ~ (all_52_13 = e1)
% 136.03/20.06
% 136.03/20.06 Begin of proof
% 136.03/20.06 |
% 136.03/20.06 | GROUND_INST: instantiating (1) with all_52_13, e1, e0, e2, simplifying with
% 136.03/20.06 | (2), (3) gives:
% 136.03/20.06 | (5) all_52_13 = e1
% 136.03/20.06 |
% 136.03/20.06 | REDUCE: (4), (5) imply:
% 136.03/20.06 | (6) $false
% 136.03/20.06 |
% 136.03/20.06 | CLOSE: (6) is inconsistent.
% 136.03/20.06 |
% 136.03/20.06 End of proof
% 136.03/20.06
% 136.03/20.06 Sub-proof #181 shows that the following formulas are inconsistent:
% 136.03/20.06 ----------------------------------------------------------------
% 136.03/20.06 (1) all_57_9 = e1 & op(e3, e0) = e1
% 136.03/20.06 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.06 (3) op(e3, e0) = all_52_12
% 136.03/20.07 (4) ~ (all_52_12 = e1)
% 136.03/20.07
% 136.03/20.07 Begin of proof
% 136.03/20.07 |
% 136.03/20.07 | ALPHA: (1) implies:
% 136.03/20.07 | (5) op(e3, e0) = e1
% 136.03/20.07 |
% 136.03/20.07 | GROUND_INST: instantiating (2) with all_52_12, e1, e0, e3, simplifying with
% 136.03/20.07 | (3), (5) gives:
% 136.03/20.07 | (6) all_52_12 = e1
% 136.03/20.07 |
% 136.03/20.07 | REDUCE: (4), (6) imply:
% 136.03/20.07 | (7) $false
% 136.03/20.07 |
% 136.03/20.07 | CLOSE: (7) is inconsistent.
% 136.03/20.07 |
% 136.03/20.07 End of proof
% 136.03/20.07
% 136.03/20.07 Sub-proof #182 shows that the following formulas are inconsistent:
% 136.03/20.07 ----------------------------------------------------------------
% 136.03/20.07 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.07 (2) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.03/20.07 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 136.03/20.07 op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.03/20.07 op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 136.03/20.07 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 136.03/20.07 e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 136.03/20.07 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 136.03/20.07 = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 136.03/20.07 $i(all_56_21) & $i(all_56_29))
% 136.03/20.07 (3) op(e1, e1) = e1
% 136.03/20.07 (4) ~ (all_52_14 = e1)
% 136.03/20.07 (5) op(e1, e0) = all_52_14
% 136.03/20.07
% 136.03/20.07 Begin of proof
% 136.03/20.07 |
% 136.03/20.07 | BETA: splitting (2) gives:
% 136.03/20.07 |
% 136.03/20.07 | Case 1:
% 136.03/20.07 | |
% 136.03/20.07 | | (6) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15
% 136.03/20.07 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0
% 136.03/20.07 | | & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.03/20.07 | | op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)
% 136.03/20.07 | |
% 136.03/20.07 | | ALPHA: (6) implies:
% 136.03/20.07 | | (7) op(e1, e0) = e1
% 136.03/20.07 | |
% 136.03/20.07 | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #327.
% 136.03/20.07 | |
% 136.03/20.07 | Case 2:
% 136.03/20.07 | |
% 136.03/20.07 | | (8) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13
% 136.03/20.07 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 136.03/20.07 | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1,
% 136.03/20.07 | | e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 136.03/20.07 | | $i(all_56_21) & $i(all_56_29)
% 136.03/20.07 | |
% 136.03/20.07 | | ALPHA: (8) implies:
% 136.03/20.07 | | (9) ~ (all_56_21 = e1)
% 136.03/20.07 | | (10) op(e1, e1) = all_56_21
% 136.03/20.07 | |
% 136.03/20.07 | | REF_CLOSE: (1), (3), (9), (10) are inconsistent by sub-proof #510.
% 136.03/20.07 | |
% 136.03/20.07 | End of split
% 136.03/20.07 |
% 136.03/20.07 End of proof
% 136.03/20.07
% 136.03/20.07 Sub-proof #183 shows that the following formulas are inconsistent:
% 136.03/20.07 ----------------------------------------------------------------
% 136.03/20.07 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.07 (2) op(e2, e2) = e1
% 136.03/20.07 (3) ~ (all_52_4 = e3)
% 136.03/20.07 (4) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 136.03/20.07 (5) op(e3, e2) = all_52_4
% 136.03/20.07 (6) ~ (e3 = e1)
% 136.03/20.07
% 136.03/20.07 Begin of proof
% 136.03/20.07 |
% 136.03/20.07 | BETA: splitting (4) gives:
% 136.03/20.07 |
% 136.03/20.07 | Case 1:
% 136.03/20.07 | |
% 136.03/20.07 | | (7) all_57_1 = e3 & op(e3, e2) = e3
% 136.03/20.07 | |
% 136.03/20.07 | | ALPHA: (7) implies:
% 136.03/20.07 | | (8) op(e3, e2) = e3
% 136.03/20.07 | |
% 136.03/20.07 | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #738.
% 136.03/20.07 | |
% 136.03/20.07 | Case 2:
% 136.03/20.07 | |
% 136.03/20.07 | | (9) all_57_3 = e3 & op(e2, e2) = e3
% 136.03/20.07 | |
% 136.03/20.07 | | ALPHA: (9) implies:
% 136.03/20.07 | | (10) op(e2, e2) = e3
% 136.03/20.07 | |
% 136.03/20.07 | | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #325.
% 136.03/20.07 | |
% 136.03/20.07 | End of split
% 136.03/20.07 |
% 136.03/20.07 End of proof
% 136.03/20.07
% 136.03/20.07 Sub-proof #184 shows that the following formulas are inconsistent:
% 136.03/20.07 ----------------------------------------------------------------
% 136.03/20.07 (1) op(e0, e0) = e0
% 136.03/20.07 (2) op(e1, e1) = all_6_2
% 136.03/20.07 (3) ~ (e2 = e0)
% 136.03/20.07 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.07 (5) ~ (e3 = e0)
% 136.03/20.07 (6) op(e2, e2) = e1
% 136.03/20.07 (7) ~ (all_6_2 = e2)
% 136.03/20.07 (8) ~ (e1 = e0)
% 136.03/20.07 (9) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.03/20.07 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 136.03/20.07 op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.03/20.07 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.03/20.07 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 &
% 136.03/20.07 all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~
% 136.03/20.07 (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2,
% 136.03/20.07 e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 136.03/20.07 op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 136.03/20.07 $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = all_56_31 &
% 136.03/20.07 $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) &
% 136.03/20.07 ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 136.03/20.07 op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) =
% 136.03/20.07 all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1)
% 136.03/20.07 & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 &
% 136.03/20.07 all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~
% 136.03/20.07 (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 136.03/20.07 op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 136.03/20.07 all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 136.03/20.07 $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 &
% 136.03/20.07 ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 136.03/20.07 (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 136.03/20.07 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 136.03/20.07 $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 &
% 136.03/20.07 all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.03/20.07 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 136.03/20.07 op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 136.03/20.07 all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 136.03/20.07 $i(all_56_21) & $i(all_56_29))))
% 136.03/20.07
% 136.03/20.07 Begin of proof
% 136.03/20.07 |
% 136.03/20.07 | BETA: splitting (9) gives:
% 136.03/20.07 |
% 136.03/20.07 | Case 1:
% 136.03/20.07 | |
% 136.03/20.07 | | (10) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ (all_56_15
% 136.03/20.07 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e2, e2) =
% 136.03/20.07 | | e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 136.03/20.07 | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 &
% 136.03/20.07 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31)
% 136.03/20.07 | |
% 136.03/20.07 | | ALPHA: (10) implies:
% 136.03/20.07 | | (11) op(e2, e2) = e0
% 136.03/20.07 | |
% 136.03/20.07 | | REF_CLOSE: (4), (6), (8), (11) are inconsistent by sub-proof #675.
% 136.03/20.07 | |
% 136.03/20.07 | Case 2:
% 136.03/20.07 | |
% 136.03/20.07 | | (12) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 136.03/20.07 | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.03/20.07 | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.03/20.07 | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1)
% 136.03/20.07 | | = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 136.03/20.07 | | $i(all_56_27)) | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 136.03/20.07 | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 136.03/20.07 | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 136.03/20.07 | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) =
% 136.03/20.07 | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 136.03/20.07 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.03/20.07 | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 136.03/20.07 | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.03/20.07 | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.03/20.07 | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.03/20.07 | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27))
% 136.03/20.07 | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.03/20.07 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.03/20.07 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 136.03/20.07 | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7)
% 136.03/20.07 | | & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 136.03/20.07 | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.03/20.07 | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5
% 136.03/20.07 | | & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 136.03/20.07 | | = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 136.03/20.07 | | $i(all_56_21) & $i(all_56_29))))
% 136.03/20.07 | |
% 136.03/20.07 | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (12) are inconsistent by
% 136.03/20.07 | | sub-proof #709.
% 136.03/20.07 | |
% 136.03/20.07 | End of split
% 136.03/20.07 |
% 136.03/20.07 End of proof
% 136.03/20.07
% 136.03/20.07 Sub-proof #185 shows that the following formulas are inconsistent:
% 136.03/20.07 ----------------------------------------------------------------
% 136.03/20.07 (1) op(e1, e0) = all_56_29
% 136.03/20.07 (2) op(e1, e1) = all_6_2
% 136.03/20.07 (3) ~ (all_52_9 = all_6_2)
% 136.03/20.07 (4) ~ (all_52_13 = e0)
% 136.03/20.07 (5) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 136.03/20.07 (6) ~ (all_56_5 = e3)
% 136.03/20.07 (7) ~ (all_52_13 = e1)
% 136.03/20.07 (8) ~ (all_6_2 = e3)
% 136.03/20.07 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.07 (10) op(e2, e1) = e2
% 136.03/20.07 (11) op(e1, e3) = all_56_5
% 136.03/20.07 (12) ~ (all_52_13 = all_52_14)
% 136.03/20.07 (13) all_48_2 = e1
% 136.03/20.07 (14) all_54_10 = all_6_2
% 136.03/20.07 (15) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e3) & op(e1, e2) = all_48_0 &
% 136.03/20.07 $i(all_48_0)) | ( ~ (all_48_1 = e0) & op(e1, e1) = all_48_1 &
% 136.03/20.07 $i(all_48_1))
% 136.03/20.07 (16) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 136.03/20.07 (17) ~ (all_56_21 = e1)
% 136.03/20.07 (18) op(e2, e1) = all_52_9
% 136.03/20.07 (19) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 136.03/20.07 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 136.03/20.07 (20) all_54_7 = all_52_13
% 136.03/20.07 (21) ~ (all_52_9 = all_52_13)
% 136.03/20.07 (22) op(e1, e0) = all_52_14
% 136.03/20.07 (23) op(e1, e1) = all_56_21
% 136.03/20.07
% 136.03/20.07 Begin of proof
% 136.03/20.07 |
% 136.03/20.07 | GROUND_INST: instantiating (9) with all_52_14, all_56_29, e0, e1, simplifying
% 136.03/20.07 | with (1), (22) gives:
% 136.03/20.07 | (24) all_56_29 = all_52_14
% 136.03/20.07 |
% 136.03/20.07 | GROUND_INST: instantiating (9) with all_6_2, all_56_21, e1, e1, simplifying
% 136.03/20.07 | with (2), (23) gives:
% 136.03/20.07 | (25) all_56_21 = all_6_2
% 136.03/20.07 |
% 136.03/20.07 | GROUND_INST: instantiating (9) with all_52_9, e2, e1, e2, simplifying with
% 136.03/20.07 | (10), (18) gives:
% 136.03/20.07 | (26) all_52_9 = e2
% 136.03/20.07 |
% 136.03/20.07 | REDUCE: (17), (25) imply:
% 136.03/20.07 | (27) ~ (all_6_2 = e1)
% 136.03/20.07 |
% 136.03/20.07 | REDUCE: (21), (26) imply:
% 136.03/20.07 | (28) ~ (all_52_13 = e2)
% 136.03/20.07 |
% 136.03/20.07 | SIMP: (28) implies:
% 136.03/20.07 | (29) ~ (all_52_13 = e2)
% 136.03/20.07 |
% 136.03/20.07 | REDUCE: (3), (26) imply:
% 136.03/20.07 | (30) ~ (all_6_2 = e2)
% 136.03/20.07 |
% 136.03/20.07 | SIMP: (30) implies:
% 136.03/20.07 | (31) ~ (all_6_2 = e2)
% 136.03/20.07 |
% 136.03/20.07 | BETA: splitting (16) gives:
% 136.03/20.07 |
% 136.03/20.07 | Case 1:
% 136.03/20.07 | |
% 136.03/20.07 | | (32) all_54_10 = e3
% 136.03/20.07 | |
% 136.03/20.07 | | REF_CLOSE: (8), (14), (32) are inconsistent by sub-proof #742.
% 136.03/20.07 | |
% 136.03/20.07 | Case 2:
% 136.03/20.07 | |
% 136.03/20.07 | | (33) ~ (all_54_10 = e3)
% 136.03/20.07 | | (34) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 136.03/20.07 | |
% 136.03/20.07 | | BETA: splitting (5) gives:
% 136.03/20.07 | |
% 136.03/20.07 | | Case 1:
% 136.03/20.07 | | |
% 136.03/20.07 | | | (35) all_54_7 = e3
% 136.03/20.07 | | |
% 136.03/20.07 | | | COMBINE_EQS: (20), (35) imply:
% 136.03/20.07 | | | (36) all_52_13 = e3
% 136.03/20.07 | | |
% 136.03/20.07 | | | SIMP: (36) implies:
% 136.03/20.07 | | | (37) all_52_13 = e3
% 136.03/20.07 | | |
% 136.03/20.07 | | | REDUCE: (12), (37) imply:
% 136.03/20.07 | | | (38) ~ (all_52_14 = e3)
% 136.03/20.07 | | |
% 136.03/20.07 | | | SIMP: (38) implies:
% 136.03/20.07 | | | (39) ~ (all_52_14 = e3)
% 136.03/20.07 | | |
% 136.03/20.07 | | | BETA: splitting (34) gives:
% 136.03/20.07 | | |
% 136.03/20.07 | | | Case 1:
% 136.03/20.07 | | | |
% 136.03/20.07 | | | | (40) all_54_10 = e2
% 136.03/20.07 | | | |
% 136.03/20.07 | | | | REF_CLOSE: (14), (31), (40) are inconsistent by sub-proof #741.
% 136.03/20.07 | | | |
% 136.03/20.07 | | | Case 2:
% 136.03/20.07 | | | |
% 136.03/20.07 | | | | (41) all_54_10 = e1 | all_54_10 = e0
% 136.03/20.07 | | | |
% 136.03/20.07 | | | | REF_CLOSE: (2), (6), (8), (9), (11), (13), (14), (15), (19), (22), (27),
% 136.03/20.07 | | | | (39), (41) are inconsistent by sub-proof #186.
% 136.03/20.07 | | | |
% 136.03/20.07 | | | End of split
% 136.03/20.07 | | |
% 136.03/20.07 | | Case 2:
% 136.03/20.07 | | |
% 136.03/20.07 | | | (42) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 136.03/20.07 | | |
% 136.03/20.07 | | | BETA: splitting (42) gives:
% 136.03/20.07 | | |
% 136.03/20.07 | | | Case 1:
% 136.03/20.07 | | | |
% 136.03/20.07 | | | | (43) all_54_7 = e2
% 136.03/20.07 | | | |
% 136.03/20.07 | | | | REF_CLOSE: (20), (29), (43) are inconsistent by sub-proof #337.
% 136.03/20.07 | | | |
% 136.03/20.07 | | | Case 2:
% 136.03/20.07 | | | |
% 136.03/20.07 | | | | (44) all_54_7 = e1 | all_54_7 = e0
% 136.03/20.07 | | | |
% 136.03/20.07 | | | | REF_CLOSE: (4), (7), (20), (44) are inconsistent by sub-proof #313.
% 136.03/20.07 | | | |
% 136.03/20.07 | | | End of split
% 136.03/20.07 | | |
% 136.03/20.07 | | End of split
% 136.03/20.07 | |
% 136.03/20.07 | End of split
% 136.03/20.07 |
% 136.03/20.07 End of proof
% 136.03/20.07
% 136.03/20.07 Sub-proof #186 shows that the following formulas are inconsistent:
% 136.03/20.07 ----------------------------------------------------------------
% 136.03/20.07 (1) op(e1, e1) = all_6_2
% 136.03/20.07 (2) ~ (all_52_14 = e3)
% 136.03/20.07 (3) ~ (all_56_5 = e3)
% 136.03/20.07 (4) ~ (all_6_2 = e3)
% 136.03/20.07 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.07 (6) op(e1, e3) = all_56_5
% 136.03/20.07 (7) all_48_2 = e1
% 136.03/20.07 (8) all_54_10 = all_6_2
% 136.03/20.07 (9) ~ (all_6_2 = e1)
% 136.03/20.07 (10) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e3) & op(e1, e2) = all_48_0 &
% 136.03/20.07 $i(all_48_0)) | ( ~ (all_48_1 = e0) & op(e1, e1) = all_48_1 &
% 136.03/20.07 $i(all_48_1))
% 136.03/20.07 (11) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 136.03/20.07 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 136.03/20.07 (12) all_54_10 = e1 | all_54_10 = e0
% 136.03/20.07 (13) op(e1, e0) = all_52_14
% 136.03/20.07
% 136.03/20.07 Begin of proof
% 136.03/20.07 |
% 136.03/20.07 | BETA: splitting (11) gives:
% 136.03/20.07 |
% 136.03/20.07 | Case 1:
% 136.03/20.07 | |
% 136.03/20.07 | | (14) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 136.03/20.07 | | e3)
% 136.03/20.07 | |
% 136.03/20.07 | | BETA: splitting (14) gives:
% 136.03/20.07 | |
% 136.03/20.07 | | Case 1:
% 136.03/20.07 | | |
% 136.03/20.07 | | | (15) all_57_6 = e3 & op(e1, e3) = e3
% 136.03/20.07 | | |
% 136.03/20.07 | | | ALPHA: (15) implies:
% 136.03/20.07 | | | (16) op(e1, e3) = e3
% 136.03/20.07 | | |
% 136.03/20.07 | | | REF_CLOSE: (3), (5), (6), (16) are inconsistent by sub-proof #724.
% 136.03/20.07 | | |
% 136.03/20.07 | | Case 2:
% 136.03/20.07 | | |
% 136.03/20.07 | | | (17) all_57_7 = e3 & op(e1, e2) = e3
% 136.03/20.07 | | |
% 136.03/20.07 | | | ALPHA: (17) implies:
% 136.03/20.07 | | | (18) op(e1, e2) = e3
% 136.03/20.07 | | |
% 136.03/20.07 | | | BETA: splitting (12) gives:
% 136.03/20.07 | | |
% 136.03/20.07 | | | Case 1:
% 136.03/20.07 | | | |
% 136.03/20.07 | | | | (19) all_54_10 = e1
% 136.03/20.07 | | | |
% 136.03/20.07 | | | | REF_CLOSE: (8), (9), (19) are inconsistent by sub-proof #736.
% 136.03/20.07 | | | |
% 136.03/20.07 | | | Case 2:
% 136.03/20.07 | | | |
% 136.03/20.07 | | | | (20) all_54_10 = e0
% 136.03/20.07 | | | |
% 136.03/20.07 | | | | COMBINE_EQS: (8), (20) imply:
% 136.03/20.07 | | | | (21) all_6_2 = e0
% 136.03/20.07 | | | |
% 136.03/20.07 | | | | SIMP: (21) implies:
% 136.03/20.07 | | | | (22) all_6_2 = e0
% 136.03/20.07 | | | |
% 136.03/20.07 | | | | REDUCE: (1), (22) imply:
% 136.03/20.07 | | | | (23) op(e1, e1) = e0
% 136.03/20.07 | | | |
% 136.03/20.07 | | | | BETA: splitting (10) gives:
% 136.03/20.07 | | | |
% 136.03/20.07 | | | | Case 1:
% 136.03/20.07 | | | | |
% 136.03/20.07 | | | | | (24) ~ (all_48_2 = e1)
% 136.03/20.07 | | | | |
% 136.03/20.07 | | | | | REDUCE: (7), (24) imply:
% 136.03/20.07 | | | | | (25) $false
% 136.03/20.07 | | | | |
% 136.03/20.07 | | | | | CLOSE: (25) is inconsistent.
% 136.03/20.07 | | | | |
% 136.03/20.07 | | | | Case 2:
% 136.03/20.07 | | | | |
% 136.03/20.07 | | | | | (26) ( ~ (all_48_0 = e3) & op(e1, e2) = all_48_0 & $i(all_48_0)) |
% 136.03/20.07 | | | | | ( ~ (all_48_1 = e0) & op(e1, e1) = all_48_1 & $i(all_48_1))
% 136.03/20.07 | | | | |
% 136.03/20.07 | | | | | BETA: splitting (26) gives:
% 136.03/20.07 | | | | |
% 136.03/20.07 | | | | | Case 1:
% 136.03/20.07 | | | | | |
% 136.03/20.07 | | | | | | (27) ~ (all_48_0 = e3) & op(e1, e2) = all_48_0 & $i(all_48_0)
% 136.03/20.07 | | | | | |
% 136.03/20.07 | | | | | | ALPHA: (27) implies:
% 136.03/20.07 | | | | | | (28) ~ (all_48_0 = e3)
% 136.03/20.07 | | | | | | (29) op(e1, e2) = all_48_0
% 136.03/20.07 | | | | | |
% 136.03/20.07 | | | | | | REF_CLOSE: (5), (18), (28), (29) are inconsistent by sub-proof #188.
% 136.03/20.07 | | | | | |
% 136.03/20.07 | | | | | Case 2:
% 136.03/20.07 | | | | | |
% 136.03/20.07 | | | | | | (30) ~ (all_48_1 = e0) & op(e1, e1) = all_48_1 & $i(all_48_1)
% 136.03/20.07 | | | | | |
% 136.03/20.07 | | | | | | REF_CLOSE: (5), (23), (30) are inconsistent by sub-proof #187.
% 136.03/20.07 | | | | | |
% 136.03/20.07 | | | | | End of split
% 136.03/20.07 | | | | |
% 136.03/20.07 | | | | End of split
% 136.03/20.07 | | | |
% 136.03/20.07 | | | End of split
% 136.03/20.07 | | |
% 136.03/20.07 | | End of split
% 136.03/20.07 | |
% 136.03/20.07 | Case 2:
% 136.03/20.07 | |
% 136.03/20.07 | | (31) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 136.03/20.07 | | e3)
% 136.03/20.07 | |
% 136.03/20.07 | | REF_CLOSE: (1), (2), (4), (5), (13), (31) are inconsistent by sub-proof
% 136.03/20.07 | | #653.
% 136.03/20.07 | |
% 136.03/20.07 | End of split
% 136.03/20.07 |
% 136.03/20.07 End of proof
% 136.03/20.07
% 136.03/20.07 Sub-proof #187 shows that the following formulas are inconsistent:
% 136.03/20.07 ----------------------------------------------------------------
% 136.03/20.07 (1) ~ (all_48_1 = e0) & op(e1, e1) = all_48_1 & $i(all_48_1)
% 136.03/20.07 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.07 (3) op(e1, e1) = e0
% 136.03/20.07
% 136.03/20.07 Begin of proof
% 136.03/20.07 |
% 136.03/20.07 | ALPHA: (1) implies:
% 136.03/20.07 | (4) ~ (all_48_1 = e0)
% 136.03/20.07 | (5) op(e1, e1) = all_48_1
% 136.03/20.07 |
% 136.03/20.07 | GROUND_INST: instantiating (2) with e0, all_48_1, e1, e1, simplifying with
% 136.03/20.07 | (3), (5) gives:
% 136.03/20.07 | (6) all_48_1 = e0
% 136.03/20.07 |
% 136.03/20.07 | REDUCE: (4), (6) imply:
% 136.03/20.07 | (7) $false
% 136.03/20.07 |
% 136.03/20.07 | CLOSE: (7) is inconsistent.
% 136.03/20.07 |
% 136.03/20.07 End of proof
% 136.03/20.07
% 136.03/20.07 Sub-proof #188 shows that the following formulas are inconsistent:
% 136.03/20.07 ----------------------------------------------------------------
% 136.03/20.07 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.07 (2) op(e1, e2) = all_48_0
% 136.03/20.07 (3) op(e1, e2) = e3
% 136.03/20.07 (4) ~ (all_48_0 = e3)
% 136.03/20.07
% 136.03/20.07 Begin of proof
% 136.03/20.07 |
% 136.03/20.07 | GROUND_INST: instantiating (1) with e3, all_48_0, e2, e1, simplifying with
% 136.03/20.07 | (2), (3) gives:
% 136.03/20.07 | (5) all_48_0 = e3
% 136.03/20.07 |
% 136.03/20.07 | REDUCE: (4), (5) imply:
% 136.03/20.07 | (6) $false
% 136.03/20.07 |
% 136.03/20.07 | CLOSE: (6) is inconsistent.
% 136.03/20.07 |
% 136.03/20.07 End of proof
% 136.03/20.07
% 136.03/20.07 Sub-proof #189 shows that the following formulas are inconsistent:
% 136.03/20.07 ----------------------------------------------------------------
% 136.03/20.07 (1) all_54_0 = all_10_2
% 136.03/20.07 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.07 (3) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2)
% 136.03/20.07 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3,
% 136.03/20.07 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 136.03/20.07 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 136.03/20.07 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 136.03/20.07 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.03/20.07 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) =
% 136.03/20.07 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.03/20.07 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 136.03/20.07 $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~
% 136.03/20.07 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 136.03/20.07 (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) =
% 136.03/20.07 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 136.03/20.07 = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 136.03/20.07 $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) &
% 136.03/20.07 ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3,
% 136.03/20.07 e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 136.03/20.07 op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 136.03/20.07 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25))
% 136.03/20.07 (4) op(e2, e2) = e1
% 136.03/20.07 (5) ~ (all_10_2 = e0)
% 136.03/20.07 (6) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 136.03/20.07 (7) op(e3, e3) = all_10_2
% 136.03/20.07 (8) op(e3, e3) = e3
% 136.03/20.07 (9) op(e3, e0) = all_52_12
% 136.03/20.07 (10) ~ (all_10_2 = e2)
% 136.03/20.07 (11) ~ (e3 = e1)
% 136.03/20.07 (12) ~ (all_10_2 = e1)
% 136.03/20.07 (13) ~ (all_52_12 = e3)
% 136.03/20.07
% 136.03/20.07 Begin of proof
% 136.03/20.07 |
% 136.03/20.07 | BETA: splitting (3) gives:
% 136.03/20.07 |
% 136.03/20.07 | Case 1:
% 136.03/20.07 | |
% 136.03/20.07 | | (14) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11
% 136.03/20.07 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) =
% 136.03/20.07 | | e2 & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 136.03/20.07 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 136.03/20.07 | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.03/20.07 | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13
% 136.03/20.07 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) =
% 136.03/20.07 | | e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 136.03/20.07 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 136.03/20.07 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 136.03/20.07 | |
% 136.03/20.07 | | BETA: splitting (14) gives:
% 136.03/20.07 | |
% 136.03/20.07 | | Case 1:
% 136.03/20.07 | | |
% 136.03/20.07 | | | (15) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11
% 136.03/20.07 | | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) =
% 136.03/20.07 | | | e2 & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 136.03/20.07 | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 136.03/20.07 | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)
% 136.03/20.07 | | |
% 136.03/20.07 | | | ALPHA: (15) implies:
% 136.03/20.07 | | | (16) op(e3, e3) = e2
% 136.03/20.07 | | |
% 136.03/20.07 | | | REF_CLOSE: (1), (2), (5), (6), (7), (10), (12), (16) are inconsistent by
% 136.03/20.07 | | | sub-proof #776.
% 136.03/20.07 | | |
% 136.03/20.07 | | Case 2:
% 136.03/20.07 | | |
% 136.03/20.07 | | | (17) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~
% 136.03/20.07 | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 136.03/20.07 | | | op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 136.03/20.07 | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 136.03/20.07 | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.03/20.07 | | | $i(all_56_29)
% 136.03/20.07 | | |
% 136.03/20.07 | | | ALPHA: (17) implies:
% 136.03/20.07 | | | (18) op(e3, e3) = e1
% 136.03/20.07 | | |
% 136.03/20.07 | | | REF_CLOSE: (2), (8), (11), (18) are inconsistent by sub-proof #775.
% 136.03/20.07 | | |
% 136.03/20.07 | | End of split
% 136.03/20.07 | |
% 136.03/20.07 | Case 2:
% 136.03/20.07 | |
% 136.03/20.07 | | (19) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15
% 136.03/20.07 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) =
% 136.03/20.07 | | e0 & op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 136.03/20.07 | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 &
% 136.03/20.07 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 136.03/20.07 | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 136.03/20.07 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.03/20.07 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.03/20.07 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 136.03/20.07 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25))
% 136.03/20.07 | |
% 136.03/20.07 | | REF_CLOSE: (2), (4), (9), (11), (13), (19) are inconsistent by sub-proof
% 136.03/20.07 | | #190.
% 136.03/20.07 | |
% 136.03/20.07 | End of split
% 136.03/20.07 |
% 136.03/20.07 End of proof
% 136.03/20.07
% 136.03/20.07 Sub-proof #190 shows that the following formulas are inconsistent:
% 136.03/20.07 ----------------------------------------------------------------
% 136.03/20.07 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.07 (2) op(e2, e2) = e1
% 136.03/20.07 (3) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.03/20.07 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 136.03/20.07 op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.03/20.07 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.03/20.07 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 &
% 136.03/20.07 all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~
% 136.03/20.07 (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3,
% 136.03/20.07 e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 136.03/20.07 op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 136.03/20.07 $i(all_56_17) & $i(all_56_25))
% 136.03/20.07 (4) op(e3, e0) = all_52_12
% 136.03/20.07 (5) ~ (e3 = e1)
% 136.03/20.07 (6) ~ (all_52_12 = e3)
% 136.03/20.07
% 136.03/20.07 Begin of proof
% 136.03/20.07 |
% 136.03/20.07 | BETA: splitting (3) gives:
% 136.03/20.07 |
% 136.03/20.07 | Case 1:
% 136.03/20.07 | |
% 136.03/20.07 | | (7) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.03/20.07 | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 136.03/20.07 | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.03/20.07 | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.03/20.07 | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)
% 136.03/20.07 | |
% 136.03/20.07 | | ALPHA: (7) implies:
% 136.03/20.07 | | (8) op(e3, e0) = e3
% 136.03/20.07 | |
% 136.03/20.07 | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #733.
% 136.03/20.07 | |
% 136.03/20.07 | Case 2:
% 136.03/20.07 | |
% 136.03/20.07 | | (9) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.03/20.07 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.03/20.07 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.03/20.07 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1)
% 136.03/20.07 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)
% 136.03/20.07 | |
% 136.03/20.07 | | ALPHA: (9) implies:
% 136.03/20.07 | | (10) op(e2, e2) = e3
% 136.03/20.07 | |
% 136.03/20.07 | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #325.
% 136.03/20.07 | |
% 136.03/20.07 | End of split
% 136.03/20.07 |
% 136.03/20.07 End of proof
% 136.03/20.07
% 136.03/20.07 Sub-proof #191 shows that the following formulas are inconsistent:
% 136.03/20.07 ----------------------------------------------------------------
% 136.03/20.07 (1) ~ (all_14_1 = e0) & op(e3, e3) = all_14_1 & $i(all_14_1)
% 136.03/20.07 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.07 (3) op(e3, e3) = e0
% 136.03/20.07
% 136.03/20.07 Begin of proof
% 136.03/20.07 |
% 136.03/20.07 | ALPHA: (1) implies:
% 136.03/20.07 | (4) ~ (all_14_1 = e0)
% 136.03/20.07 | (5) op(e3, e3) = all_14_1
% 136.03/20.07 |
% 136.03/20.07 | GROUND_INST: instantiating (2) with e0, all_14_1, e3, e3, simplifying with
% 136.03/20.07 | (3), (5) gives:
% 136.03/20.07 | (6) all_14_1 = e0
% 136.03/20.07 |
% 136.03/20.07 | REDUCE: (4), (6) imply:
% 136.03/20.07 | (7) $false
% 136.03/20.07 |
% 136.03/20.07 | CLOSE: (7) is inconsistent.
% 136.03/20.07 |
% 136.03/20.07 End of proof
% 136.03/20.07
% 136.03/20.07 Sub-proof #192 shows that the following formulas are inconsistent:
% 136.03/20.07 ----------------------------------------------------------------
% 136.03/20.07 (1) all_54_1 = e1 | all_54_1 = e0
% 136.03/20.07 (2) all_54_1 = all_14_0
% 136.03/20.07 (3) ~ (all_14_0 = e1)
% 136.03/20.07 (4) ~ (all_14_0 = e0)
% 136.03/20.07
% 136.03/20.07 Begin of proof
% 136.03/20.07 |
% 136.03/20.07 | BETA: splitting (1) gives:
% 136.03/20.07 |
% 136.03/20.07 | Case 1:
% 136.03/20.07 | |
% 136.03/20.07 | | (5) all_54_1 = e1
% 136.03/20.07 | |
% 136.03/20.07 | | COMBINE_EQS: (2), (5) imply:
% 136.03/20.07 | | (6) all_14_0 = e1
% 136.03/20.08 | |
% 136.03/20.08 | | SIMP: (6) implies:
% 136.03/20.08 | | (7) all_14_0 = e1
% 136.03/20.08 | |
% 136.03/20.08 | | REDUCE: (3), (7) imply:
% 136.03/20.08 | | (8) $false
% 136.03/20.08 | |
% 136.03/20.08 | | CLOSE: (8) is inconsistent.
% 136.03/20.08 | |
% 136.03/20.08 | Case 2:
% 136.03/20.08 | |
% 136.03/20.08 | | (9) all_54_1 = e0
% 136.03/20.08 | |
% 136.03/20.08 | | COMBINE_EQS: (2), (9) imply:
% 136.03/20.08 | | (10) all_14_0 = e0
% 136.03/20.08 | |
% 136.03/20.08 | | SIMP: (10) implies:
% 136.03/20.08 | | (11) all_14_0 = e0
% 136.03/20.08 | |
% 136.03/20.08 | | REDUCE: (4), (11) imply:
% 136.03/20.08 | | (12) $false
% 136.03/20.08 | |
% 136.03/20.08 | | CLOSE: (12) is inconsistent.
% 136.03/20.08 | |
% 136.03/20.08 | End of split
% 136.03/20.08 |
% 136.03/20.08 End of proof
% 136.03/20.08
% 136.03/20.08 Sub-proof #193 shows that the following formulas are inconsistent:
% 136.03/20.08 ----------------------------------------------------------------
% 136.03/20.08 (1) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 136.03/20.08 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 136.03/20.08 (2) ~ (e2 = e0)
% 136.03/20.08 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.08 (4) ~ (e2 = e1)
% 136.03/20.08 (5) ~ (e3 = e0)
% 136.03/20.08 (6) all_57_13 = e2 & op(e0, e2) = e2
% 136.03/20.08 (7) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 136.03/20.08 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 136.03/20.08 (8) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 136.03/20.08 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 136.03/20.08 (9) ~ (all_52_8 = e2)
% 136.03/20.08 (10) op(e3, e0) = all_52_12
% 136.03/20.08 (11) ~ (all_52_12 = e2)
% 136.03/20.08 (12) all_57_3 = e3
% 136.03/20.08 (13) op(e3, e1) = all_52_8
% 136.03/20.08 (14) op(e3, e3) = e0
% 136.03/20.08 (15) ~ (e3 = e1)
% 136.03/20.08 (16) ~ (e1 = e0)
% 136.03/20.08
% 136.03/20.08 Begin of proof
% 136.03/20.08 |
% 136.03/20.08 | ALPHA: (6) implies:
% 136.03/20.08 | (17) all_57_13 = e2
% 136.03/20.08 |
% 136.03/20.08 | BETA: splitting (7) gives:
% 136.03/20.08 |
% 136.03/20.08 | Case 1:
% 136.03/20.08 | |
% 136.03/20.08 | | (18) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) =
% 136.03/20.08 | | e2)
% 136.03/20.08 | |
% 136.03/20.08 | | BETA: splitting (18) gives:
% 136.03/20.08 | |
% 136.03/20.08 | | Case 1:
% 136.03/20.08 | | |
% 136.03/20.08 | | | (19) all_57_0 = e2 & op(e3, e3) = e2
% 136.03/20.08 | | |
% 136.03/20.08 | | | ALPHA: (19) implies:
% 136.03/20.08 | | | (20) op(e3, e3) = e2
% 136.03/20.08 | | |
% 136.03/20.08 | | | REF_CLOSE: (2), (3), (14), (20) are inconsistent by sub-proof #495.
% 136.03/20.08 | | |
% 136.03/20.08 | | Case 2:
% 136.03/20.08 | | |
% 136.03/20.08 | | | (21) all_57_1 = e2 & op(e3, e2) = e2
% 136.03/20.08 | | |
% 136.03/20.08 | | | ALPHA: (21) implies:
% 136.03/20.08 | | | (22) all_57_1 = e2
% 136.03/20.08 | | |
% 136.03/20.08 | | | REF_CLOSE: (1), (2), (4), (5), (8), (12), (15), (16), (17), (22) are
% 136.03/20.08 | | | inconsistent by sub-proof #301.
% 136.03/20.08 | | |
% 136.03/20.08 | | End of split
% 136.03/20.08 | |
% 136.03/20.08 | Case 2:
% 136.03/20.08 | |
% 136.03/20.08 | | (23) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) =
% 136.03/20.08 | | e2)
% 136.03/20.08 | |
% 136.03/20.08 | | BETA: splitting (23) gives:
% 136.03/20.08 | |
% 136.03/20.08 | | Case 1:
% 136.03/20.08 | | |
% 136.03/20.08 | | | (24) all_57_4 = e2 & op(e3, e1) = e2
% 136.03/20.08 | | |
% 136.03/20.08 | | | REF_CLOSE: (3), (9), (13), (24) are inconsistent by sub-proof #442.
% 136.03/20.08 | | |
% 136.03/20.08 | | Case 2:
% 136.03/20.08 | | |
% 136.03/20.08 | | | (25) all_57_9 = e2 & op(e3, e0) = e2
% 136.03/20.08 | | |
% 136.03/20.08 | | | REF_CLOSE: (3), (10), (11), (25) are inconsistent by sub-proof #460.
% 136.03/20.08 | | |
% 136.03/20.08 | | End of split
% 136.03/20.08 | |
% 136.03/20.08 | End of split
% 136.03/20.08 |
% 136.03/20.08 End of proof
% 136.03/20.08
% 136.03/20.08 Sub-proof #194 shows that the following formulas are inconsistent:
% 136.03/20.08 ----------------------------------------------------------------
% 136.03/20.08 (1) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.03/20.08 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 136.03/20.08 op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.03/20.08 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.03/20.08 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 &
% 136.03/20.08 all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~
% 136.03/20.08 (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3,
% 136.03/20.08 e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 136.03/20.08 op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 136.03/20.08 $i(all_56_17) & $i(all_56_25))
% 136.03/20.08 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.08 (3) op(e0, e3) = e3
% 136.03/20.08 (4) op(e3, e2) = e2
% 136.03/20.08
% 136.03/20.08 Begin of proof
% 136.03/20.08 |
% 136.03/20.08 | BETA: splitting (1) gives:
% 136.03/20.08 |
% 136.03/20.08 | Case 1:
% 136.03/20.08 | |
% 136.03/20.08 | | (5) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.03/20.08 | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 136.03/20.08 | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.03/20.08 | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.03/20.08 | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)
% 136.03/20.08 | |
% 136.03/20.08 | | ALPHA: (5) implies:
% 136.03/20.08 | | (6) ~ (all_56_7 = e3)
% 136.03/20.08 | | (7) op(e0, e3) = all_56_7
% 136.03/20.08 | |
% 136.03/20.08 | | REF_CLOSE: (2), (3), (6), (7) are inconsistent by sub-proof #209.
% 136.03/20.08 | |
% 136.03/20.08 | Case 2:
% 136.03/20.08 | |
% 136.03/20.08 | | (8) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.03/20.08 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.03/20.08 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.03/20.08 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1)
% 136.03/20.08 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)
% 136.03/20.08 | |
% 136.03/20.08 | | ALPHA: (8) implies:
% 136.03/20.08 | | (9) ~ (all_56_9 = e2)
% 136.03/20.08 | | (10) op(e3, e2) = all_56_9
% 136.03/20.08 | |
% 136.03/20.08 | | REF_CLOSE: (2), (4), (9), (10) are inconsistent by sub-proof #199.
% 136.03/20.08 | |
% 136.03/20.08 | End of split
% 136.03/20.08 |
% 136.03/20.08 End of proof
% 136.03/20.08
% 136.03/20.08 Sub-proof #195 shows that the following formulas are inconsistent:
% 136.03/20.08 ----------------------------------------------------------------
% 136.03/20.08 (1) all_57_2 = e1
% 136.03/20.08 (2) ~ (e2 = e0)
% 136.03/20.08 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.08 (4) ~ (e2 = e1)
% 136.03/20.08 (5) ~ (e3 = e0)
% 136.03/20.08 (6) ~ (e3 = e2)
% 136.03/20.08 (7) all_57_12 = e3
% 136.03/20.08 (8) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2)
% 136.03/20.08 & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3,
% 136.03/20.08 e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1)
% 136.03/20.08 = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 136.03/20.08 $i(all_56_21) & $i(all_56_29)
% 136.03/20.08 (9) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 136.03/20.08 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 136.03/20.08 (10) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 136.03/20.08 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 136.03/20.08 (11) ~ (e1 = e0)
% 136.03/20.08 (12) op(e2, e3) = e1
% 136.03/20.08
% 136.03/20.08 Begin of proof
% 136.03/20.08 |
% 136.03/20.08 | ALPHA: (8) implies:
% 136.03/20.08 | (13) op(e3, e3) = e1
% 136.03/20.08 |
% 136.03/20.08 | BETA: splitting (10) gives:
% 136.03/20.08 |
% 136.03/20.08 | Case 1:
% 136.03/20.08 | |
% 136.03/20.08 | | (14) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) =
% 136.03/20.08 | | e2)
% 136.03/20.08 | |
% 136.03/20.08 | | BETA: splitting (14) gives:
% 136.03/20.08 | |
% 136.03/20.08 | | Case 1:
% 136.03/20.08 | | |
% 136.03/20.08 | | | (15) all_57_0 = e2 & op(e3, e3) = e2
% 136.03/20.08 | | |
% 136.03/20.08 | | | ALPHA: (15) implies:
% 136.03/20.08 | | | (16) op(e3, e3) = e2
% 136.03/20.08 | | |
% 136.03/20.08 | | | REF_CLOSE: (3), (4), (13), (16) are inconsistent by sub-proof #743.
% 136.03/20.08 | | |
% 136.03/20.08 | | Case 2:
% 136.03/20.08 | | |
% 136.03/20.08 | | | (17) all_57_2 = e2 & op(e2, e3) = e2
% 136.03/20.08 | | |
% 136.03/20.08 | | | ALPHA: (17) implies:
% 136.03/20.08 | | | (18) op(e2, e3) = e2
% 136.03/20.08 | | |
% 136.03/20.08 | | | REF_CLOSE: (3), (4), (12), (18) are inconsistent by sub-proof #450.
% 136.03/20.08 | | |
% 136.03/20.08 | | End of split
% 136.03/20.08 | |
% 136.03/20.08 | Case 2:
% 136.03/20.08 | |
% 136.03/20.08 | | (19) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) =
% 136.03/20.08 | | e2)
% 136.03/20.08 | |
% 136.03/20.08 | | BETA: splitting (19) gives:
% 136.03/20.08 | |
% 136.03/20.08 | | Case 1:
% 136.03/20.08 | | |
% 136.03/20.08 | | | (20) all_57_6 = e2 & op(e1, e3) = e2
% 136.03/20.08 | | |
% 136.03/20.08 | | | ALPHA: (20) implies:
% 136.03/20.08 | | | (21) all_57_6 = e2
% 136.03/20.08 | | |
% 136.03/20.08 | | | BETA: splitting (9) gives:
% 136.03/20.08 | | |
% 136.03/20.08 | | | Case 1:
% 136.03/20.08 | | | |
% 136.03/20.08 | | | | (22) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3)
% 136.03/20.08 | | | | = e0)
% 136.03/20.08 | | | |
% 136.03/20.08 | | | | BETA: splitting (22) gives:
% 136.03/20.08 | | | |
% 136.03/20.08 | | | | Case 1:
% 136.03/20.08 | | | | |
% 136.03/20.08 | | | | | (23) all_57_0 = e0 & op(e3, e3) = e0
% 136.03/20.08 | | | | |
% 136.03/20.08 | | | | | ALPHA: (23) implies:
% 136.03/20.08 | | | | | (24) op(e3, e3) = e0
% 136.03/20.08 | | | | |
% 136.03/20.08 | | | | | REF_CLOSE: (3), (11), (13), (24) are inconsistent by sub-proof #717.
% 136.03/20.08 | | | | |
% 136.03/20.08 | | | | Case 2:
% 136.03/20.08 | | | | |
% 136.03/20.08 | | | | | (25) all_57_2 = e0 & op(e2, e3) = e0
% 136.03/20.08 | | | | |
% 136.03/20.08 | | | | | REF_CLOSE: (1), (11), (25) are inconsistent by sub-proof #272.
% 136.03/20.08 | | | | |
% 136.03/20.08 | | | | End of split
% 136.03/20.08 | | | |
% 136.03/20.08 | | | Case 2:
% 136.03/20.08 | | | |
% 136.03/20.08 | | | | (26) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3)
% 136.03/20.08 | | | | = e0)
% 136.03/20.08 | | | |
% 136.03/20.08 | | | | BETA: splitting (26) gives:
% 136.03/20.08 | | | |
% 136.03/20.08 | | | | Case 1:
% 136.03/20.08 | | | | |
% 136.03/20.08 | | | | | (27) all_57_6 = e0 & op(e1, e3) = e0
% 136.03/20.08 | | | | |
% 136.03/20.08 | | | | | REF_CLOSE: (2), (21), (27) are inconsistent by sub-proof #520.
% 136.03/20.08 | | | | |
% 136.03/20.08 | | | | Case 2:
% 136.03/20.08 | | | | |
% 136.03/20.08 | | | | | (28) all_57_12 = e0 & op(e0, e3) = e0
% 136.03/20.08 | | | | |
% 136.03/20.08 | | | | | REF_CLOSE: (5), (7), (28) are inconsistent by sub-proof #436.
% 136.03/20.08 | | | | |
% 136.03/20.08 | | | | End of split
% 136.03/20.08 | | | |
% 136.03/20.08 | | | End of split
% 136.03/20.08 | | |
% 136.03/20.08 | | Case 2:
% 136.03/20.08 | | |
% 136.03/20.08 | | | (29) all_57_12 = e2 & op(e0, e3) = e2
% 136.03/20.08 | | |
% 136.03/20.08 | | | REF_CLOSE: (6), (7), (29) are inconsistent by sub-proof #196.
% 136.03/20.08 | | |
% 136.03/20.08 | | End of split
% 136.03/20.08 | |
% 136.03/20.08 | End of split
% 136.03/20.08 |
% 136.03/20.08 End of proof
% 136.03/20.08
% 136.03/20.08 Sub-proof #196 shows that the following formulas are inconsistent:
% 136.03/20.08 ----------------------------------------------------------------
% 136.03/20.08 (1) all_57_12 = e2 & op(e0, e3) = e2
% 136.03/20.08 (2) all_57_12 = e3
% 136.03/20.08 (3) ~ (e3 = e2)
% 136.03/20.08
% 136.03/20.08 Begin of proof
% 136.03/20.08 |
% 136.03/20.08 | ALPHA: (1) implies:
% 136.03/20.08 | (4) all_57_12 = e2
% 136.03/20.08 |
% 136.03/20.08 | COMBINE_EQS: (2), (4) imply:
% 136.03/20.08 | (5) e3 = e2
% 136.03/20.08 |
% 136.03/20.08 | REDUCE: (3), (5) imply:
% 136.03/20.08 | (6) $false
% 136.03/20.08 |
% 136.03/20.08 | CLOSE: (6) is inconsistent.
% 136.03/20.08 |
% 136.03/20.08 End of proof
% 136.03/20.08
% 136.03/20.08 Sub-proof #197 shows that the following formulas are inconsistent:
% 136.03/20.08 ----------------------------------------------------------------
% 136.03/20.08 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.08 (2) ~ (e3 = e0)
% 136.03/20.08 (3) ~ (all_52_4 = e3)
% 136.03/20.08 (4) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3)
% 136.03/20.08 (5) op(e3, e2) = all_52_4
% 136.03/20.08 (6) op(e3, e3) = e0
% 136.03/20.08
% 136.03/20.08 Begin of proof
% 136.03/20.08 |
% 136.03/20.08 | BETA: splitting (4) gives:
% 136.03/20.08 |
% 136.03/20.08 | Case 1:
% 136.03/20.08 | |
% 136.03/20.08 | | (7) all_57_0 = e3 & op(e3, e3) = e3
% 136.03/20.08 | |
% 136.03/20.08 | | ALPHA: (7) implies:
% 136.03/20.08 | | (8) op(e3, e3) = e3
% 136.03/20.08 | |
% 136.03/20.08 | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #773.
% 136.03/20.08 | |
% 136.03/20.08 | Case 2:
% 136.03/20.08 | |
% 136.03/20.08 | | (9) all_57_1 = e3 & op(e3, e2) = e3
% 136.03/20.08 | |
% 136.03/20.08 | | ALPHA: (9) implies:
% 136.03/20.08 | | (10) op(e3, e2) = e3
% 136.03/20.08 | |
% 136.03/20.08 | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #738.
% 136.03/20.08 | |
% 136.03/20.08 | End of split
% 136.03/20.08 |
% 136.03/20.08 End of proof
% 136.03/20.08
% 136.03/20.08 Sub-proof #198 shows that the following formulas are inconsistent:
% 136.03/20.08 ----------------------------------------------------------------
% 136.03/20.08 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.08 (2) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.03/20.08 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 136.03/20.08 op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.03/20.08 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.03/20.08 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 &
% 136.03/20.08 all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~
% 136.03/20.08 (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3,
% 136.03/20.08 e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 136.03/20.08 op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 136.03/20.08 $i(all_56_17) & $i(all_56_25))
% 136.03/20.08 (3) op(e3, e0) = all_52_12
% 136.03/20.08 (4) op(e3, e2) = e2
% 136.03/20.08 (5) ~ (all_52_12 = e3)
% 136.03/20.08
% 136.03/20.08 Begin of proof
% 136.03/20.08 |
% 136.03/20.08 | BETA: splitting (2) gives:
% 136.03/20.08 |
% 136.03/20.08 | Case 1:
% 136.03/20.08 | |
% 136.03/20.08 | | (6) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.03/20.08 | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 136.03/20.08 | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.03/20.08 | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.03/20.08 | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)
% 136.03/20.08 | |
% 136.03/20.08 | | ALPHA: (6) implies:
% 136.03/20.08 | | (7) op(e3, e0) = e3
% 136.03/20.08 | |
% 136.03/20.08 | | REF_CLOSE: (1), (3), (5), (7) are inconsistent by sub-proof #733.
% 136.03/20.08 | |
% 136.03/20.08 | Case 2:
% 136.03/20.08 | |
% 136.03/20.08 | | (8) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.03/20.08 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.03/20.08 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.03/20.08 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1)
% 136.03/20.08 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)
% 136.03/20.08 | |
% 136.03/20.08 | | ALPHA: (8) implies:
% 136.03/20.08 | | (9) ~ (all_56_9 = e2)
% 136.03/20.08 | | (10) op(e3, e2) = all_56_9
% 136.03/20.08 | |
% 136.03/20.08 | | REF_CLOSE: (1), (4), (9), (10) are inconsistent by sub-proof #199.
% 136.03/20.08 | |
% 136.03/20.08 | End of split
% 136.03/20.08 |
% 136.03/20.08 End of proof
% 136.03/20.08
% 136.03/20.08 Sub-proof #199 shows that the following formulas are inconsistent:
% 136.03/20.08 ----------------------------------------------------------------
% 136.03/20.08 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.08 (2) op(e3, e2) = all_56_9
% 136.03/20.08 (3) op(e3, e2) = e2
% 136.03/20.08 (4) ~ (all_56_9 = e2)
% 136.03/20.08
% 136.03/20.08 Begin of proof
% 136.03/20.08 |
% 136.03/20.08 | GROUND_INST: instantiating (1) with e2, all_56_9, e2, e3, simplifying with
% 136.03/20.08 | (2), (3) gives:
% 136.03/20.08 | (5) all_56_9 = e2
% 136.03/20.08 |
% 136.03/20.08 | REDUCE: (4), (5) imply:
% 136.03/20.08 | (6) $false
% 136.03/20.08 |
% 136.03/20.08 | CLOSE: (6) is inconsistent.
% 136.03/20.08 |
% 136.03/20.08 End of proof
% 136.03/20.08
% 136.03/20.08 Sub-proof #200 shows that the following formulas are inconsistent:
% 136.03/20.08 ----------------------------------------------------------------
% 136.03/20.08 (1) ~ (e2 = e0)
% 136.03/20.08 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.08 (3) op(e2, e0) = e0
% 136.03/20.08 (4) op(e3, e0) = all_52_12
% 136.03/20.08 (5) ~ (all_52_12 = e2)
% 136.03/20.08 (6) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 136.03/20.08
% 136.03/20.08 Begin of proof
% 136.03/20.08 |
% 136.03/20.08 | BETA: splitting (6) gives:
% 136.03/20.08 |
% 136.03/20.08 | Case 1:
% 136.03/20.08 | |
% 136.03/20.08 | | (7) all_57_9 = e2 & op(e3, e0) = e2
% 136.03/20.08 | |
% 136.03/20.08 | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #460.
% 136.03/20.08 | |
% 136.03/20.08 | Case 2:
% 136.03/20.08 | |
% 136.03/20.08 | | (8) all_57_10 = e2 & op(e2, e0) = e2
% 136.03/20.08 | |
% 136.03/20.08 | | ALPHA: (8) implies:
% 136.03/20.08 | | (9) op(e2, e0) = e2
% 136.03/20.08 | |
% 136.03/20.08 | | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #451.
% 136.03/20.08 | |
% 136.03/20.08 | End of split
% 136.03/20.08 |
% 136.03/20.08 End of proof
% 136.03/20.08
% 136.03/20.08 Sub-proof #201 shows that the following formulas are inconsistent:
% 136.03/20.08 ----------------------------------------------------------------
% 136.03/20.08 (1) ~ (all_52_6 = e3)
% 136.03/20.08 (2) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 136.03/20.08 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 136.03/20.08 (3) ~ (e2 = e0)
% 136.03/20.08 (4) all_57_1 = e2
% 136.03/20.08 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.08 (6) ~ (e2 = e1)
% 136.03/20.08 (7) ~ (e3 = e0)
% 136.03/20.08 (8) ~ (e3 = e2)
% 136.03/20.08 (9) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 136.03/20.08 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 136.03/20.08 (10) op(e1, e2) = all_52_6
% 136.03/20.08 (11) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 136.03/20.08 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 136.03/20.08 (12) all_57_11 = e3
% 136.03/20.08 (13) all_57_3 = e3
% 136.03/20.08 (14) all_57_11 = e2
% 136.03/20.08 (15) ~ (e3 = e1)
% 136.03/20.08 (16) ~ (e1 = e0)
% 136.03/20.08
% 136.03/20.08 Begin of proof
% 136.03/20.08 |
% 136.03/20.08 | COMBINE_EQS: (12), (14) imply:
% 136.03/20.08 | (17) e3 = e2
% 136.03/20.08 |
% 136.03/20.08 | SIMP: (17) implies:
% 136.03/20.08 | (18) e3 = e2
% 136.03/20.08 |
% 136.03/20.08 | COMBINE_EQS: (13), (18) imply:
% 136.03/20.08 | (19) all_57_3 = e2
% 136.03/20.08 |
% 136.03/20.08 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (15),
% 136.03/20.08 | (16), (19) are inconsistent by sub-proof #463.
% 136.03/20.08 |
% 136.03/20.08 End of proof
% 136.03/20.08
% 136.03/20.08 Sub-proof #202 shows that the following formulas are inconsistent:
% 136.03/20.08 ----------------------------------------------------------------
% 136.03/20.08 (1) ~ (all_52_4 = e0)
% 136.03/20.08 (2) all_57_1 = e2
% 136.03/20.08 (3) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 136.03/20.08 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 136.03/20.08 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.08 (5) ~ (e2 = e1)
% 136.03/20.08 (6) ~ (e3 = e0)
% 136.03/20.08 (7) ~ (all_52_12 = e0)
% 136.03/20.08 (8) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1)
% 136.03/20.08 (9) op(e3, e2) = all_52_4
% 136.03/20.08 (10) op(e3, e0) = all_52_12
% 136.03/20.08 (11) op(e3, e1) = all_52_8
% 136.03/20.08 (12) ~ (e1 = e0)
% 136.03/20.08 (13) op(e3, e1) = e3
% 136.03/20.08
% 136.03/20.08 Begin of proof
% 136.03/20.08 |
% 136.03/20.08 | BETA: splitting (8) gives:
% 136.03/20.08 |
% 136.03/20.08 | Case 1:
% 136.03/20.08 | |
% 136.03/20.08 | | (14) all_57_0 = e1 & op(e3, e3) = e1
% 136.03/20.08 | |
% 136.03/20.08 | | ALPHA: (14) implies:
% 136.03/20.08 | | (15) op(e3, e3) = e1
% 136.03/20.08 | |
% 136.03/20.08 | | REF_CLOSE: (1), (3), (4), (6), (7), (9), (10), (11), (12), (13), (15) are
% 136.03/20.08 | | inconsistent by sub-proof #599.
% 136.03/20.08 | |
% 136.03/20.08 | Case 2:
% 136.03/20.08 | |
% 136.03/20.08 | | (16) all_57_1 = e1 & op(e3, e2) = e1
% 136.03/20.08 | |
% 136.03/20.08 | | REF_CLOSE: (2), (5), (16) are inconsistent by sub-proof #465.
% 136.03/20.08 | |
% 136.03/20.08 | End of split
% 136.03/20.08 |
% 136.03/20.08 End of proof
% 136.03/20.08
% 136.03/20.08 Sub-proof #203 shows that the following formulas are inconsistent:
% 136.03/20.08 ----------------------------------------------------------------
% 136.03/20.08 (1) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 136.03/20.08 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.08 (3) ~ (e3 = e0)
% 136.03/20.08 (4) ~ (all_52_1 = e0)
% 136.03/20.08 (5) op(e2, e2) = e3
% 136.03/20.08 (6) op(e2, e3) = all_52_1
% 136.03/20.08
% 136.03/20.08 Begin of proof
% 136.03/20.08 |
% 136.03/20.08 | BETA: splitting (1) gives:
% 136.03/20.08 |
% 136.03/20.08 | Case 1:
% 136.03/20.08 | |
% 136.03/20.08 | | (7) all_57_2 = e0 & op(e2, e3) = e0
% 136.03/20.08 | |
% 136.03/20.08 | | REF_CLOSE: (2), (4), (6), (7) are inconsistent by sub-proof #225.
% 136.03/20.08 | |
% 136.03/20.08 | Case 2:
% 136.03/20.08 | |
% 136.03/20.08 | | (8) all_57_3 = e0 & op(e2, e2) = e0
% 136.03/20.08 | |
% 136.03/20.08 | | ALPHA: (8) implies:
% 136.03/20.08 | | (9) op(e2, e2) = e0
% 136.03/20.08 | |
% 136.03/20.08 | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #641.
% 136.03/20.08 | |
% 136.03/20.08 | End of split
% 136.03/20.08 |
% 136.03/20.08 End of proof
% 136.03/20.08
% 136.03/20.08 Sub-proof #204 shows that the following formulas are inconsistent:
% 136.03/20.08 ----------------------------------------------------------------
% 136.03/20.08 (1) ~ (all_24_1 = e2) & op(e0, e0) = all_24_1 & $i(all_24_1)
% 136.03/20.08 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.08 (3) op(e0, e0) = e2
% 136.03/20.08
% 136.03/20.08 Begin of proof
% 136.03/20.08 |
% 136.03/20.08 | ALPHA: (1) implies:
% 136.03/20.08 | (4) ~ (all_24_1 = e2)
% 136.03/20.08 | (5) op(e0, e0) = all_24_1
% 136.03/20.08 |
% 136.03/20.08 | GROUND_INST: instantiating (2) with e2, all_24_1, e0, e0, simplifying with
% 136.03/20.08 | (3), (5) gives:
% 136.03/20.08 | (6) all_24_1 = e2
% 136.03/20.08 |
% 136.03/20.08 | REDUCE: (4), (6) imply:
% 136.03/20.08 | (7) $false
% 136.03/20.08 |
% 136.03/20.08 | CLOSE: (7) is inconsistent.
% 136.03/20.08 |
% 136.03/20.08 End of proof
% 136.03/20.08
% 136.03/20.08 Sub-proof #205 shows that the following formulas are inconsistent:
% 136.03/20.08 ----------------------------------------------------------------
% 136.03/20.08 (1) ~ (all_24_0 = e1)
% 136.03/20.08 (2) ~ (all_24_0 = e2)
% 136.03/20.08 (3) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 136.03/20.08 (4) all_54_12 = all_24_0
% 136.03/20.08 (5) ~ (all_24_0 = e0)
% 136.03/20.08
% 136.03/20.08 Begin of proof
% 136.03/20.08 |
% 136.03/20.08 | BETA: splitting (3) gives:
% 136.03/20.08 |
% 136.03/20.08 | Case 1:
% 136.03/20.08 | |
% 136.03/20.08 | | (6) all_54_12 = e2
% 136.03/20.08 | |
% 136.03/20.08 | | COMBINE_EQS: (4), (6) imply:
% 136.03/20.08 | | (7) all_24_0 = e2
% 136.03/20.08 | |
% 136.03/20.08 | | REDUCE: (2), (7) imply:
% 136.03/20.08 | | (8) $false
% 136.03/20.08 | |
% 136.03/20.08 | | CLOSE: (8) is inconsistent.
% 136.03/20.08 | |
% 136.03/20.08 | Case 2:
% 136.03/20.08 | |
% 136.03/20.08 | | (9) all_54_12 = e1 | all_54_12 = e0
% 136.03/20.08 | |
% 136.03/20.08 | | BETA: splitting (9) gives:
% 136.03/20.08 | |
% 136.03/20.08 | | Case 1:
% 136.03/20.08 | | |
% 136.03/20.08 | | | (10) all_54_12 = e1
% 136.03/20.08 | | |
% 136.03/20.08 | | | COMBINE_EQS: (4), (10) imply:
% 136.03/20.08 | | | (11) all_24_0 = e1
% 136.03/20.08 | | |
% 136.03/20.08 | | | REDUCE: (1), (11) imply:
% 136.03/20.08 | | | (12) $false
% 136.03/20.08 | | |
% 136.03/20.08 | | | CLOSE: (12) is inconsistent.
% 136.03/20.08 | | |
% 136.03/20.08 | | Case 2:
% 136.03/20.08 | | |
% 136.03/20.08 | | | (13) all_54_12 = e0
% 136.03/20.08 | | |
% 136.03/20.08 | | | COMBINE_EQS: (4), (13) imply:
% 136.03/20.08 | | | (14) all_24_0 = e0
% 136.03/20.08 | | |
% 136.03/20.08 | | | REDUCE: (5), (14) imply:
% 136.03/20.08 | | | (15) $false
% 136.03/20.08 | | |
% 136.03/20.08 | | | CLOSE: (15) is inconsistent.
% 136.03/20.08 | | |
% 136.03/20.08 | | End of split
% 136.03/20.08 | |
% 136.03/20.08 | End of split
% 136.03/20.08 |
% 136.03/20.08 End of proof
% 136.03/20.08
% 136.03/20.08 Sub-proof #206 shows that the following formulas are inconsistent:
% 136.03/20.08 ----------------------------------------------------------------
% 136.03/20.08 (1) op(e3, e1) = all_28_0
% 136.03/20.08 (2) all_57_1 = e3
% 136.03/20.08 (3) ~ (e2 = e0)
% 136.03/20.08 (4) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 136.03/20.08 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 136.03/20.08 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.08 (6) ~ (e2 = e1)
% 136.03/20.08 (7) ~ (e3 = e0)
% 136.03/20.08 (8) ~ (all_28_0 = e2)
% 136.03/20.08 (9) ~ (e3 = e2)
% 136.03/20.08 (10) op(e0, e1) = all_52_11
% 136.03/20.08 (11) ~ (all_52_11 = e3)
% 136.03/20.08 (12) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 136.03/20.08 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 136.03/20.08 (13) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 136.03/20.08 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 136.03/20.08 e1)
% 136.03/20.08 (14) all_57_12 = e3
% 136.03/20.08 (15) op(e3, e0) = all_52_12
% 136.03/20.08 (16) ~ (all_52_12 = e2)
% 136.03/20.08 (17) op(e0, e0) = e2
% 136.03/20.08 (18) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 136.03/20.08 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 136.03/20.08 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 136.03/20.08 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 136.03/20.08 (19) op(e3, e3) = e0
% 136.03/20.08 (20) ~ (e3 = e1)
% 136.03/20.08 (21) ~ (e1 = e0)
% 136.03/20.08
% 136.03/20.08 Begin of proof
% 136.03/20.08 |
% 136.03/20.08 | BETA: splitting (12) gives:
% 136.03/20.08 |
% 136.03/20.08 | Case 1:
% 136.03/20.08 | |
% 136.03/20.08 | | (22) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) =
% 136.03/20.08 | | e2)
% 136.03/20.08 | |
% 136.03/20.08 | | BETA: splitting (22) gives:
% 136.03/20.08 | |
% 136.03/20.08 | | Case 1:
% 136.03/20.08 | | |
% 136.03/20.08 | | | (23) all_57_0 = e2 & op(e3, e3) = e2
% 136.03/20.08 | | |
% 136.03/20.08 | | | ALPHA: (23) implies:
% 136.03/20.08 | | | (24) op(e3, e3) = e2
% 136.03/20.08 | | |
% 136.03/20.08 | | | REF_CLOSE: (3), (5), (19), (24) are inconsistent by sub-proof #495.
% 136.03/20.08 | | |
% 136.03/20.08 | | Case 2:
% 136.03/20.08 | | |
% 136.03/20.08 | | | (25) all_57_1 = e2 & op(e3, e2) = e2
% 136.03/20.08 | | |
% 136.03/20.08 | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (11), (13), (14),
% 136.03/20.08 | | | (17), (18), (20), (21), (25) are inconsistent by sub-proof
% 136.03/20.08 | | | #207.
% 136.03/20.08 | | |
% 136.03/20.08 | | End of split
% 136.03/20.08 | |
% 136.03/20.08 | Case 2:
% 136.03/20.08 | |
% 136.03/20.08 | | (26) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) =
% 136.03/20.08 | | e2)
% 136.03/20.08 | |
% 136.03/20.08 | | BETA: splitting (26) gives:
% 136.03/20.08 | |
% 136.03/20.08 | | Case 1:
% 136.03/20.08 | | |
% 136.03/20.08 | | | (27) all_57_4 = e2 & op(e3, e1) = e2
% 136.03/20.08 | | |
% 136.03/20.08 | | | REF_CLOSE: (1), (5), (8), (27) are inconsistent by sub-proof #218.
% 136.03/20.08 | | |
% 136.03/20.08 | | Case 2:
% 136.03/20.08 | | |
% 136.03/20.08 | | | (28) all_57_9 = e2 & op(e3, e0) = e2
% 136.03/20.08 | | |
% 136.03/20.08 | | | REF_CLOSE: (5), (15), (16), (28) are inconsistent by sub-proof #460.
% 136.03/20.08 | | |
% 136.03/20.08 | | End of split
% 136.03/20.08 | |
% 136.03/20.08 | End of split
% 136.03/20.08 |
% 136.03/20.08 End of proof
% 136.03/20.08
% 136.03/20.08 Sub-proof #207 shows that the following formulas are inconsistent:
% 136.03/20.08 ----------------------------------------------------------------
% 136.03/20.08 (1) all_57_1 = e3
% 136.03/20.08 (2) ~ (e2 = e0)
% 136.03/20.08 (3) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 136.03/20.08 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 136.03/20.08 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.08 (5) ~ (e2 = e1)
% 136.03/20.08 (6) ~ (e3 = e0)
% 136.03/20.08 (7) ~ (e3 = e2)
% 136.03/20.08 (8) op(e0, e1) = all_52_11
% 136.03/20.08 (9) ~ (all_52_11 = e3)
% 136.03/20.08 (10) all_57_1 = e2 & op(e3, e2) = e2
% 136.03/20.08 (11) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 136.03/20.08 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 136.03/20.08 e1)
% 136.03/20.08 (12) all_57_12 = e3
% 136.03/20.08 (13) op(e0, e0) = e2
% 136.03/20.09 (14) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 136.03/20.09 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 136.03/20.09 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 136.03/20.09 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 136.03/20.09 (15) ~ (e3 = e1)
% 136.03/20.09 (16) ~ (e1 = e0)
% 136.03/20.09
% 136.03/20.09 Begin of proof
% 136.03/20.09 |
% 136.03/20.09 | ALPHA: (10) implies:
% 136.03/20.09 | (17) all_57_1 = e2
% 136.03/20.09 |
% 136.03/20.09 | COMBINE_EQS: (1), (17) imply:
% 136.03/20.09 | (18) e3 = e2
% 136.03/20.09 |
% 136.03/20.09 | COMBINE_EQS: (12), (18) imply:
% 136.03/20.09 | (19) all_57_12 = e2
% 136.03/20.09 |
% 136.03/20.09 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (13), (14), (15),
% 136.03/20.09 | (16), (19) are inconsistent by sub-proof #458.
% 136.03/20.09 |
% 136.03/20.09 End of proof
% 136.03/20.09
% 136.03/20.09 Sub-proof #208 shows that the following formulas are inconsistent:
% 136.03/20.09 ----------------------------------------------------------------
% 136.03/20.09 (1) op(e2, e2) = all_8_2
% 136.03/20.09 (2) ~ (e2 = e0)
% 136.03/20.09 (3) ~ (all_8_2 = e1)
% 136.03/20.09 (4) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 136.03/20.09 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 136.03/20.09 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.09 (6) ~ (e2 = e1)
% 136.03/20.09 (7) ~ (e3 = e0)
% 136.03/20.09 (8) ~ (e3 = e2)
% 136.03/20.09 (9) op(e0, e1) = all_52_11
% 136.03/20.09 (10) op(e0, e2) = all_52_7
% 136.03/20.09 (11) ~ (all_52_11 = e3)
% 136.03/20.09 (12) op(e0, e3) = e3
% 136.03/20.09 (13) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 136.03/20.09 (14) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 136.03/20.09 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 136.03/20.09 e1)
% 136.03/20.09 (15) all_54_5 = all_8_2
% 136.03/20.09 (16) all_57_12 = e3
% 136.03/20.09 (17) op(e0, e0) = e2
% 136.03/20.09 (18) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 136.03/20.09 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 136.03/20.09 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 136.03/20.09 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 136.03/20.09 (19) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.03/20.09 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.03/20.09 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0)
% 136.03/20.09 = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 136.03/20.09 $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~
% 136.03/20.09 (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 136.03/20.09 (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 136.03/20.09 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.03/20.09 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.03/20.09 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.03/20.09 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 136.03/20.09 op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.03/20.09 op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 136.03/20.09 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13
% 136.03/20.09 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 136.03/20.09 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1,
% 136.03/20.09 e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 136.03/20.09 $i(all_56_21) & $i(all_56_29))
% 136.03/20.09 (20) ~ (e3 = e1)
% 136.03/20.09 (21) ~ (all_52_7 = all_8_2)
% 136.03/20.09 (22) ~ (e1 = e0)
% 136.03/20.09 (23) ~ (all_8_2 = e3)
% 136.03/20.09 (24) op(e0, e0) = all_56_31
% 136.03/20.09
% 136.03/20.09 Begin of proof
% 136.03/20.09 |
% 136.03/20.09 | GROUND_INST: instantiating (5) with e2, all_56_31, e0, e0, simplifying with
% 136.03/20.09 | (17), (24) gives:
% 136.03/20.09 | (25) all_56_31 = e2
% 136.03/20.09 |
% 136.03/20.09 | BETA: splitting (19) gives:
% 136.03/20.09 |
% 136.03/20.09 | Case 1:
% 136.03/20.09 | |
% 136.03/20.09 | | (26) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 136.03/20.09 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.03/20.09 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.03/20.09 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9)
% 136.03/20.09 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 136.03/20.09 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 136.03/20.09 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 136.03/20.09 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 136.03/20.09 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 136.03/20.09 | | $i(all_56_27))
% 136.03/20.09 | |
% 136.03/20.09 | | BETA: splitting (26) gives:
% 136.03/20.09 | |
% 136.03/20.09 | | Case 1:
% 136.03/20.09 | | |
% 136.03/20.09 | | | (27) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 136.03/20.09 | | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.03/20.09 | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.03/20.09 | | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9)
% 136.03/20.09 | | | & $i(all_56_17) & $i(all_56_25)
% 136.03/20.09 | | |
% 136.03/20.09 | | | ALPHA: (27) implies:
% 136.03/20.09 | | | (28) all_56_31 = e3
% 136.03/20.09 | | |
% 136.03/20.09 | | | COMBINE_EQS: (25), (28) imply:
% 136.03/20.09 | | | (29) e3 = e2
% 136.03/20.09 | | |
% 136.03/20.09 | | | SIMP: (29) implies:
% 136.03/20.09 | | | (30) e3 = e2
% 136.03/20.09 | | |
% 136.03/20.09 | | | COMBINE_EQS: (16), (30) imply:
% 136.03/20.09 | | | (31) all_57_12 = e2
% 136.03/20.09 | | |
% 136.03/20.09 | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (11), (14), (17), (18),
% 136.03/20.09 | | | (20), (22), (31) are inconsistent by sub-proof #458.
% 136.03/20.09 | | |
% 136.03/20.09 | | Case 2:
% 136.03/20.09 | | |
% 136.03/20.09 | | | (32) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 136.03/20.09 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.03/20.09 | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.03/20.09 | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.03/20.09 | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)
% 136.03/20.09 | | |
% 136.03/20.09 | | | ALPHA: (32) implies:
% 136.03/20.09 | | | (33) ~ (all_56_11 = e2)
% 136.03/20.09 | | | (34) op(e0, e2) = e0
% 136.03/20.09 | | | (35) op(e2, e2) = all_56_11
% 136.03/20.09 | | |
% 136.03/20.09 | | | REF_CLOSE: (1), (3), (5), (10), (13), (15), (21), (23), (33), (34), (35)
% 136.03/20.09 | | | are inconsistent by sub-proof #227.
% 136.03/20.09 | | |
% 136.03/20.09 | | End of split
% 136.03/20.09 | |
% 136.03/20.09 | Case 2:
% 136.03/20.09 | |
% 136.03/20.09 | | (36) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.03/20.09 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.03/20.09 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 136.03/20.09 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 136.03/20.09 | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 136.03/20.09 | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 136.03/20.09 | | ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 136.03/20.09 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 136.03/20.09 | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.03/20.09 | | $i(all_56_29))
% 136.03/20.09 | |
% 136.03/20.09 | | BETA: splitting (36) gives:
% 136.03/20.09 | |
% 136.03/20.09 | | Case 1:
% 136.03/20.09 | | |
% 136.03/20.09 | | | (37) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.03/20.09 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.03/20.09 | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 136.03/20.09 | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 136.03/20.09 | | | $i(all_56_15) & $i(all_56_23)
% 136.03/20.09 | | |
% 136.03/20.09 | | | ALPHA: (37) implies:
% 136.03/20.09 | | | (38) ~ (all_56_7 = e3)
% 136.03/20.09 | | | (39) op(e0, e3) = all_56_7
% 136.03/20.09 | | |
% 136.03/20.09 | | | REF_CLOSE: (5), (12), (38), (39) are inconsistent by sub-proof #209.
% 136.03/20.09 | | |
% 136.03/20.09 | | Case 2:
% 136.03/20.09 | | |
% 136.03/20.09 | | | (40) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 136.03/20.09 | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 136.03/20.09 | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.03/20.09 | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 136.03/20.09 | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 136.03/20.09 | | |
% 136.03/20.09 | | | REF_CLOSE: (6), (25), (40) are inconsistent by sub-proof #525.
% 136.03/20.09 | | |
% 136.03/20.09 | | End of split
% 136.03/20.09 | |
% 136.03/20.09 | End of split
% 136.03/20.09 |
% 136.03/20.09 End of proof
% 136.03/20.09
% 136.03/20.09 Sub-proof #209 shows that the following formulas are inconsistent:
% 136.03/20.09 ----------------------------------------------------------------
% 136.03/20.09 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.09 (2) op(e0, e3) = all_56_7
% 136.03/20.09 (3) op(e0, e3) = e3
% 136.03/20.09 (4) ~ (all_56_7 = e3)
% 136.03/20.09
% 136.03/20.09 Begin of proof
% 136.03/20.09 |
% 136.03/20.09 | GROUND_INST: instantiating (1) with e3, all_56_7, e3, e0, simplifying with
% 136.03/20.09 | (2), (3) gives:
% 136.03/20.09 | (5) all_56_7 = e3
% 136.03/20.09 |
% 136.03/20.09 | REDUCE: (4), (5) imply:
% 136.03/20.09 | (6) $false
% 136.03/20.09 |
% 136.03/20.09 | CLOSE: (6) is inconsistent.
% 136.03/20.09 |
% 136.03/20.09 End of proof
% 136.03/20.09
% 136.03/20.09 Sub-proof #210 shows that the following formulas are inconsistent:
% 136.03/20.09 ----------------------------------------------------------------
% 136.03/20.09 (1) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3)
% 136.03/20.09 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.09 (3) ~ (e3 = e0)
% 136.03/20.09 (4) ~ (all_52_1 = e3)
% 136.03/20.09 (5) op(e2, e3) = all_52_1
% 136.03/20.09 (6) op(e3, e3) = e0
% 136.03/20.09
% 136.03/20.09 Begin of proof
% 136.03/20.09 |
% 136.03/20.09 | BETA: splitting (1) gives:
% 136.03/20.09 |
% 136.03/20.09 | Case 1:
% 136.03/20.09 | |
% 136.03/20.09 | | (7) all_57_0 = e3 & op(e3, e3) = e3
% 136.03/20.09 | |
% 136.03/20.09 | | ALPHA: (7) implies:
% 136.03/20.09 | | (8) op(e3, e3) = e3
% 136.03/20.09 | |
% 136.03/20.09 | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #773.
% 136.03/20.09 | |
% 136.03/20.09 | Case 2:
% 136.03/20.09 | |
% 136.03/20.09 | | (9) all_57_2 = e3 & op(e2, e3) = e3
% 136.03/20.09 | |
% 136.03/20.09 | | ALPHA: (9) implies:
% 136.03/20.09 | | (10) op(e2, e3) = e3
% 136.03/20.09 | |
% 136.03/20.09 | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #763.
% 136.03/20.09 | |
% 136.03/20.09 | End of split
% 136.03/20.09 |
% 136.03/20.09 End of proof
% 136.03/20.09
% 136.03/20.09 Sub-proof #211 shows that the following formulas are inconsistent:
% 136.03/20.09 ----------------------------------------------------------------
% 136.03/20.09 (1) ~ (all_28_1 = e0) & op(e3, e3) = all_28_1 & $i(all_28_1)
% 136.03/20.09 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.09 (3) op(e3, e3) = e0
% 136.03/20.09
% 136.03/20.09 Begin of proof
% 136.03/20.09 |
% 136.03/20.09 | ALPHA: (1) implies:
% 136.03/20.09 | (4) ~ (all_28_1 = e0)
% 136.03/20.09 | (5) op(e3, e3) = all_28_1
% 136.03/20.09 |
% 136.03/20.09 | GROUND_INST: instantiating (2) with e0, all_28_1, e3, e3, simplifying with
% 136.03/20.09 | (3), (5) gives:
% 136.03/20.09 | (6) all_28_1 = e0
% 136.03/20.09 |
% 136.03/20.09 | REDUCE: (4), (6) imply:
% 136.03/20.09 | (7) $false
% 136.03/20.09 |
% 136.03/20.09 | CLOSE: (7) is inconsistent.
% 136.03/20.09 |
% 136.03/20.09 End of proof
% 136.03/20.09
% 136.03/20.09 Sub-proof #212 shows that the following formulas are inconsistent:
% 136.03/20.09 ----------------------------------------------------------------
% 136.03/20.09 (1) op(e3, e1) = all_28_0
% 136.03/20.09 (2) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 136.03/20.09 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 136.03/20.09 (3) op(e1, e1) = all_6_2
% 136.03/20.09 (4) ~ (e2 = e0)
% 136.03/20.09 (5) op(e3, e1) = e1
% 136.03/20.09 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.09 (7) ~ (e2 = e1)
% 136.03/20.09 (8) ~ (e3 = e0)
% 136.03/20.09 (9) ~ (all_28_0 = e2)
% 136.03/20.09 (10) op(e1, e1) = e3
% 136.03/20.09 (11) ~ (all_6_2 = e2)
% 136.03/20.09 (12) ~ (e1 = e0)
% 136.03/20.09 (13) all_57_14 = e1
% 136.03/20.09 (14) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 136.03/20.09 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 136.03/20.09
% 136.03/20.09 Begin of proof
% 136.03/20.09 |
% 136.03/20.09 | BETA: splitting (2) gives:
% 136.03/20.09 |
% 136.03/20.09 | Case 1:
% 136.03/20.09 | |
% 136.03/20.09 | | (15) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) =
% 136.03/20.09 | | e0)
% 136.03/20.09 | |
% 136.03/20.09 | | BETA: splitting (15) gives:
% 136.03/20.09 | |
% 136.03/20.09 | | Case 1:
% 136.03/20.09 | | |
% 136.03/20.09 | | | (16) all_57_4 = e0 & op(e3, e1) = e0
% 136.03/20.09 | | |
% 136.03/20.09 | | | ALPHA: (16) implies:
% 136.03/20.09 | | | (17) op(e3, e1) = e0
% 136.03/20.09 | | |
% 136.03/20.09 | | | REF_CLOSE: (5), (6), (12), (17) are inconsistent by sub-proof #343.
% 136.03/20.09 | | |
% 136.03/20.09 | | Case 2:
% 136.03/20.09 | | |
% 136.03/20.09 | | | (18) all_57_5 = e0 & op(e2, e1) = e0
% 136.03/20.09 | | |
% 136.03/20.09 | | | ALPHA: (18) implies:
% 136.03/20.09 | | | (19) all_57_5 = e0
% 136.03/20.09 | | |
% 136.03/20.09 | | | BETA: splitting (14) gives:
% 136.03/20.09 | | |
% 136.03/20.09 | | | Case 1:
% 136.03/20.09 | | | |
% 136.03/20.09 | | | | (20) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1)
% 136.03/20.09 | | | | = e2)
% 136.03/20.09 | | | |
% 136.03/20.09 | | | | BETA: splitting (20) gives:
% 136.03/20.09 | | | |
% 136.03/20.09 | | | | Case 1:
% 136.03/20.09 | | | | |
% 136.03/20.09 | | | | | (21) all_57_4 = e2 & op(e3, e1) = e2
% 136.03/20.09 | | | | |
% 136.03/20.09 | | | | | REF_CLOSE: (1), (6), (9), (21) are inconsistent by sub-proof #218.
% 136.03/20.09 | | | | |
% 136.03/20.09 | | | | Case 2:
% 136.03/20.09 | | | | |
% 136.03/20.09 | | | | | (22) all_57_5 = e2 & op(e2, e1) = e2
% 136.03/20.09 | | | | |
% 136.03/20.09 | | | | | ALPHA: (22) implies:
% 136.03/20.09 | | | | | (23) all_57_5 = e2
% 136.03/20.09 | | | | |
% 136.03/20.09 | | | | | COMBINE_EQS: (19), (23) imply:
% 136.03/20.09 | | | | | (24) e2 = e0
% 136.03/20.09 | | | | |
% 136.03/20.09 | | | | | REDUCE: (4), (24) imply:
% 136.03/20.09 | | | | | (25) $false
% 136.03/20.09 | | | | |
% 136.03/20.09 | | | | | CLOSE: (25) is inconsistent.
% 136.03/20.09 | | | | |
% 136.03/20.09 | | | | End of split
% 136.03/20.09 | | | |
% 136.03/20.09 | | | Case 2:
% 136.03/20.09 | | | |
% 136.03/20.09 | | | | (26) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1)
% 136.03/20.09 | | | | = e2)
% 136.03/20.09 | | | |
% 136.03/20.09 | | | | BETA: splitting (26) gives:
% 136.03/20.09 | | | |
% 136.03/20.09 | | | | Case 1:
% 136.03/20.09 | | | | |
% 136.03/20.09 | | | | | (27) all_57_8 = e2 & op(e1, e1) = e2
% 136.03/20.09 | | | | |
% 136.03/20.09 | | | | | ALPHA: (27) implies:
% 136.03/20.09 | | | | | (28) op(e1, e1) = e2
% 136.03/20.09 | | | | |
% 136.03/20.09 | | | | | REF_CLOSE: (3), (6), (11), (28) are inconsistent by sub-proof #767.
% 136.03/20.09 | | | | |
% 136.03/20.09 | | | | Case 2:
% 136.03/20.09 | | | | |
% 136.03/20.09 | | | | | (29) all_57_14 = e2 & op(e0, e1) = e2
% 136.03/20.09 | | | | |
% 136.03/20.09 | | | | | REF_CLOSE: (7), (13), (29) are inconsistent by sub-proof #213.
% 136.03/20.09 | | | | |
% 136.03/20.09 | | | | End of split
% 136.03/20.09 | | | |
% 136.03/20.09 | | | End of split
% 136.03/20.09 | | |
% 136.03/20.09 | | End of split
% 136.03/20.09 | |
% 136.03/20.09 | Case 2:
% 136.03/20.09 | |
% 136.03/20.09 | | (30) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 136.03/20.09 | | e0)
% 136.03/20.09 | |
% 136.03/20.09 | | BETA: splitting (30) gives:
% 136.03/20.09 | |
% 136.03/20.09 | | Case 1:
% 136.03/20.09 | | |
% 136.03/20.09 | | | (31) all_57_8 = e0 & op(e1, e1) = e0
% 136.03/20.09 | | |
% 136.03/20.09 | | | ALPHA: (31) implies:
% 136.03/20.09 | | | (32) op(e1, e1) = e0
% 136.03/20.09 | | |
% 136.03/20.09 | | | REF_CLOSE: (6), (8), (10), (32) are inconsistent by sub-proof #753.
% 136.03/20.09 | | |
% 136.03/20.09 | | Case 2:
% 136.03/20.09 | | |
% 136.03/20.09 | | | (33) all_57_14 = e0 & op(e0, e1) = e0
% 136.03/20.09 | | |
% 136.03/20.09 | | | REF_CLOSE: (12), (13), (33) are inconsistent by sub-proof #483.
% 136.03/20.09 | | |
% 136.03/20.09 | | End of split
% 136.03/20.09 | |
% 136.03/20.09 | End of split
% 136.03/20.09 |
% 136.03/20.09 End of proof
% 136.03/20.09
% 136.03/20.09 Sub-proof #213 shows that the following formulas are inconsistent:
% 136.03/20.09 ----------------------------------------------------------------
% 136.03/20.09 (1) all_57_14 = e2 & op(e0, e1) = e2
% 136.03/20.09 (2) all_57_14 = e1
% 136.03/20.09 (3) ~ (e2 = e1)
% 136.03/20.09
% 136.03/20.09 Begin of proof
% 136.03/20.09 |
% 136.03/20.09 | ALPHA: (1) implies:
% 136.03/20.09 | (4) all_57_14 = e2
% 136.03/20.09 |
% 136.03/20.09 | COMBINE_EQS: (2), (4) imply:
% 136.03/20.09 | (5) e2 = e1
% 136.03/20.09 |
% 136.03/20.09 | REDUCE: (3), (5) imply:
% 136.03/20.09 | (6) $false
% 136.03/20.09 |
% 136.03/20.09 | CLOSE: (6) is inconsistent.
% 136.03/20.09 |
% 136.03/20.09 End of proof
% 136.03/20.09
% 136.03/20.09 Sub-proof #214 shows that the following formulas are inconsistent:
% 136.03/20.09 ----------------------------------------------------------------
% 136.03/20.09 (1) op(e3, e1) = all_28_0
% 136.03/20.09 (2) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 136.03/20.09 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 136.03/20.09 (3) op(e1, e1) = all_6_2
% 136.03/20.09 (4) all_57_5 = e1
% 136.03/20.09 (5) ~ (e2 = e0)
% 136.03/20.09 (6) op(e3, e1) = e1
% 136.03/20.09 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.09 (8) ~ (e2 = e1)
% 136.03/20.09 (9) ~ (e3 = e0)
% 136.03/20.09 (10) ~ (all_28_0 = e2)
% 136.03/20.09 (11) op(e1, e1) = e3
% 136.03/20.09 (12) ~ (all_6_2 = e2)
% 136.03/20.09 (13) ~ (e1 = e0)
% 136.03/20.09 (14) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 136.03/20.09 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 136.03/20.09
% 136.03/20.09 Begin of proof
% 136.03/20.09 |
% 136.03/20.09 | BETA: splitting (2) gives:
% 136.03/20.09 |
% 136.03/20.09 | Case 1:
% 136.03/20.09 | |
% 136.03/20.09 | | (15) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) =
% 136.03/20.09 | | e0)
% 136.03/20.09 | |
% 136.03/20.09 | | BETA: splitting (15) gives:
% 136.03/20.09 | |
% 136.03/20.09 | | Case 1:
% 136.03/20.09 | | |
% 136.03/20.09 | | | (16) all_57_4 = e0 & op(e3, e1) = e0
% 136.03/20.09 | | |
% 136.03/20.09 | | | ALPHA: (16) implies:
% 136.03/20.09 | | | (17) op(e3, e1) = e0
% 136.03/20.09 | | |
% 136.03/20.09 | | | REF_CLOSE: (6), (7), (13), (17) are inconsistent by sub-proof #343.
% 136.03/20.09 | | |
% 136.03/20.09 | | Case 2:
% 136.03/20.09 | | |
% 136.03/20.09 | | | (18) all_57_5 = e0 & op(e2, e1) = e0
% 136.03/20.09 | | |
% 136.03/20.09 | | | REF_CLOSE: (4), (13), (18) are inconsistent by sub-proof #461.
% 136.03/20.09 | | |
% 136.03/20.09 | | End of split
% 136.03/20.09 | |
% 136.03/20.09 | Case 2:
% 136.03/20.09 | |
% 136.03/20.09 | | (19) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 136.03/20.09 | | e0)
% 136.03/20.09 | |
% 136.03/20.09 | | BETA: splitting (19) gives:
% 136.03/20.09 | |
% 136.03/20.09 | | Case 1:
% 136.03/20.09 | | |
% 136.03/20.09 | | | (20) all_57_8 = e0 & op(e1, e1) = e0
% 136.03/20.09 | | |
% 136.03/20.09 | | | ALPHA: (20) implies:
% 136.03/20.09 | | | (21) op(e1, e1) = e0
% 136.03/20.09 | | |
% 136.03/20.09 | | | REF_CLOSE: (7), (9), (11), (21) are inconsistent by sub-proof #753.
% 136.03/20.09 | | |
% 136.03/20.09 | | Case 2:
% 136.03/20.09 | | |
% 136.03/20.09 | | | (22) all_57_14 = e0 & op(e0, e1) = e0
% 136.03/20.09 | | |
% 136.03/20.09 | | | ALPHA: (22) implies:
% 136.03/20.09 | | | (23) op(e0, e1) = e0
% 136.03/20.09 | | |
% 136.03/20.09 | | | BETA: splitting (14) gives:
% 136.03/20.09 | | |
% 136.03/20.09 | | | Case 1:
% 136.03/20.09 | | | |
% 136.03/20.09 | | | | (24) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1)
% 136.03/20.09 | | | | = e2)
% 136.03/20.09 | | | |
% 136.03/20.09 | | | | BETA: splitting (24) gives:
% 136.03/20.09 | | | |
% 136.03/20.09 | | | | Case 1:
% 136.03/20.09 | | | | |
% 136.03/20.09 | | | | | (25) all_57_4 = e2 & op(e3, e1) = e2
% 136.03/20.09 | | | | |
% 136.03/20.09 | | | | | REF_CLOSE: (1), (7), (10), (25) are inconsistent by sub-proof #218.
% 136.03/20.09 | | | | |
% 136.03/20.09 | | | | Case 2:
% 136.03/20.09 | | | | |
% 136.03/20.09 | | | | | (26) all_57_5 = e2 & op(e2, e1) = e2
% 136.03/20.09 | | | | |
% 136.03/20.09 | | | | | ALPHA: (26) implies:
% 136.03/20.09 | | | | | (27) all_57_5 = e2
% 136.03/20.09 | | | | |
% 136.03/20.09 | | | | | REF_CLOSE: (4), (8), (27) are inconsistent by sub-proof #418.
% 136.03/20.09 | | | | |
% 136.03/20.09 | | | | End of split
% 136.03/20.09 | | | |
% 136.03/20.09 | | | Case 2:
% 136.03/20.09 | | | |
% 136.03/20.09 | | | | (28) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1)
% 136.03/20.09 | | | | = e2)
% 136.03/20.09 | | | |
% 136.03/20.09 | | | | REF_CLOSE: (3), (5), (7), (12), (23), (28) are inconsistent by sub-proof
% 136.03/20.09 | | | | #659.
% 136.03/20.09 | | | |
% 136.03/20.09 | | | End of split
% 136.03/20.09 | | |
% 136.03/20.09 | | End of split
% 136.03/20.09 | |
% 136.03/20.09 | End of split
% 136.03/20.09 |
% 136.03/20.09 End of proof
% 136.03/20.09
% 136.03/20.09 Sub-proof #215 shows that the following formulas are inconsistent:
% 136.03/20.09 ----------------------------------------------------------------
% 136.03/20.09 (1) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 136.03/20.09 (2) ~ (all_52_4 = e0)
% 136.03/20.09 (3) op(e2, e2) = e0
% 136.03/20.09 (4) ~ (all_52_4 = all_52_12)
% 136.03/20.09 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.09 (6) ~ (e3 = e0)
% 136.03/20.09 (7) ~ (all_52_4 = e2)
% 136.03/20.09 (8) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.03/20.09 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 136.03/20.09 op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.03/20.09 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.03/20.09 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 &
% 136.03/20.09 all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~
% 136.03/20.09 (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3,
% 136.03/20.09 e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 136.03/20.09 op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 136.03/20.09 $i(all_56_17) & $i(all_56_25))
% 136.03/20.09 (9) all_54_1 = all_52_4
% 136.03/20.09 (10) op(e3, e0) = all_52_12
% 136.03/20.09 (11) ~ (all_52_4 = e1)
% 136.03/20.09
% 136.03/20.09 Begin of proof
% 136.03/20.09 |
% 136.03/20.09 | BETA: splitting (8) gives:
% 136.03/20.09 |
% 136.03/20.09 | Case 1:
% 136.03/20.09 | |
% 136.03/20.09 | | (12) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15
% 136.03/20.09 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) =
% 136.03/20.09 | | e0 & op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 136.03/20.09 | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 &
% 136.03/20.09 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31)
% 136.03/20.09 | |
% 136.03/20.09 | | REF_CLOSE: (1), (2), (4), (5), (7), (9), (10), (11), (12) are inconsistent
% 136.03/20.09 | | by sub-proof #217.
% 136.03/20.09 | |
% 136.03/20.09 | Case 2:
% 136.03/20.09 | |
% 136.03/20.09 | | (13) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.03/20.09 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.03/20.09 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.03/20.09 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1)
% 136.03/20.09 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)
% 136.03/20.09 | |
% 136.03/20.09 | | ALPHA: (13) implies:
% 136.03/20.09 | | (14) op(e2, e2) = e3
% 136.03/20.09 | |
% 136.03/20.09 | | REF_CLOSE: (3), (5), (6), (14) are inconsistent by sub-proof #641.
% 136.03/20.09 | |
% 136.03/20.09 | End of split
% 136.03/20.09 |
% 136.03/20.09 End of proof
% 136.03/20.09
% 136.03/20.09 Sub-proof #216 shows that the following formulas are inconsistent:
% 136.03/20.09 ----------------------------------------------------------------
% 136.03/20.09 (1) all_54_3 = all_52_12
% 136.03/20.09 (2) all_54_3 = e3
% 136.03/20.09 (3) ~ (all_52_12 = e3)
% 136.03/20.09
% 136.03/20.09 Begin of proof
% 136.03/20.09 |
% 136.03/20.09 | COMBINE_EQS: (1), (2) imply:
% 136.03/20.09 | (4) all_52_12 = e3
% 136.03/20.09 |
% 136.03/20.09 | SIMP: (4) implies:
% 136.03/20.09 | (5) all_52_12 = e3
% 136.03/20.09 |
% 136.03/20.09 | REDUCE: (3), (5) imply:
% 136.03/20.09 | (6) $false
% 136.03/20.09 |
% 136.03/20.09 | CLOSE: (6) is inconsistent.
% 136.03/20.09 |
% 136.03/20.09 End of proof
% 136.03/20.09
% 136.03/20.09 Sub-proof #217 shows that the following formulas are inconsistent:
% 136.03/20.09 ----------------------------------------------------------------
% 136.03/20.09 (1) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = e2)
% 136.03/20.09 & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3,
% 136.03/20.09 e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1)
% 136.03/20.09 = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 136.03/20.09 $i(all_56_23) & $i(all_56_31)
% 136.03/20.09 (2) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 136.03/20.09 (3) ~ (all_52_4 = e0)
% 136.03/20.09 (4) ~ (all_52_4 = all_52_12)
% 136.03/20.09 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.09 (6) ~ (all_52_4 = e2)
% 136.03/20.09 (7) all_54_1 = all_52_4
% 136.03/20.09 (8) op(e3, e0) = all_52_12
% 136.03/20.09 (9) ~ (all_52_4 = e1)
% 136.03/20.09
% 136.03/20.09 Begin of proof
% 136.03/20.09 |
% 136.03/20.09 | ALPHA: (1) implies:
% 136.03/20.09 | (10) op(e3, e0) = e3
% 136.03/20.09 |
% 136.03/20.09 | BETA: splitting (2) gives:
% 136.03/20.09 |
% 136.03/20.09 | Case 1:
% 136.03/20.09 | |
% 136.03/20.09 | | (11) all_54_1 = e3
% 136.03/20.09 | |
% 136.03/20.09 | | COMBINE_EQS: (7), (11) imply:
% 136.03/20.09 | | (12) all_52_4 = e3
% 136.03/20.09 | |
% 136.03/20.09 | | SIMP: (12) implies:
% 136.03/20.09 | | (13) all_52_4 = e3
% 136.03/20.09 | |
% 136.03/20.09 | | REDUCE: (4), (13) imply:
% 136.03/20.09 | | (14) ~ (all_52_12 = e3)
% 136.03/20.09 | |
% 136.03/20.09 | | SIMP: (14) implies:
% 136.03/20.09 | | (15) ~ (all_52_12 = e3)
% 136.03/20.09 | |
% 136.03/20.09 | | REF_CLOSE: (5), (8), (10), (15) are inconsistent by sub-proof #733.
% 136.03/20.09 | |
% 136.03/20.09 | Case 2:
% 136.03/20.09 | |
% 136.03/20.09 | | (16) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 136.03/20.09 | |
% 136.03/20.09 | | REF_CLOSE: (3), (6), (7), (9), (16) are inconsistent by sub-proof #701.
% 136.03/20.09 | |
% 136.03/20.09 | End of split
% 136.03/20.09 |
% 136.03/20.09 End of proof
% 136.03/20.09
% 136.03/20.09 Sub-proof #218 shows that the following formulas are inconsistent:
% 136.03/20.09 ----------------------------------------------------------------
% 136.03/20.09 (1) all_57_4 = e2 & op(e3, e1) = e2
% 136.03/20.09 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.09 (3) op(e3, e1) = all_28_0
% 136.03/20.09 (4) ~ (all_28_0 = e2)
% 136.03/20.09
% 136.03/20.09 Begin of proof
% 136.03/20.09 |
% 136.03/20.09 | ALPHA: (1) implies:
% 136.03/20.09 | (5) op(e3, e1) = e2
% 136.03/20.09 |
% 136.03/20.09 | GROUND_INST: instantiating (2) with e2, all_28_0, e1, e3, simplifying with
% 136.03/20.09 | (3), (5) gives:
% 136.03/20.09 | (6) all_28_0 = e2
% 136.03/20.09 |
% 136.03/20.09 | REDUCE: (4), (6) imply:
% 136.03/20.09 | (7) $false
% 136.03/20.09 |
% 136.03/20.09 | CLOSE: (7) is inconsistent.
% 136.03/20.09 |
% 136.03/20.09 End of proof
% 136.03/20.09
% 136.03/20.09 Sub-proof #219 shows that the following formulas are inconsistent:
% 136.03/20.09 ----------------------------------------------------------------
% 136.03/20.09 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.09 (2) op(e0, e3) = all_52_3
% 136.03/20.09 (3) op(e0, e3) = e0
% 136.03/20.09 (4) ~ (all_52_3 = e0)
% 136.03/20.09
% 136.03/20.09 Begin of proof
% 136.03/20.09 |
% 136.03/20.09 | GROUND_INST: instantiating (1) with all_52_3, e0, e3, e0, simplifying with
% 136.03/20.09 | (2), (3) gives:
% 136.03/20.09 | (5) all_52_3 = e0
% 136.03/20.09 |
% 136.03/20.09 | REDUCE: (4), (5) imply:
% 136.03/20.09 | (6) $false
% 136.03/20.09 |
% 136.03/20.09 | CLOSE: (6) is inconsistent.
% 136.03/20.09 |
% 136.03/20.09 End of proof
% 136.03/20.09
% 136.03/20.09 Sub-proof #220 shows that the following formulas are inconsistent:
% 136.03/20.09 ----------------------------------------------------------------
% 136.03/20.09 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.09 (2) op(e0, e0) = e1
% 136.03/20.09 (3) op(e0, e0) = e0
% 136.03/20.09 (4) ~ (e1 = e0)
% 136.03/20.09
% 136.03/20.09 Begin of proof
% 136.03/20.09 |
% 136.03/20.09 | GROUND_INST: instantiating (1) with e0, e1, e0, e0, simplifying with (2), (3)
% 136.03/20.09 | gives:
% 136.03/20.09 | (5) e1 = e0
% 136.03/20.09 |
% 136.03/20.09 | REDUCE: (4), (5) imply:
% 136.03/20.09 | (6) $false
% 136.03/20.09 |
% 136.03/20.09 | CLOSE: (6) is inconsistent.
% 136.03/20.09 |
% 136.03/20.09 End of proof
% 136.03/20.09
% 136.03/20.09 Sub-proof #221 shows that the following formulas are inconsistent:
% 136.03/20.09 ----------------------------------------------------------------
% 136.03/20.09 (1) all_57_14 = e1
% 136.03/20.10 (2) all_57_14 = e0
% 136.03/20.10 (3) ~ (e1 = e0)
% 136.03/20.10
% 136.03/20.10 Begin of proof
% 136.03/20.10 |
% 136.03/20.10 | COMBINE_EQS: (1), (2) imply:
% 136.03/20.10 | (4) e1 = e0
% 136.03/20.10 |
% 136.03/20.10 | SIMP: (4) implies:
% 136.03/20.10 | (5) e1 = e0
% 136.03/20.10 |
% 136.03/20.10 | REDUCE: (3), (5) imply:
% 136.03/20.10 | (6) $false
% 136.03/20.10 |
% 136.03/20.10 | CLOSE: (6) is inconsistent.
% 136.03/20.10 |
% 136.03/20.10 End of proof
% 136.03/20.10
% 136.03/20.10 Sub-proof #222 shows that the following formulas are inconsistent:
% 136.03/20.10 ----------------------------------------------------------------
% 136.03/20.10 (1) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 136.03/20.10 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 136.03/20.10 (2) op(e1, e1) = all_6_2
% 136.03/20.10 (3) ~ (all_52_4 = e0)
% 136.03/20.10 (4) ~ (e2 = e0)
% 136.03/20.10 (5) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 136.03/20.10 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 136.03/20.10 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.10 (7) ~ (e2 = e1)
% 136.03/20.10 (8) ~ (e3 = e0)
% 136.03/20.10 (9) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2)
% 136.03/20.10 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3,
% 136.03/20.10 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1)
% 136.03/20.10 = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 136.03/20.10 $i(all_56_19) & $i(all_56_27)
% 136.03/20.10 (10) ~ (e3 = e2)
% 136.03/20.10 (11) all_57_14 = e0
% 136.03/20.10 (12) ~ (all_52_12 = e0)
% 136.03/20.10 (13) ~ (all_6_2 = e2)
% 136.03/20.10 (14) op(e3, e2) = all_52_4
% 136.03/20.10 (15) op(e3, e0) = all_52_12
% 136.03/20.10 (16) op(e0, e1) = e0
% 136.03/20.10 (17) ~ (e3 = e1)
% 136.03/20.10 (18) ~ (e1 = e0)
% 136.03/20.10 (19) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 136.03/20.10 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 136.03/20.10 (20) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 136.03/20.10 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 136.03/20.10
% 136.03/20.10 Begin of proof
% 136.03/20.10 |
% 136.03/20.10 | ALPHA: (9) implies:
% 136.03/20.10 | (21) op(e3, e3) = e2
% 136.03/20.10 |
% 136.03/20.10 | BETA: splitting (5) gives:
% 136.03/20.10 |
% 136.03/20.10 | Case 1:
% 136.03/20.10 | |
% 136.03/20.10 | | (22) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 136.03/20.10 | | e0)
% 136.03/20.10 | |
% 136.03/20.10 | | REF_CLOSE: (3), (4), (6), (14), (21), (22) are inconsistent by sub-proof
% 136.03/20.10 | | #421.
% 136.03/20.10 | |
% 136.03/20.10 | Case 2:
% 136.03/20.10 | |
% 136.03/20.10 | | (23) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 136.03/20.10 | | e0)
% 136.03/20.10 | |
% 136.03/20.10 | | BETA: splitting (23) gives:
% 136.03/20.10 | |
% 136.03/20.10 | | Case 1:
% 136.03/20.10 | | |
% 136.03/20.10 | | | (24) all_57_4 = e0 & op(e3, e1) = e0
% 136.03/20.10 | | |
% 136.03/20.10 | | | ALPHA: (24) implies:
% 136.03/20.10 | | | (25) all_57_4 = e0
% 136.03/20.10 | | |
% 136.03/20.10 | | | BETA: splitting (20) gives:
% 136.03/20.10 | | |
% 136.03/20.10 | | | Case 1:
% 136.03/20.10 | | | |
% 136.03/20.10 | | | | (26) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1)
% 136.03/20.10 | | | | = e2)
% 136.03/20.10 | | | |
% 136.03/20.10 | | | | BETA: splitting (26) gives:
% 136.03/20.10 | | | |
% 136.03/20.10 | | | | Case 1:
% 136.03/20.10 | | | | |
% 136.03/20.10 | | | | | (27) all_57_4 = e2 & op(e3, e1) = e2
% 136.03/20.10 | | | | |
% 136.03/20.10 | | | | | REF_CLOSE: (4), (25), (27) are inconsistent by sub-proof #689.
% 136.03/20.10 | | | | |
% 136.03/20.10 | | | | Case 2:
% 136.03/20.10 | | | | |
% 136.03/20.10 | | | | | (28) all_57_5 = e2 & op(e2, e1) = e2
% 136.03/20.10 | | | | |
% 136.03/20.10 | | | | | ALPHA: (28) implies:
% 136.03/20.10 | | | | | (29) all_57_5 = e2
% 136.03/20.10 | | | | |
% 136.03/20.10 | | | | | BETA: splitting (19) gives:
% 136.03/20.10 | | | | |
% 136.03/20.10 | | | | | Case 1:
% 136.03/20.10 | | | | | |
% 136.03/20.10 | | | | | | (30) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2,
% 136.03/20.10 | | | | | | e1) = e3)
% 136.03/20.10 | | | | | |
% 136.03/20.10 | | | | | | BETA: splitting (30) gives:
% 136.03/20.10 | | | | | |
% 136.03/20.10 | | | | | | Case 1:
% 136.03/20.10 | | | | | | |
% 136.03/20.10 | | | | | | | (31) all_57_4 = e3 & op(e3, e1) = e3
% 136.03/20.10 | | | | | | |
% 136.03/20.10 | | | | | | | ALPHA: (31) implies:
% 136.03/20.10 | | | | | | | (32) all_57_4 = e3
% 136.03/20.10 | | | | | | |
% 136.03/20.10 | | | | | | | COMBINE_EQS: (25), (32) imply:
% 136.03/20.10 | | | | | | | (33) e3 = e0
% 136.03/20.10 | | | | | | |
% 136.03/20.10 | | | | | | | REDUCE: (8), (33) imply:
% 136.03/20.10 | | | | | | | (34) $false
% 136.03/20.10 | | | | | | |
% 136.03/20.10 | | | | | | | CLOSE: (34) is inconsistent.
% 136.03/20.10 | | | | | | |
% 136.03/20.10 | | | | | | Case 2:
% 136.03/20.10 | | | | | | |
% 136.03/20.10 | | | | | | | (35) all_57_5 = e3 & op(e2, e1) = e3
% 136.03/20.10 | | | | | | |
% 136.03/20.10 | | | | | | | ALPHA: (35) implies:
% 136.03/20.10 | | | | | | | (36) all_57_5 = e3
% 136.03/20.10 | | | | | | |
% 136.03/20.10 | | | | | | | REF_CLOSE: (10), (29), (36) are inconsistent by sub-proof #501.
% 136.03/20.10 | | | | | | |
% 136.03/20.10 | | | | | | End of split
% 136.03/20.10 | | | | | |
% 136.03/20.10 | | | | | Case 2:
% 136.03/20.10 | | | | | |
% 136.03/20.10 | | | | | | (37) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0,
% 136.03/20.10 | | | | | | e1) = e3)
% 136.03/20.10 | | | | | |
% 136.03/20.10 | | | | | | BETA: splitting (37) gives:
% 136.03/20.10 | | | | | |
% 136.03/20.10 | | | | | | Case 1:
% 136.03/20.10 | | | | | | |
% 136.03/20.10 | | | | | | | (38) all_57_8 = e3 & op(e1, e1) = e3
% 136.03/20.10 | | | | | | |
% 136.03/20.10 | | | | | | | ALPHA: (38) implies:
% 136.03/20.10 | | | | | | | (39) op(e1, e1) = e3
% 136.03/20.10 | | | | | | |
% 136.03/20.10 | | | | | | | REF_CLOSE: (1), (2), (6), (7), (11), (17), (18), (25), (29), (39)
% 136.03/20.10 | | | | | | | are inconsistent by sub-proof #230.
% 136.03/20.10 | | | | | | |
% 136.03/20.10 | | | | | | Case 2:
% 136.03/20.10 | | | | | | |
% 136.03/20.10 | | | | | | | (40) all_57_14 = e3 & op(e0, e1) = e3
% 136.03/20.10 | | | | | | |
% 136.03/20.10 | | | | | | | ALPHA: (40) implies:
% 136.03/20.10 | | | | | | | (41) all_57_14 = e3
% 136.03/20.10 | | | | | | |
% 136.03/20.10 | | | | | | | REF_CLOSE: (8), (11), (41) are inconsistent by sub-proof #400.
% 136.03/20.10 | | | | | | |
% 136.03/20.10 | | | | | | End of split
% 136.03/20.10 | | | | | |
% 136.03/20.10 | | | | | End of split
% 136.03/20.10 | | | | |
% 136.03/20.10 | | | | End of split
% 136.03/20.10 | | | |
% 136.03/20.10 | | | Case 2:
% 136.03/20.10 | | | |
% 136.03/20.10 | | | | (42) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1)
% 136.03/20.10 | | | | = e2)
% 136.03/20.10 | | | |
% 136.03/20.10 | | | | REF_CLOSE: (2), (4), (6), (13), (16), (42) are inconsistent by sub-proof
% 136.03/20.10 | | | | #659.
% 136.03/20.10 | | | |
% 136.03/20.10 | | | End of split
% 136.03/20.10 | | |
% 136.03/20.10 | | Case 2:
% 136.03/20.10 | | |
% 136.03/20.10 | | | (43) all_57_9 = e0 & op(e3, e0) = e0
% 136.03/20.10 | | |
% 136.03/20.10 | | | REF_CLOSE: (6), (12), (15), (43) are inconsistent by sub-proof #618.
% 136.03/20.10 | | |
% 136.03/20.10 | | End of split
% 136.03/20.10 | |
% 136.03/20.10 | End of split
% 136.03/20.10 |
% 136.03/20.10 End of proof
% 136.03/20.10
% 136.03/20.10 Sub-proof #223 shows that the following formulas are inconsistent:
% 136.03/20.10 ----------------------------------------------------------------
% 136.03/20.10 (1) op(e0, e0) = e0
% 136.03/20.10 (2) op(e2, e2) = e0
% 136.03/20.10 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.10 (4) ~ (e3 = e0)
% 136.03/20.10 (5) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.03/20.10 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 136.03/20.10 op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.03/20.10 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.03/20.10 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 &
% 136.03/20.10 all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~
% 136.03/20.10 (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3,
% 136.03/20.10 e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 136.03/20.10 op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 136.03/20.10 $i(all_56_17) & $i(all_56_25))
% 136.03/20.10
% 136.03/20.10 Begin of proof
% 136.03/20.10 |
% 136.03/20.10 | BETA: splitting (5) gives:
% 136.03/20.10 |
% 136.03/20.10 | Case 1:
% 136.03/20.10 | |
% 136.03/20.10 | | (6) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.03/20.10 | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 136.03/20.10 | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.03/20.10 | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.03/20.10 | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)
% 136.03/20.10 | |
% 136.03/20.10 | | ALPHA: (6) implies:
% 136.03/20.10 | | (7) ~ (all_56_31 = e0)
% 136.03/20.10 | | (8) op(e0, e0) = all_56_31
% 136.03/20.10 | |
% 136.03/20.10 | | REF_CLOSE: (1), (3), (7), (8) are inconsistent by sub-proof #712.
% 136.03/20.10 | |
% 136.03/20.10 | Case 2:
% 136.03/20.10 | |
% 136.03/20.10 | | (9) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.03/20.10 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.03/20.10 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.03/20.10 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1)
% 136.03/20.10 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)
% 136.03/20.10 | |
% 136.03/20.10 | | ALPHA: (9) implies:
% 136.03/20.10 | | (10) op(e2, e2) = e3
% 136.03/20.10 | |
% 136.03/20.10 | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #641.
% 136.03/20.10 | |
% 136.03/20.10 | End of split
% 136.03/20.10 |
% 136.03/20.10 End of proof
% 136.03/20.10
% 136.03/20.10 Sub-proof #224 shows that the following formulas are inconsistent:
% 136.03/20.10 ----------------------------------------------------------------
% 136.03/20.10 (1) all_57_4 = e0 & op(e3, e1) = e0
% 136.03/20.10 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.10 (3) op(e3, e1) = all_52_8
% 136.03/20.10 (4) ~ (all_52_8 = e0)
% 136.03/20.10
% 136.03/20.10 Begin of proof
% 136.03/20.10 |
% 136.03/20.10 | ALPHA: (1) implies:
% 136.03/20.10 | (5) op(e3, e1) = e0
% 136.03/20.10 |
% 136.03/20.10 | GROUND_INST: instantiating (2) with all_52_8, e0, e1, e3, simplifying with
% 136.03/20.10 | (3), (5) gives:
% 136.03/20.10 | (6) all_52_8 = e0
% 136.03/20.10 |
% 136.03/20.10 | REDUCE: (4), (6) imply:
% 136.03/20.10 | (7) $false
% 136.03/20.10 |
% 136.03/20.10 | CLOSE: (7) is inconsistent.
% 136.03/20.10 |
% 136.03/20.10 End of proof
% 136.03/20.10
% 136.03/20.10 Sub-proof #225 shows that the following formulas are inconsistent:
% 136.03/20.10 ----------------------------------------------------------------
% 136.03/20.10 (1) all_57_2 = e0 & op(e2, e3) = e0
% 136.03/20.10 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.10 (3) op(e2, e3) = all_52_1
% 136.03/20.10 (4) ~ (all_52_1 = e0)
% 136.03/20.10
% 136.03/20.10 Begin of proof
% 136.03/20.10 |
% 136.03/20.10 | ALPHA: (1) implies:
% 136.03/20.10 | (5) op(e2, e3) = e0
% 136.03/20.10 |
% 136.03/20.10 | GROUND_INST: instantiating (2) with all_52_1, e0, e3, e2, simplifying with
% 136.03/20.10 | (3), (5) gives:
% 136.03/20.10 | (6) all_52_1 = e0
% 136.03/20.10 |
% 136.03/20.10 | REDUCE: (4), (6) imply:
% 136.03/20.10 | (7) $false
% 136.03/20.10 |
% 136.03/20.10 | CLOSE: (7) is inconsistent.
% 136.03/20.10 |
% 136.03/20.10 End of proof
% 136.03/20.10
% 136.03/20.10 Sub-proof #226 shows that the following formulas are inconsistent:
% 136.03/20.10 ----------------------------------------------------------------
% 136.03/20.10 (1) op(e2, e2) = all_8_2
% 136.03/20.10 (2) op(e1, e1) = all_6_2
% 136.03/20.10 (3) op(e0, e0) = e3
% 136.03/20.10 (4) ~ (all_8_2 = e1)
% 136.03/20.10 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.10 (6) ~ (all_46_2 = e0) | ( ~ (all_46_0 = e2) & op(e0, e1) = all_46_0 &
% 136.03/20.10 $i(all_46_0)) | ( ~ (all_46_1 = e3) & op(e0, e0) = all_46_1 &
% 136.03/20.10 $i(all_46_1))
% 136.03/20.10 (7) ~ (all_52_11 = all_6_2)
% 136.03/20.10 (8) op(e0, e1) = all_52_11
% 136.03/20.10 (9) op(e0, e2) = all_52_7
% 136.03/20.10 (10) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 136.03/20.10 (11) ~ (all_52_11 = e3)
% 136.03/20.10 (12) ~ (all_6_2 = e2)
% 136.03/20.10 (13) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 136.03/20.10 (14) all_54_5 = all_8_2
% 136.03/20.10 (15) op(e0, e3) = all_52_3
% 136.03/20.10 (16) all_46_2 = all_6_2
% 136.03/20.10 (17) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 136.03/20.10 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 136.03/20.10 all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 136.03/20.10 e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 136.03/20.10 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 136.03/20.10 all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~
% 136.03/20.10 (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 136.03/20.10 (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 &
% 136.03/20.10 op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0
% 136.03/20.10 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.03/20.10 (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 136.03/20.10 (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.03/20.10 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.03/20.10 all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.03/20.10 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.03/20.10 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.03/20.10 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.03/20.10 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 136.03/20.10 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 136.03/20.10 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 136.03/20.10 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 136.03/20.10 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 136.03/20.10 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 136.03/20.10 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.03/20.10 $i(all_56_29))))
% 136.03/20.10 (18) all_54_14 = all_52_11
% 136.03/20.10 (19) ~ (e3 = e1)
% 136.03/20.10 (20) ~ (all_52_7 = all_8_2)
% 136.03/20.10 (21) ~ (all_8_2 = e3)
% 136.03/20.10 (22) ~ (all_52_3 = e0)
% 136.03/20.10
% 136.03/20.10 Begin of proof
% 136.03/20.10 |
% 136.03/20.10 | BETA: splitting (17) gives:
% 136.03/20.10 |
% 136.03/20.10 | Case 1:
% 136.03/20.10 | |
% 136.03/20.10 | | (23) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11
% 136.03/20.10 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 136.03/20.10 | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 136.03/20.10 | | e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3)
% 136.03/20.10 | | & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)
% 136.03/20.10 | |
% 136.03/20.10 | | ALPHA: (23) implies:
% 136.03/20.10 | | (24) op(e1, e1) = e2
% 136.03/20.10 | |
% 136.03/20.10 | | REF_CLOSE: (2), (5), (12), (24) are inconsistent by sub-proof #767.
% 136.03/20.10 | |
% 136.03/20.10 | Case 2:
% 136.03/20.10 | |
% 136.03/20.10 | | (25) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31
% 136.03/20.10 | | = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 136.03/20.10 | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2)
% 136.03/20.10 | | = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 136.03/20.10 | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 136.03/20.10 | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3
% 136.03/20.10 | | = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 136.03/20.10 | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 136.03/20.10 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 136.03/20.10 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 136.03/20.10 | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7
% 136.03/20.10 | | = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 136.03/20.10 | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 136.03/20.10 | | e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) =
% 136.03/20.10 | | all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 136.03/20.10 | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 136.03/20.10 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 136.03/20.10 | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.03/20.10 | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 136.03/20.10 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)))
% 136.03/20.10 | |
% 136.03/20.10 | | ALPHA: (25) implies:
% 136.03/20.10 | | (26) op(e0, e0) = all_56_31
% 136.03/20.10 | | (27) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 136.03/20.10 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.03/20.10 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.03/20.10 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9)
% 136.03/20.10 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 136.03/20.10 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 136.03/20.10 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 136.03/20.10 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 136.03/20.10 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 136.03/20.10 | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 136.03/20.10 | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31
% 136.03/20.10 | | = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 136.03/20.10 | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 136.03/20.10 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 &
% 136.03/20.10 | | all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.03/20.10 | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 136.03/20.10 | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 136.03/20.10 | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 136.03/20.10 | | $i(all_56_21) & $i(all_56_29))
% 136.03/20.10 | |
% 136.03/20.10 | | GROUND_INST: instantiating (5) with e3, all_56_31, e0, e0, simplifying with
% 136.03/20.10 | | (3), (26) gives:
% 136.03/20.10 | | (28) all_56_31 = e3
% 136.03/20.10 | |
% 136.03/20.10 | | BETA: splitting (27) gives:
% 136.03/20.10 | |
% 136.03/20.10 | | Case 1:
% 136.03/20.10 | | |
% 136.03/20.10 | | | (29) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 136.03/20.10 | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 136.03/20.10 | | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) =
% 136.03/20.10 | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 136.03/20.10 | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.03/20.10 | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 136.03/20.10 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.03/20.10 | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.03/20.10 | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.03/20.10 | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27))
% 136.03/20.10 | | |
% 136.03/20.10 | | | BETA: splitting (29) gives:
% 136.03/20.10 | | |
% 136.03/20.10 | | | Case 1:
% 136.03/20.10 | | | |
% 136.03/20.10 | | | | (30) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 136.03/20.10 | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 136.03/20.10 | | | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) =
% 136.03/20.10 | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 136.03/20.10 | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)
% 136.03/20.10 | | | |
% 136.03/20.10 | | | | ALPHA: (30) implies:
% 136.03/20.10 | | | | (31) op(e0, e3) = e0
% 136.03/20.10 | | | |
% 136.03/20.10 | | | | GROUND_INST: instantiating (5) with all_52_3, e0, e3, e0, simplifying
% 136.03/20.10 | | | | with (15), (31) gives:
% 136.03/20.10 | | | | (32) all_52_3 = e0
% 136.03/20.10 | | | |
% 136.03/20.10 | | | | REDUCE: (22), (32) imply:
% 136.03/20.10 | | | | (33) $false
% 136.03/20.10 | | | |
% 136.03/20.10 | | | | CLOSE: (33) is inconsistent.
% 136.03/20.10 | | | |
% 136.03/20.10 | | | Case 2:
% 136.03/20.10 | | | |
% 136.03/20.10 | | | | (34) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 136.03/20.10 | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.03/20.10 | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.03/20.10 | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.03/20.10 | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)
% 136.03/20.10 | | | |
% 136.03/20.10 | | | | ALPHA: (34) implies:
% 136.03/20.10 | | | | (35) ~ (all_56_11 = e2)
% 136.03/20.10 | | | | (36) op(e0, e2) = e0
% 136.03/20.10 | | | | (37) op(e2, e2) = all_56_11
% 136.03/20.10 | | | |
% 136.03/20.10 | | | | REF_CLOSE: (1), (4), (5), (9), (13), (14), (20), (21), (35), (36), (37)
% 136.03/20.10 | | | | are inconsistent by sub-proof #227.
% 136.03/20.10 | | | |
% 136.03/20.10 | | | End of split
% 136.03/20.10 | | |
% 136.03/20.10 | | Case 2:
% 136.03/20.10 | | |
% 136.03/20.10 | | | (38) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.03/20.10 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.03/20.10 | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 136.03/20.10 | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 136.03/20.10 | | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 =
% 136.03/20.10 | | | e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 136.03/20.10 | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 136.03/20.10 | | | = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 136.03/20.10 | | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.03/20.10 | | | $i(all_56_29))
% 136.03/20.10 | | |
% 136.03/20.10 | | | BETA: splitting (38) gives:
% 136.03/20.10 | | |
% 136.03/20.10 | | | Case 1:
% 136.03/20.10 | | | |
% 136.03/20.10 | | | | (39) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.03/20.10 | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.03/20.10 | | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 136.03/20.10 | | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 136.03/20.10 | | | | $i(all_56_15) & $i(all_56_23)
% 136.03/20.10 | | | |
% 136.03/20.10 | | | | ALPHA: (39) implies:
% 136.03/20.10 | | | | (40) ~ (all_56_23 = e1)
% 136.03/20.10 | | | | (41) op(e0, e1) = all_56_23
% 136.03/20.10 | | | | (42) op(e1, e1) = e0
% 136.03/20.10 | | | |
% 136.03/20.10 | | | | GROUND_INST: instantiating (5) with all_52_11, all_56_23, e1, e0,
% 136.03/20.10 | | | | simplifying with (8), (41) gives:
% 136.03/20.10 | | | | (43) all_56_23 = all_52_11
% 136.03/20.10 | | | |
% 136.03/20.10 | | | | REF_CLOSE: (2), (3), (5), (6), (7), (10), (11), (16), (18), (40), (41),
% 136.03/20.10 | | | | (42), (43) are inconsistent by sub-proof #608.
% 136.03/20.10 | | | |
% 136.03/20.10 | | | Case 2:
% 136.03/20.10 | | | |
% 136.03/20.10 | | | | (44) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 136.03/20.10 | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 136.03/20.10 | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.03/20.10 | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 136.03/20.10 | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 136.03/20.10 | | | |
% 136.03/20.10 | | | | REF_CLOSE: (19), (28), (44) are inconsistent by sub-proof #752.
% 136.03/20.10 | | | |
% 136.03/20.10 | | | End of split
% 136.03/20.10 | | |
% 136.03/20.10 | | End of split
% 136.03/20.10 | |
% 136.03/20.10 | End of split
% 136.03/20.10 |
% 136.03/20.10 End of proof
% 136.03/20.10
% 136.03/20.10 Sub-proof #227 shows that the following formulas are inconsistent:
% 136.03/20.10 ----------------------------------------------------------------
% 136.03/20.10 (1) op(e2, e2) = all_8_2
% 136.03/20.10 (2) ~ (all_8_2 = e1)
% 136.03/20.10 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.10 (4) op(e0, e2) = all_52_7
% 136.03/20.10 (5) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 136.03/20.10 (6) all_54_5 = all_8_2
% 136.03/20.10 (7) op(e0, e2) = e0
% 136.03/20.10 (8) ~ (all_56_11 = e2)
% 136.03/20.10 (9) ~ (all_52_7 = all_8_2)
% 136.03/20.10 (10) ~ (all_8_2 = e3)
% 136.03/20.10 (11) op(e2, e2) = all_56_11
% 136.03/20.10
% 136.03/20.10 Begin of proof
% 136.03/20.10 |
% 136.03/20.10 | GROUND_INST: instantiating (3) with all_52_7, e0, e2, e0, simplifying with
% 136.03/20.10 | (4), (7) gives:
% 136.03/20.10 | (12) all_52_7 = e0
% 136.03/20.10 |
% 136.03/20.10 | GROUND_INST: instantiating (3) with all_8_2, all_56_11, e2, e2, simplifying
% 136.03/20.10 | with (1), (11) gives:
% 136.03/20.10 | (13) all_56_11 = all_8_2
% 136.03/20.10 |
% 136.03/20.10 | REDUCE: (8), (13) imply:
% 136.03/20.10 | (14) ~ (all_8_2 = e2)
% 136.03/20.10 |
% 136.03/20.10 | REDUCE: (9), (12) imply:
% 136.03/20.10 | (15) ~ (all_8_2 = e0)
% 136.03/20.10 |
% 136.03/20.10 | SIMP: (15) implies:
% 136.03/20.10 | (16) ~ (all_8_2 = e0)
% 136.03/20.10 |
% 136.03/20.10 | BETA: splitting (5) gives:
% 136.03/20.10 |
% 136.03/20.10 | Case 1:
% 136.03/20.10 | |
% 136.03/20.10 | | (17) all_54_5 = e3
% 136.03/20.10 | |
% 136.03/20.10 | | COMBINE_EQS: (6), (17) imply:
% 136.03/20.10 | | (18) all_8_2 = e3
% 136.03/20.10 | |
% 136.03/20.10 | | REDUCE: (10), (18) imply:
% 136.03/20.10 | | (19) $false
% 136.03/20.10 | |
% 136.03/20.10 | | CLOSE: (19) is inconsistent.
% 136.03/20.10 | |
% 136.03/20.10 | Case 2:
% 136.03/20.10 | |
% 136.03/20.10 | | (20) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 136.03/20.10 | |
% 136.03/20.10 | | BETA: splitting (20) gives:
% 136.03/20.10 | |
% 136.03/20.10 | | Case 1:
% 136.03/20.10 | | |
% 136.03/20.10 | | | (21) all_54_5 = e2
% 136.03/20.10 | | |
% 136.03/20.10 | | | COMBINE_EQS: (6), (21) imply:
% 136.03/20.10 | | | (22) all_8_2 = e2
% 136.03/20.10 | | |
% 136.03/20.10 | | | REDUCE: (14), (22) imply:
% 136.03/20.10 | | | (23) $false
% 136.03/20.10 | | |
% 136.03/20.10 | | | CLOSE: (23) is inconsistent.
% 136.03/20.10 | | |
% 136.03/20.10 | | Case 2:
% 136.03/20.10 | | |
% 136.03/20.10 | | | (24) all_54_5 = e1 | all_54_5 = e0
% 136.03/20.10 | | |
% 136.03/20.10 | | | REF_CLOSE: (2), (6), (16), (24) are inconsistent by sub-proof #624.
% 136.03/20.10 | | |
% 136.03/20.10 | | End of split
% 136.03/20.10 | |
% 136.03/20.10 | End of split
% 136.03/20.10 |
% 136.03/20.10 End of proof
% 136.03/20.10
% 136.03/20.10 Sub-proof #228 shows that the following formulas are inconsistent:
% 136.03/20.10 ----------------------------------------------------------------
% 136.03/20.10 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.10 (2) op(e2, e2) = all_8_2
% 136.03/20.10 (3) op(e2, e2) = e3
% 136.03/20.10 (4) ~ (all_8_2 = e3)
% 136.03/20.10
% 136.03/20.10 Begin of proof
% 136.03/20.10 |
% 136.03/20.10 | GROUND_INST: instantiating (1) with all_8_2, e3, e2, e2, simplifying with (2),
% 136.03/20.10 | (3) gives:
% 136.03/20.10 | (5) all_8_2 = e3
% 136.03/20.10 |
% 136.03/20.10 | REDUCE: (4), (5) imply:
% 136.03/20.10 | (6) $false
% 136.03/20.10 |
% 136.03/20.10 | CLOSE: (6) is inconsistent.
% 136.03/20.10 |
% 136.03/20.10 End of proof
% 136.03/20.10
% 136.03/20.10 Sub-proof #229 shows that the following formulas are inconsistent:
% 136.03/20.10 ----------------------------------------------------------------
% 136.03/20.10 (1) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2)
% 136.03/20.10 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3,
% 136.03/20.10 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 136.03/20.10 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 136.03/20.10 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 136.03/20.10 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.03/20.10 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) =
% 136.03/20.10 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.03/20.10 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 136.03/20.10 $i(all_56_21) & $i(all_56_29))
% 136.03/20.10 (2) ~ (e2 = e0)
% 136.03/20.10 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.10 (4) op(e3, e3) = e0
% 136.03/20.10 (5) ~ (e1 = e0)
% 136.03/20.10
% 136.03/20.10 Begin of proof
% 136.03/20.10 |
% 136.03/20.10 | BETA: splitting (1) gives:
% 136.03/20.10 |
% 136.03/20.10 | Case 1:
% 136.03/20.10 | |
% 136.03/20.10 | | (6) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 136.03/20.10 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 136.03/20.10 | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 136.03/20.10 | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 136.03/20.10 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)
% 136.03/20.10 | |
% 136.03/20.10 | | ALPHA: (6) implies:
% 136.03/20.10 | | (7) op(e3, e3) = e2
% 136.03/20.10 | |
% 136.03/20.10 | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #495.
% 136.03/20.10 | |
% 136.03/20.10 | Case 2:
% 136.03/20.10 | |
% 136.03/20.10 | | (8) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 136.03/20.10 | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 136.03/20.10 | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 136.03/20.10 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 136.03/20.10 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 136.03/20.10 | |
% 136.03/20.10 | | ALPHA: (8) implies:
% 136.03/20.10 | | (9) op(e3, e3) = e1
% 136.03/20.10 | |
% 136.03/20.10 | | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #717.
% 136.03/20.10 | |
% 136.03/20.10 | End of split
% 136.03/20.10 |
% 136.03/20.10 End of proof
% 136.03/20.10
% 136.03/20.10 Sub-proof #230 shows that the following formulas are inconsistent:
% 136.03/20.10 ----------------------------------------------------------------
% 136.03/20.10 (1) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 136.03/20.10 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 136.03/20.10 (2) op(e1, e1) = all_6_2
% 136.03/20.10 (3) all_57_5 = e2
% 136.03/20.11 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.11 (5) ~ (e2 = e1)
% 136.03/20.11 (6) all_57_14 = e0
% 136.03/20.11 (7) op(e1, e1) = e3
% 136.03/20.11 (8) all_57_4 = e0
% 136.03/20.11 (9) ~ (e3 = e1)
% 136.03/20.11 (10) ~ (e1 = e0)
% 136.03/20.11
% 136.03/20.11 Begin of proof
% 136.03/20.11 |
% 136.03/20.11 | BETA: splitting (1) gives:
% 136.03/20.11 |
% 136.03/20.11 | Case 1:
% 136.03/20.11 | |
% 136.03/20.11 | | (11) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) =
% 136.03/20.11 | | e1)
% 136.03/20.11 | |
% 136.03/20.11 | | BETA: splitting (11) gives:
% 136.03/20.11 | |
% 136.03/20.11 | | Case 1:
% 136.03/20.11 | | |
% 136.03/20.11 | | | (12) all_57_4 = e1 & op(e3, e1) = e1
% 136.03/20.11 | | |
% 136.03/20.11 | | | REF_CLOSE: (8), (10), (12) are inconsistent by sub-proof #419.
% 136.03/20.11 | | |
% 136.03/20.11 | | Case 2:
% 136.03/20.11 | | |
% 136.03/20.11 | | | (13) all_57_5 = e1 & op(e2, e1) = e1
% 136.03/20.11 | | |
% 136.03/20.11 | | | REF_CLOSE: (3), (5), (13) are inconsistent by sub-proof #500.
% 136.03/20.11 | | |
% 136.03/20.11 | | End of split
% 136.03/20.11 | |
% 136.03/20.11 | Case 2:
% 136.03/20.11 | |
% 136.03/20.11 | | (14) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) =
% 136.03/20.11 | | e1)
% 136.03/20.11 | |
% 136.03/20.11 | | BETA: splitting (14) gives:
% 136.03/20.11 | |
% 136.03/20.11 | | Case 1:
% 136.03/20.11 | | |
% 136.03/20.11 | | | (15) all_57_8 = e1 & op(e1, e1) = e1
% 136.03/20.11 | | |
% 136.03/20.11 | | | ALPHA: (15) implies:
% 136.03/20.11 | | | (16) op(e1, e1) = e1
% 136.03/20.11 | | |
% 136.03/20.11 | | | REF_CLOSE: (2), (4), (7), (9), (16) are inconsistent by sub-proof #662.
% 136.03/20.11 | | |
% 136.03/20.11 | | Case 2:
% 136.03/20.11 | | |
% 136.03/20.11 | | | (17) all_57_14 = e1 & op(e0, e1) = e1
% 136.03/20.11 | | |
% 136.03/20.11 | | | REF_CLOSE: (6), (10), (17) are inconsistent by sub-proof #231.
% 136.03/20.11 | | |
% 136.03/20.11 | | End of split
% 136.03/20.11 | |
% 136.03/20.11 | End of split
% 136.03/20.11 |
% 136.03/20.11 End of proof
% 136.03/20.11
% 136.03/20.11 Sub-proof #231 shows that the following formulas are inconsistent:
% 136.03/20.11 ----------------------------------------------------------------
% 136.03/20.11 (1) all_57_14 = e1 & op(e0, e1) = e1
% 136.03/20.11 (2) all_57_14 = e0
% 136.03/20.11 (3) ~ (e1 = e0)
% 136.03/20.11
% 136.03/20.11 Begin of proof
% 136.03/20.11 |
% 136.03/20.11 | ALPHA: (1) implies:
% 136.03/20.11 | (4) all_57_14 = e1
% 136.03/20.11 |
% 136.03/20.11 | COMBINE_EQS: (2), (4) imply:
% 136.03/20.11 | (5) e1 = e0
% 136.03/20.11 |
% 136.03/20.11 | REDUCE: (3), (5) imply:
% 136.03/20.11 | (6) $false
% 136.03/20.11 |
% 136.03/20.11 | CLOSE: (6) is inconsistent.
% 136.03/20.11 |
% 136.03/20.11 End of proof
% 136.03/20.11
% 136.03/20.11 Sub-proof #232 shows that the following formulas are inconsistent:
% 136.03/20.11 ----------------------------------------------------------------
% 136.03/20.11 (1) ~ (all_52_11 = e1)
% 136.03/20.11 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.11 (3) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 136.03/20.11 (4) ~ (all_4_2 = e2)
% 136.03/20.11 (5) ~ (all_52_11 = all_4_2)
% 136.03/20.11 (6) op(e0, e1) = all_52_11
% 136.03/20.11 (7) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 136.03/20.11 (8) ~ (all_52_11 = e3)
% 136.03/20.11 (9) ~ (all_4_2 = e1)
% 136.03/20.11 (10) all_54_15 = all_4_2
% 136.03/20.11 (11) op(e0, e1) = e0
% 136.03/20.11 (12) all_54_14 = all_52_11
% 136.03/20.11
% 136.03/20.11 Begin of proof
% 136.03/20.11 |
% 136.03/20.11 | BETA: splitting (3) gives:
% 136.03/20.11 |
% 136.03/20.11 | Case 1:
% 136.03/20.11 | |
% 136.03/20.11 | | (13) all_54_15 = e2
% 136.03/20.11 | |
% 136.03/20.11 | | REF_CLOSE: (4), (10), (13) are inconsistent by sub-proof #748.
% 136.03/20.11 | |
% 136.03/20.11 | Case 2:
% 136.03/20.11 | |
% 136.03/20.11 | | (14) all_54_15 = e1 | all_54_15 = e0
% 136.03/20.11 | |
% 136.03/20.11 | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (11), (12), (14) are
% 136.03/20.11 | | inconsistent by sub-proof #233.
% 136.03/20.11 | |
% 136.03/20.11 | End of split
% 136.03/20.11 |
% 136.03/20.11 End of proof
% 136.03/20.11
% 136.03/20.11 Sub-proof #233 shows that the following formulas are inconsistent:
% 136.03/20.11 ----------------------------------------------------------------
% 136.03/20.11 (1) ~ (all_52_11 = e1)
% 136.03/20.11 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.11 (3) ~ (all_52_11 = all_4_2)
% 136.03/20.11 (4) op(e0, e1) = all_52_11
% 136.03/20.11 (5) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 136.03/20.11 (6) ~ (all_52_11 = e3)
% 136.03/20.11 (7) ~ (all_4_2 = e1)
% 136.03/20.11 (8) all_54_15 = all_4_2
% 136.03/20.11 (9) all_54_15 = e1 | all_54_15 = e0
% 136.03/20.11 (10) op(e0, e1) = e0
% 136.03/20.11 (11) all_54_14 = all_52_11
% 136.03/20.11
% 136.03/20.11 Begin of proof
% 136.03/20.11 |
% 136.03/20.11 | BETA: splitting (9) gives:
% 136.03/20.11 |
% 136.03/20.11 | Case 1:
% 136.03/20.11 | |
% 136.03/20.11 | | (12) all_54_15 = e1
% 136.03/20.11 | |
% 136.03/20.11 | | REF_CLOSE: (7), (8), (12) are inconsistent by sub-proof #747.
% 136.03/20.11 | |
% 136.03/20.11 | Case 2:
% 136.03/20.11 | |
% 136.03/20.11 | | (13) all_54_15 = e0
% 136.03/20.11 | |
% 136.03/20.11 | | COMBINE_EQS: (8), (13) imply:
% 136.03/20.11 | | (14) all_4_2 = e0
% 136.03/20.11 | |
% 136.03/20.11 | | SIMP: (14) implies:
% 136.03/20.11 | | (15) all_4_2 = e0
% 136.03/20.11 | |
% 136.03/20.11 | | REDUCE: (3), (15) imply:
% 136.03/20.11 | | (16) ~ (all_52_11 = e0)
% 136.03/20.11 | |
% 136.03/20.11 | | BETA: splitting (5) gives:
% 136.03/20.11 | |
% 136.03/20.11 | | Case 1:
% 136.03/20.11 | | |
% 136.03/20.11 | | | (17) all_54_14 = e3
% 136.03/20.11 | | |
% 136.03/20.11 | | | REF_CLOSE: (6), (11), (17) are inconsistent by sub-proof #760.
% 136.03/20.11 | | |
% 136.03/20.11 | | Case 2:
% 136.03/20.11 | | |
% 136.03/20.11 | | | (18) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 136.03/20.11 | | |
% 136.03/20.11 | | | REF_CLOSE: (1), (2), (4), (10), (11), (16), (18) are inconsistent by
% 136.03/20.11 | | | sub-proof #351.
% 136.03/20.11 | | |
% 136.03/20.11 | | End of split
% 136.03/20.11 | |
% 136.03/20.11 | End of split
% 136.03/20.11 |
% 136.03/20.11 End of proof
% 136.03/20.11
% 136.03/20.11 Sub-proof #234 shows that the following formulas are inconsistent:
% 136.03/20.11 ----------------------------------------------------------------
% 136.03/20.11 (1) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 136.03/20.11 (2) op(e3, e3) = e2
% 136.03/20.11 (3) ~ (all_52_4 = all_36_0)
% 136.03/20.11 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.11 (5) ~ (e2 = e1)
% 136.03/20.11 (6) all_57_9 = e3
% 136.03/20.11 (7) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 136.03/20.11 (8) ~ (all_36_0 = e2)
% 136.03/20.11 (9) ~ (all_52_4 = e3)
% 136.03/20.11 (10) all_54_2 = all_36_0
% 136.03/20.11 (11) ~ (all_52_4 = e2)
% 136.03/20.11 (12) all_54_1 = all_52_4
% 136.03/20.11 (13) op(e3, e2) = all_52_4
% 136.03/20.11 (14) ~ (all_36_0 = e0)
% 136.03/20.11 (15) all_57_4 = e0
% 136.03/20.11 (16) ~ (e3 = e1)
% 136.03/20.11 (17) ~ (e1 = e0)
% 136.03/20.11 (18) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 136.03/20.11 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 136.03/20.11
% 136.03/20.11 Begin of proof
% 136.03/20.11 |
% 136.03/20.11 | BETA: splitting (18) gives:
% 136.03/20.11 |
% 136.03/20.11 | Case 1:
% 136.03/20.11 | |
% 136.03/20.11 | | (19) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 136.03/20.11 | | e1)
% 136.03/20.11 | |
% 136.03/20.11 | | BETA: splitting (19) gives:
% 136.03/20.11 | |
% 136.03/20.11 | | Case 1:
% 136.03/20.11 | | |
% 136.03/20.11 | | | (20) all_57_0 = e1 & op(e3, e3) = e1
% 136.03/20.11 | | |
% 136.03/20.11 | | | ALPHA: (20) implies:
% 136.03/20.11 | | | (21) op(e3, e3) = e1
% 136.03/20.11 | | |
% 136.03/20.11 | | | REF_CLOSE: (2), (4), (5), (21) are inconsistent by sub-proof #743.
% 136.03/20.11 | | |
% 136.03/20.11 | | Case 2:
% 136.03/20.11 | | |
% 136.03/20.11 | | | (22) all_57_1 = e1 & op(e3, e2) = e1
% 136.03/20.11 | | |
% 136.03/20.11 | | | ALPHA: (22) implies:
% 136.03/20.11 | | | (23) op(e3, e2) = e1
% 136.03/20.11 | | |
% 136.03/20.11 | | | REF_CLOSE: (1), (3), (4), (7), (8), (9), (10), (11), (12), (13), (14),
% 136.03/20.11 | | | (23) are inconsistent by sub-proof #235.
% 136.03/20.11 | | |
% 136.03/20.11 | | End of split
% 136.03/20.11 | |
% 136.03/20.11 | Case 2:
% 136.03/20.11 | |
% 136.03/20.11 | | (24) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 136.03/20.11 | | e1)
% 136.03/20.11 | |
% 136.03/20.11 | | BETA: splitting (24) gives:
% 136.03/20.11 | |
% 136.03/20.11 | | Case 1:
% 136.03/20.11 | | |
% 136.03/20.11 | | | (25) all_57_4 = e1 & op(e3, e1) = e1
% 136.03/20.11 | | |
% 136.03/20.11 | | | ALPHA: (25) implies:
% 136.03/20.11 | | | (26) all_57_4 = e1
% 136.03/20.11 | | |
% 136.03/20.11 | | | COMBINE_EQS: (15), (26) imply:
% 136.03/20.11 | | | (27) e1 = e0
% 136.03/20.11 | | |
% 136.03/20.11 | | | REDUCE: (17), (27) imply:
% 136.03/20.11 | | | (28) $false
% 136.03/20.11 | | |
% 136.03/20.11 | | | CLOSE: (28) is inconsistent.
% 136.03/20.11 | | |
% 136.03/20.11 | | Case 2:
% 136.03/20.11 | | |
% 136.03/20.11 | | | (29) all_57_9 = e1 & op(e3, e0) = e1
% 136.03/20.11 | | |
% 136.03/20.11 | | | ALPHA: (29) implies:
% 136.03/20.11 | | | (30) all_57_9 = e1
% 136.03/20.11 | | |
% 136.03/20.11 | | | REF_CLOSE: (6), (16), (30) are inconsistent by sub-proof #690.
% 136.03/20.11 | | |
% 136.03/20.11 | | End of split
% 136.03/20.11 | |
% 136.03/20.11 | End of split
% 136.03/20.11 |
% 136.03/20.11 End of proof
% 136.03/20.11
% 136.03/20.11 Sub-proof #235 shows that the following formulas are inconsistent:
% 136.03/20.11 ----------------------------------------------------------------
% 136.03/20.11 (1) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 136.03/20.11 (2) op(e3, e2) = e1
% 136.03/20.11 (3) ~ (all_52_4 = all_36_0)
% 136.03/20.11 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.11 (5) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 136.03/20.11 (6) ~ (all_36_0 = e2)
% 136.03/20.11 (7) ~ (all_52_4 = e3)
% 136.03/20.11 (8) all_54_2 = all_36_0
% 136.03/20.11 (9) ~ (all_52_4 = e2)
% 136.03/20.11 (10) all_54_1 = all_52_4
% 136.03/20.11 (11) op(e3, e2) = all_52_4
% 136.03/20.11 (12) ~ (all_36_0 = e0)
% 136.03/20.11
% 136.03/20.11 Begin of proof
% 136.03/20.11 |
% 136.03/20.11 | BETA: splitting (5) gives:
% 136.03/20.11 |
% 136.03/20.11 | Case 1:
% 136.03/20.11 | |
% 136.03/20.11 | | (13) all_54_2 = e2
% 136.03/20.11 | |
% 136.03/20.11 | | REF_CLOSE: (6), (8), (13) are inconsistent by sub-proof #244.
% 136.03/20.11 | |
% 136.03/20.11 | Case 2:
% 136.03/20.11 | |
% 136.03/20.11 | | (14) all_54_2 = e1 | all_54_2 = e0
% 136.03/20.11 | |
% 136.03/20.11 | | BETA: splitting (14) gives:
% 136.03/20.11 | |
% 136.03/20.11 | | Case 1:
% 136.03/20.11 | | |
% 136.03/20.11 | | | (15) all_54_2 = e1
% 136.03/20.11 | | |
% 136.03/20.11 | | | COMBINE_EQS: (8), (15) imply:
% 136.03/20.11 | | | (16) all_36_0 = e1
% 136.03/20.11 | | |
% 136.03/20.11 | | | SIMP: (16) implies:
% 136.03/20.11 | | | (17) all_36_0 = e1
% 136.03/20.11 | | |
% 136.03/20.11 | | | REDUCE: (3), (17) imply:
% 136.03/20.11 | | | (18) ~ (all_52_4 = e1)
% 136.03/20.11 | | |
% 136.03/20.11 | | | BETA: splitting (1) gives:
% 136.03/20.11 | | |
% 136.03/20.11 | | | Case 1:
% 136.03/20.11 | | | |
% 136.03/20.11 | | | | (19) all_54_1 = e3
% 136.03/20.11 | | | |
% 136.03/20.11 | | | | COMBINE_EQS: (10), (19) imply:
% 136.03/20.11 | | | | (20) all_52_4 = e3
% 136.03/20.11 | | | |
% 136.03/20.11 | | | | REDUCE: (7), (20) imply:
% 136.03/20.11 | | | | (21) $false
% 136.03/20.11 | | | |
% 136.03/20.11 | | | | CLOSE: (21) is inconsistent.
% 136.03/20.11 | | | |
% 136.03/20.11 | | | Case 2:
% 136.03/20.11 | | | |
% 136.03/20.11 | | | | (22) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 136.03/20.11 | | | |
% 136.03/20.11 | | | | BETA: splitting (22) gives:
% 136.03/20.11 | | | |
% 136.03/20.11 | | | | Case 1:
% 136.03/20.11 | | | | |
% 136.03/20.11 | | | | | (23) all_54_1 = e2
% 136.03/20.11 | | | | |
% 136.03/20.11 | | | | | REF_CLOSE: (9), (10), (23) are inconsistent by sub-proof #739.
% 136.03/20.11 | | | | |
% 136.03/20.11 | | | | Case 2:
% 136.03/20.11 | | | | |
% 136.03/20.11 | | | | | (24) all_54_1 = e1 | all_54_1 = e0
% 136.03/20.11 | | | | |
% 136.03/20.11 | | | | | REF_CLOSE: (2), (4), (10), (11), (18), (24) are inconsistent by
% 136.03/20.11 | | | | | sub-proof #729.
% 136.03/20.11 | | | | |
% 136.03/20.11 | | | | End of split
% 136.03/20.11 | | | |
% 136.03/20.11 | | | End of split
% 136.03/20.11 | | |
% 136.03/20.11 | | Case 2:
% 136.03/20.11 | | |
% 136.03/20.11 | | | (25) all_54_2 = e0
% 136.03/20.11 | | |
% 136.03/20.11 | | | REF_CLOSE: (8), (12), (25) are inconsistent by sub-proof #242.
% 136.03/20.11 | | |
% 136.03/20.11 | | End of split
% 136.03/20.11 | |
% 136.03/20.11 | End of split
% 136.03/20.11 |
% 136.03/20.11 End of proof
% 136.03/20.11
% 136.03/20.11 Sub-proof #236 shows that the following formulas are inconsistent:
% 136.03/20.11 ----------------------------------------------------------------
% 136.03/20.11 (1) op(e3, e3) = e2
% 136.03/20.11 (2) ~ (e2 = e0)
% 136.03/20.11 (3) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 136.03/20.11 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 136.03/20.11 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.11 (5) ~ (e2 = e1)
% 136.03/20.11 (6) ~ (e3 = e0)
% 136.03/20.11 (7) all_57_9 = e3
% 136.03/20.11 (8) ~ (e3 = e2)
% 136.03/20.11 (9) ~ (all_52_4 = e3)
% 136.03/20.11 (10) all_57_3 = e2 & op(e2, e2) = e2
% 136.03/20.11 (11) op(e3, e2) = all_52_4
% 136.03/20.11 (12) all_57_3 = e3
% 136.03/20.11 (13) ~ (e3 = e1)
% 136.03/20.11 (14) ~ (e1 = e0)
% 136.03/20.11 (15) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 136.03/20.11 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 136.03/20.11 (16) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 136.03/20.11 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 136.03/20.11
% 136.03/20.11 Begin of proof
% 136.03/20.11 |
% 136.03/20.11 | ALPHA: (10) implies:
% 136.03/20.11 | (17) all_57_3 = e2
% 136.03/20.11 |
% 136.03/20.11 | COMBINE_EQS: (12), (17) imply:
% 136.03/20.11 | (18) e3 = e2
% 136.03/20.11 |
% 136.03/20.11 | SIMP: (18) implies:
% 136.03/20.11 | (19) e3 = e2
% 136.03/20.11 |
% 136.03/20.11 | COMBINE_EQS: (7), (19) imply:
% 136.03/20.11 | (20) all_57_9 = e2
% 136.03/20.11 |
% 136.03/20.11 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (11), (13), (14), (15),
% 136.03/20.11 | (16), (20) are inconsistent by sub-proof #250.
% 136.03/20.11 |
% 136.03/20.11 End of proof
% 136.03/20.11
% 136.03/20.11 Sub-proof #237 shows that the following formulas are inconsistent:
% 136.03/20.11 ----------------------------------------------------------------
% 136.03/20.11 (1) op(e3, e3) = e2
% 136.03/20.11 (2) ~ (e2 = e0)
% 136.03/20.11 (3) all_57_1 = e2
% 136.03/20.11 (4) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 136.03/20.11 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 136.03/20.11 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.11 (6) ~ (e2 = e1)
% 136.03/20.11 (7) ~ (e3 = e0)
% 136.03/20.11 (8) all_57_9 = e3
% 136.03/20.11 (9) ~ (e3 = e2)
% 136.03/20.11 (10) ~ (all_52_4 = e3)
% 136.03/20.11 (11) op(e3, e2) = all_52_4
% 136.03/20.11 (12) ~ (e3 = e1)
% 136.03/20.11 (13) ~ (e1 = e0)
% 136.03/20.11 (14) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 136.03/20.11 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 136.03/20.11 (15) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 136.03/20.11 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 136.03/20.11
% 136.03/20.11 Begin of proof
% 136.03/20.11 |
% 136.03/20.11 | BETA: splitting (4) gives:
% 136.03/20.11 |
% 136.03/20.11 | Case 1:
% 136.03/20.11 | |
% 136.03/20.11 | | (16) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 136.03/20.11 | | e0)
% 136.03/20.11 | |
% 136.03/20.11 | | REF_CLOSE: (1), (2), (3), (5), (16) are inconsistent by sub-proof #240.
% 136.03/20.11 | |
% 136.03/20.11 | Case 2:
% 136.03/20.11 | |
% 136.03/20.11 | | (17) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 136.03/20.11 | | e0)
% 136.03/20.11 | |
% 136.03/20.11 | | BETA: splitting (17) gives:
% 136.03/20.11 | |
% 136.03/20.11 | | Case 1:
% 136.03/20.11 | | |
% 136.03/20.11 | | | (18) all_57_4 = e0 & op(e3, e1) = e0
% 136.03/20.11 | | |
% 136.03/20.11 | | | ALPHA: (18) implies:
% 136.03/20.11 | | | (19) all_57_4 = e0
% 136.03/20.11 | | |
% 136.03/20.11 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 136.03/20.11 | | | (14), (15), (19) are inconsistent by sub-proof #238.
% 136.03/20.11 | | |
% 136.03/20.11 | | Case 2:
% 136.03/20.11 | | |
% 136.03/20.11 | | | (20) all_57_9 = e0 & op(e3, e0) = e0
% 136.03/20.11 | | |
% 136.03/20.11 | | | REF_CLOSE: (7), (8), (20) are inconsistent by sub-proof #299.
% 136.03/20.11 | | |
% 136.03/20.11 | | End of split
% 136.03/20.11 | |
% 136.03/20.11 | End of split
% 136.03/20.11 |
% 136.03/20.11 End of proof
% 136.03/20.11
% 136.03/20.11 Sub-proof #238 shows that the following formulas are inconsistent:
% 136.03/20.11 ----------------------------------------------------------------
% 136.03/20.11 (1) op(e3, e3) = e2
% 136.03/20.11 (2) ~ (e2 = e0)
% 136.03/20.11 (3) all_57_1 = e2
% 136.03/20.11 (4) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 136.03/20.11 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 136.03/20.11 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.11 (6) ~ (e2 = e1)
% 136.03/20.11 (7) ~ (e3 = e0)
% 136.03/20.11 (8) ~ (e3 = e2)
% 136.03/20.11 (9) ~ (all_52_4 = e3)
% 136.03/20.11 (10) op(e3, e2) = all_52_4
% 136.03/20.11 (11) all_57_4 = e0
% 136.03/20.11 (12) ~ (e3 = e1)
% 136.03/20.11 (13) ~ (e1 = e0)
% 136.03/20.11 (14) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 136.03/20.11 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 136.03/20.11 (15) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 136.03/20.11 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 136.03/20.11
% 136.03/20.11 Begin of proof
% 136.03/20.11 |
% 136.03/20.11 | BETA: splitting (15) gives:
% 136.03/20.11 |
% 136.03/20.11 | Case 1:
% 136.03/20.11 | |
% 136.03/20.11 | | (16) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 136.03/20.11 | | e1)
% 136.03/20.11 | |
% 136.03/20.11 | | REF_CLOSE: (1), (3), (5), (6), (16) are inconsistent by sub-proof #239.
% 136.03/20.11 | |
% 136.03/20.11 | Case 2:
% 136.03/20.11 | |
% 136.03/20.11 | | (17) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 136.03/20.11 | | e1)
% 136.03/20.11 | |
% 136.03/20.11 | | BETA: splitting (17) gives:
% 136.03/20.11 | |
% 136.03/20.11 | | Case 1:
% 136.03/20.11 | | |
% 136.03/20.11 | | | (18) all_57_4 = e1 & op(e3, e1) = e1
% 136.03/20.11 | | |
% 136.03/20.11 | | | REF_CLOSE: (11), (13), (18) are inconsistent by sub-proof #419.
% 136.03/20.11 | | |
% 136.03/20.11 | | Case 2:
% 136.03/20.11 | | |
% 136.03/20.11 | | | (19) all_57_9 = e1 & op(e3, e0) = e1
% 136.03/20.11 | | |
% 136.03/20.11 | | | ALPHA: (19) implies:
% 136.03/20.11 | | | (20) all_57_9 = e1
% 136.03/20.11 | | |
% 136.03/20.11 | | | BETA: splitting (14) gives:
% 136.03/20.11 | | |
% 136.03/20.11 | | | Case 1:
% 136.03/20.11 | | | |
% 136.03/20.11 | | | | (21) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2)
% 136.03/20.11 | | | | = e3)
% 136.03/20.11 | | | |
% 136.03/20.11 | | | | REF_CLOSE: (1), (5), (8), (9), (10), (21) are inconsistent by sub-proof
% 136.03/20.11 | | | | #282.
% 136.03/20.11 | | | |
% 136.03/20.11 | | | Case 2:
% 136.03/20.11 | | | |
% 136.03/20.11 | | | | (22) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0)
% 136.03/20.11 | | | | = e3)
% 136.03/20.11 | | | |
% 136.03/20.11 | | | | BETA: splitting (22) gives:
% 136.03/20.11 | | | |
% 136.03/20.11 | | | | Case 1:
% 136.03/20.11 | | | | |
% 136.03/20.11 | | | | | (23) all_57_4 = e3 & op(e3, e1) = e3
% 136.03/20.11 | | | | |
% 136.03/20.11 | | | | | ALPHA: (23) implies:
% 136.03/20.11 | | | | | (24) all_57_4 = e3
% 136.03/20.11 | | | | |
% 136.03/20.11 | | | | | BETA: splitting (4) gives:
% 136.03/20.11 | | | | |
% 136.03/20.11 | | | | | Case 1:
% 136.03/20.11 | | | | | |
% 136.03/20.11 | | | | | | (25) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3,
% 136.03/20.11 | | | | | | e2) = e0)
% 136.03/20.11 | | | | | |
% 136.03/20.11 | | | | | | REF_CLOSE: (1), (2), (3), (5), (25) are inconsistent by sub-proof
% 136.03/20.11 | | | | | | #240.
% 136.03/20.11 | | | | | |
% 136.03/20.11 | | | | | Case 2:
% 136.03/20.11 | | | | | |
% 136.03/20.11 | | | | | | (26) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3,
% 136.03/20.11 | | | | | | e0) = e0)
% 136.03/20.11 | | | | | |
% 136.03/20.11 | | | | | | BETA: splitting (26) gives:
% 136.03/20.11 | | | | | |
% 136.03/20.11 | | | | | | Case 1:
% 136.03/20.11 | | | | | | |
% 136.03/20.11 | | | | | | | (27) all_57_4 = e0 & op(e3, e1) = e0
% 136.03/20.11 | | | | | | |
% 136.03/20.11 | | | | | | | REF_CLOSE: (7), (24), (27) are inconsistent by sub-proof #384.
% 136.03/20.11 | | | | | | |
% 136.03/20.11 | | | | | | Case 2:
% 136.03/20.11 | | | | | | |
% 136.03/20.11 | | | | | | | (28) all_57_9 = e0 & op(e3, e0) = e0
% 136.03/20.11 | | | | | | |
% 136.03/20.11 | | | | | | | REF_CLOSE: (13), (20), (28) are inconsistent by sub-proof #687.
% 136.03/20.11 | | | | | | |
% 136.03/20.11 | | | | | | End of split
% 136.03/20.11 | | | | | |
% 136.03/20.11 | | | | | End of split
% 136.03/20.11 | | | | |
% 136.03/20.11 | | | | Case 2:
% 136.03/20.11 | | | | |
% 136.03/20.11 | | | | | (29) all_57_9 = e3 & op(e3, e0) = e3
% 136.03/20.11 | | | | |
% 136.03/20.11 | | | | | ALPHA: (29) implies:
% 136.03/20.11 | | | | | (30) all_57_9 = e3
% 136.03/20.11 | | | | |
% 136.03/20.11 | | | | | REF_CLOSE: (12), (20), (30) are inconsistent by sub-proof #690.
% 136.03/20.11 | | | | |
% 136.03/20.11 | | | | End of split
% 136.03/20.11 | | | |
% 136.03/20.11 | | | End of split
% 136.03/20.11 | | |
% 136.03/20.11 | | End of split
% 136.03/20.11 | |
% 136.03/20.11 | End of split
% 136.03/20.11 |
% 136.03/20.11 End of proof
% 136.03/20.11
% 136.03/20.11 Sub-proof #239 shows that the following formulas are inconsistent:
% 136.03/20.11 ----------------------------------------------------------------
% 136.03/20.11 (1) op(e3, e3) = e2
% 136.03/20.11 (2) all_57_1 = e2
% 136.03/20.11 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.11 (4) ~ (e2 = e1)
% 136.03/20.11 (5) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1)
% 136.03/20.11
% 136.03/20.11 Begin of proof
% 136.03/20.11 |
% 136.03/20.11 | BETA: splitting (5) gives:
% 136.03/20.11 |
% 136.03/20.11 | Case 1:
% 136.03/20.11 | |
% 136.03/20.11 | | (6) all_57_0 = e1 & op(e3, e3) = e1
% 136.03/20.11 | |
% 136.03/20.11 | | ALPHA: (6) implies:
% 136.03/20.11 | | (7) op(e3, e3) = e1
% 136.03/20.11 | |
% 136.03/20.11 | | REF_CLOSE: (1), (3), (4), (7) are inconsistent by sub-proof #743.
% 136.03/20.11 | |
% 136.03/20.11 | Case 2:
% 136.03/20.11 | |
% 136.03/20.11 | | (8) all_57_1 = e1 & op(e3, e2) = e1
% 136.03/20.11 | |
% 136.03/20.11 | | REF_CLOSE: (2), (4), (8) are inconsistent by sub-proof #465.
% 136.03/20.11 | |
% 136.03/20.11 | End of split
% 136.03/20.11 |
% 136.03/20.11 End of proof
% 136.03/20.11
% 136.03/20.11 Sub-proof #240 shows that the following formulas are inconsistent:
% 136.03/20.11 ----------------------------------------------------------------
% 136.03/20.11 (1) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0)
% 136.03/20.11 (2) op(e3, e3) = e2
% 136.03/20.11 (3) ~ (e2 = e0)
% 136.03/20.11 (4) all_57_1 = e2
% 136.03/20.11 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.11
% 136.03/20.11 Begin of proof
% 136.03/20.11 |
% 136.03/20.11 | BETA: splitting (1) gives:
% 136.03/20.11 |
% 136.03/20.11 | Case 1:
% 136.03/20.11 | |
% 136.03/20.11 | | (6) all_57_0 = e0 & op(e3, e3) = e0
% 136.03/20.11 | |
% 136.03/20.11 | | ALPHA: (6) implies:
% 136.03/20.11 | | (7) op(e3, e3) = e0
% 136.03/20.11 | |
% 136.03/20.11 | | REF_CLOSE: (2), (3), (5), (7) are inconsistent by sub-proof #495.
% 136.03/20.11 | |
% 136.03/20.11 | Case 2:
% 136.03/20.11 | |
% 136.03/20.11 | | (8) all_57_1 = e0 & op(e3, e2) = e0
% 136.03/20.11 | |
% 136.03/20.11 | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #466.
% 136.03/20.11 | |
% 136.03/20.11 | End of split
% 136.03/20.11 |
% 136.03/20.11 End of proof
% 136.03/20.11
% 136.03/20.11 Sub-proof #241 shows that the following formulas are inconsistent:
% 136.03/20.11 ----------------------------------------------------------------
% 136.03/20.11 (1) op(e3, e3) = e2
% 136.03/20.11 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.11 (3) ~ (e2 = e1)
% 136.03/20.11 (4) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1)
% 136.03/20.11 (5) op(e3, e2) = e0
% 136.03/20.11 (6) ~ (e1 = e0)
% 136.03/20.11
% 136.03/20.11 Begin of proof
% 136.03/20.11 |
% 136.03/20.11 | BETA: splitting (4) gives:
% 136.03/20.11 |
% 136.03/20.11 | Case 1:
% 136.03/20.11 | |
% 136.03/20.11 | | (7) all_57_0 = e1 & op(e3, e3) = e1
% 136.03/20.11 | |
% 136.03/20.11 | | ALPHA: (7) implies:
% 136.03/20.11 | | (8) op(e3, e3) = e1
% 136.03/20.11 | |
% 136.03/20.11 | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #743.
% 136.03/20.11 | |
% 136.03/20.11 | Case 2:
% 136.03/20.11 | |
% 136.03/20.11 | | (9) all_57_1 = e1 & op(e3, e2) = e1
% 136.03/20.11 | |
% 136.03/20.11 | | ALPHA: (9) implies:
% 136.03/20.11 | | (10) op(e3, e2) = e1
% 136.03/20.11 | |
% 136.03/20.11 | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #730.
% 136.03/20.11 | |
% 136.03/20.11 | End of split
% 136.03/20.11 |
% 136.03/20.11 End of proof
% 136.03/20.11
% 136.03/20.11 Sub-proof #242 shows that the following formulas are inconsistent:
% 136.03/20.11 ----------------------------------------------------------------
% 136.03/20.11 (1) all_54_2 = all_36_0
% 136.03/20.11 (2) all_54_2 = e0
% 136.03/20.11 (3) ~ (all_36_0 = e0)
% 136.03/20.11
% 136.03/20.11 Begin of proof
% 136.03/20.11 |
% 136.03/20.11 | COMBINE_EQS: (1), (2) imply:
% 136.03/20.11 | (4) all_36_0 = e0
% 136.03/20.11 |
% 136.03/20.11 | SIMP: (4) implies:
% 136.03/20.11 | (5) all_36_0 = e0
% 136.03/20.11 |
% 136.03/20.11 | REDUCE: (3), (5) imply:
% 136.03/20.11 | (6) $false
% 136.03/20.11 |
% 136.03/20.11 | CLOSE: (6) is inconsistent.
% 136.03/20.11 |
% 136.03/20.11 End of proof
% 136.03/20.11
% 136.03/20.11 Sub-proof #243 shows that the following formulas are inconsistent:
% 136.03/20.11 ----------------------------------------------------------------
% 136.03/20.11 (1) ~ (all_52_1 = all_52_2)
% 136.03/20.11 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.11 (3) ~ (all_52_1 = e0)
% 136.03/20.11 (4) all_54_4 = e1 | all_54_4 = e0
% 136.03/20.11 (5) op(e1, e3) = e1
% 136.03/20.11 (6) op(e1, e3) = all_52_2
% 136.03/20.11 (7) all_54_4 = all_52_1
% 136.03/20.11
% 136.03/20.11 Begin of proof
% 136.03/20.11 |
% 136.03/20.11 | BETA: splitting (4) gives:
% 136.03/20.11 |
% 136.03/20.11 | Case 1:
% 136.03/20.11 | |
% 136.03/20.11 | | (8) all_54_4 = e1
% 136.03/20.11 | |
% 136.03/20.11 | | COMBINE_EQS: (7), (8) imply:
% 136.03/20.11 | | (9) all_52_1 = e1
% 136.03/20.11 | |
% 136.03/20.11 | | REDUCE: (1), (9) imply:
% 136.03/20.11 | | (10) ~ (all_52_2 = e1)
% 136.03/20.11 | |
% 136.03/20.11 | | SIMP: (10) implies:
% 136.03/20.11 | | (11) ~ (all_52_2 = e1)
% 136.03/20.11 | |
% 136.03/20.11 | | REF_CLOSE: (2), (5), (6), (11) are inconsistent by sub-proof #725.
% 136.03/20.11 | |
% 136.03/20.11 | Case 2:
% 136.03/20.11 | |
% 136.03/20.11 | | (12) all_54_4 = e0
% 136.03/20.11 | |
% 136.03/20.11 | | COMBINE_EQS: (7), (12) imply:
% 136.03/20.11 | | (13) all_52_1 = e0
% 136.03/20.11 | |
% 136.03/20.11 | | REDUCE: (3), (13) imply:
% 136.03/20.11 | | (14) $false
% 136.03/20.11 | |
% 136.03/20.11 | | CLOSE: (14) is inconsistent.
% 136.03/20.11 | |
% 136.03/20.11 | End of split
% 136.03/20.11 |
% 136.03/20.11 End of proof
% 136.03/20.11
% 136.03/20.11 Sub-proof #244 shows that the following formulas are inconsistent:
% 136.03/20.11 ----------------------------------------------------------------
% 136.03/20.11 (1) all_54_2 = all_36_0
% 136.03/20.11 (2) all_54_2 = e2
% 136.03/20.11 (3) ~ (all_36_0 = e2)
% 136.03/20.11
% 136.03/20.11 Begin of proof
% 136.03/20.11 |
% 136.03/20.11 | COMBINE_EQS: (1), (2) imply:
% 136.03/20.11 | (4) all_36_0 = e2
% 136.03/20.11 |
% 136.03/20.11 | SIMP: (4) implies:
% 136.03/20.11 | (5) all_36_0 = e2
% 136.03/20.11 |
% 136.03/20.11 | REDUCE: (3), (5) imply:
% 136.03/20.11 | (6) $false
% 136.03/20.11 |
% 136.03/20.11 | CLOSE: (6) is inconsistent.
% 136.03/20.11 |
% 136.03/20.11 End of proof
% 136.03/20.11
% 136.03/20.11 Sub-proof #245 shows that the following formulas are inconsistent:
% 136.03/20.11 ----------------------------------------------------------------
% 136.03/20.11 (1) ~ (e2 = e1)
% 136.03/20.11 (2) all_57_13 = e2
% 136.03/20.11 (3) all_57_12 = e3
% 136.03/20.11 (4) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 136.03/20.11 (5) ~ (e3 = e1)
% 136.03/20.11
% 136.03/20.11 Begin of proof
% 136.03/20.11 |
% 136.03/20.11 | BETA: splitting (4) gives:
% 136.03/20.11 |
% 136.03/20.11 | Case 1:
% 136.03/20.11 | |
% 136.03/20.11 | | (6) all_57_12 = e1 & op(e0, e3) = e1
% 136.03/20.11 | |
% 136.03/20.11 | | ALPHA: (6) implies:
% 136.03/20.11 | | (7) all_57_12 = e1
% 136.03/20.11 | |
% 136.03/20.11 | | REF_CLOSE: (3), (5), (7) are inconsistent by sub-proof #591.
% 136.03/20.11 | |
% 136.03/20.11 | Case 2:
% 136.03/20.11 | |
% 136.03/20.11 | | (8) all_57_13 = e1 & op(e0, e2) = e1
% 136.03/20.11 | |
% 136.03/20.11 | | REF_CLOSE: (1), (2), (8) are inconsistent by sub-proof #248.
% 136.03/20.11 | |
% 136.03/20.11 | End of split
% 136.03/20.11 |
% 136.03/20.11 End of proof
% 136.03/20.11
% 136.03/20.11 Sub-proof #246 shows that the following formulas are inconsistent:
% 136.03/20.11 ----------------------------------------------------------------
% 136.03/20.11 (1) op(e1, e1) = all_6_2
% 136.03/20.11 (2) op(e0, e0) = e3
% 136.03/20.11 (3) op(e3, e3) = e2
% 136.03/20.11 (4) ~ (e2 = e0)
% 136.03/20.11 (5) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 136.03/20.11 (all_57_14 = e0 & op(e0, e1) = e0)
% 136.03/20.11 (6) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 136.03/20.11 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 136.03/20.11 (7) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 136.03/20.11 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 136.03/20.11 (8) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 136.03/20.11 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 136.03/20.11 (9) ~ (all_52_7 = e3)
% 136.03/20.11 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.03/20.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.03/20.11 (11) ~ (e2 = e1)
% 136.03/20.11 (12) ~ (e3 = e0)
% 136.03/20.11 (13) all_57_9 = e3
% 136.03/20.11 (14) ~ (e3 = e2)
% 136.03/20.11 (15) all_57_6 = e3
% 136.03/20.12 (16) op(e2, e2) = e3
% 136.03/20.12 (17) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 136.03/20.12 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 136.03/20.12 (18) op(e0, e2) = all_52_7
% 136.03/20.12 (19) ~ (all_52_4 = e3)
% 136.03/20.12 (20) ~ (all_6_2 = e2)
% 136.03/20.12 (21) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 136.03/20.12 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 136.03/20.12 e1)
% 136.03/20.12 (22) all_57_13 = e2
% 136.03/20.12 (23) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 136.03/20.12 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 136.03/20.12 (24) op(e3, e2) = all_52_4
% 136.03/20.12 (25) all_57_14 = e3
% 136.03/20.12 (26) all_57_3 = e3
% 136.03/20.12 (27) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 136.03/20.12 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 136.03/20.12 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 136.03/20.12 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 136.03/20.12 (28) ~ (e3 = e1)
% 136.03/20.12 (29) ~ (e1 = e0)
% 136.03/20.12 (30) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 136.03/20.12 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 136.03/20.12 (31) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 136.03/20.12 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 136.03/20.12 (32) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 136.03/20.12 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 136.03/20.12 (33) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 136.03/20.12 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 136.03/20.12 (34) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 136.03/20.12 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 136.03/20.12
% 136.03/20.12 Begin of proof
% 136.03/20.12 |
% 136.03/20.12 | BETA: splitting (34) gives:
% 136.03/20.12 |
% 136.03/20.12 | Case 1:
% 136.03/20.12 | |
% 136.03/20.12 | | (35) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 136.03/20.12 | | e2)
% 136.03/20.12 | |
% 136.03/20.12 | | BETA: splitting (35) gives:
% 136.03/20.12 | |
% 136.03/20.12 | | Case 1:
% 136.03/20.12 | | |
% 136.03/20.12 | | | (36) all_57_4 = e2 & op(e3, e1) = e2
% 136.03/20.12 | | |
% 136.03/20.12 | | | ALPHA: (36) implies:
% 136.03/20.12 | | | (37) all_57_4 = e2
% 136.03/20.12 | | |
% 136.03/20.12 | | | REF_CLOSE: (3), (4), (6), (10), (11), (12), (13), (28), (29), (33), (37)
% 136.03/20.12 | | | are inconsistent by sub-proof #279.
% 136.03/20.12 | | |
% 136.03/20.12 | | Case 2:
% 136.03/20.12 | | |
% 136.03/20.12 | | | (38) all_57_5 = e2 & op(e2, e1) = e2
% 136.03/20.12 | | |
% 136.03/20.12 | | | ALPHA: (38) implies:
% 136.03/20.12 | | | (39) all_57_5 = e2
% 136.03/20.12 | | |
% 136.03/20.12 | | | BETA: splitting (5) gives:
% 136.03/20.12 | | |
% 136.03/20.12 | | | Case 1:
% 136.03/20.12 | | | |
% 136.03/20.12 | | | | (40) all_57_12 = e0 & op(e0, e3) = e0
% 136.03/20.12 | | | |
% 136.03/20.12 | | | | BETA: splitting (8) gives:
% 136.03/20.12 | | | |
% 136.03/20.12 | | | | Case 1:
% 136.03/20.12 | | | | |
% 136.03/20.12 | | | | | (41) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2,
% 136.03/20.12 | | | | | e3) = e1)
% 136.03/20.12 | | | | |
% 136.03/20.12 | | | | | BETA: splitting (41) gives:
% 136.03/20.12 | | | | |
% 136.03/20.12 | | | | | Case 1:
% 136.03/20.12 | | | | | |
% 136.03/20.12 | | | | | | (42) all_57_0 = e1 & op(e3, e3) = e1
% 136.03/20.12 | | | | | |
% 136.03/20.12 | | | | | | ALPHA: (42) implies:
% 136.03/20.12 | | | | | | (43) op(e3, e3) = e1
% 136.03/20.12 | | | | | |
% 136.03/20.12 | | | | | | REF_CLOSE: (3), (10), (11), (43) are inconsistent by sub-proof #743.
% 136.03/20.12 | | | | | |
% 136.03/20.12 | | | | | Case 2:
% 136.03/20.12 | | | | | |
% 136.03/20.12 | | | | | | (44) all_57_2 = e1 & op(e2, e3) = e1
% 136.03/20.12 | | | | | |
% 136.03/20.12 | | | | | | ALPHA: (44) implies:
% 136.03/20.12 | | | | | | (45) all_57_2 = e1
% 136.03/20.12 | | | | | |
% 136.03/20.12 | | | | | | BETA: splitting (21) gives:
% 136.03/20.12 | | | | | |
% 136.03/20.12 | | | | | | Case 1:
% 136.03/20.12 | | | | | | |
% 136.03/20.12 | | | | | | | (46) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 &
% 136.03/20.12 | | | | | | | op(e0, e2) = e1)
% 136.03/20.12 | | | | | | |
% 136.03/20.12 | | | | | | | BETA: splitting (46) gives:
% 136.03/20.12 | | | | | | |
% 136.03/20.12 | | | | | | | Case 1:
% 136.03/20.12 | | | | | | | |
% 136.03/20.12 | | | | | | | | (47) all_57_12 = e1 & op(e0, e3) = e1
% 136.03/20.12 | | | | | | | |
% 136.03/20.12 | | | | | | | | ALPHA: (47) implies:
% 136.03/20.12 | | | | | | | | (48) all_57_12 = e1
% 136.03/20.12 | | | | | | | |
% 136.03/20.12 | | | | | | | | REF_CLOSE: (4), (5), (12), (22), (25), (29), (48) are
% 136.03/20.12 | | | | | | | | inconsistent by sub-proof #399.
% 136.03/20.12 | | | | | | | |
% 136.03/20.12 | | | | | | | Case 2:
% 136.03/20.12 | | | | | | | |
% 136.03/20.12 | | | | | | | | (49) all_57_13 = e1 & op(e0, e2) = e1
% 136.03/20.12 | | | | | | | |
% 136.03/20.12 | | | | | | | | REF_CLOSE: (11), (22), (49) are inconsistent by sub-proof #248.
% 136.03/20.12 | | | | | | | |
% 136.03/20.12 | | | | | | | End of split
% 136.03/20.12 | | | | | | |
% 136.03/20.12 | | | | | | Case 2:
% 136.03/20.12 | | | | | | |
% 136.03/20.12 | | | | | | | (50) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 &
% 136.03/20.12 | | | | | | | op(e0, e0) = e1)
% 136.03/20.12 | | | | | | |
% 136.03/20.12 | | | | | | | BETA: splitting (50) gives:
% 136.03/20.12 | | | | | | |
% 136.03/20.12 | | | | | | | Case 1:
% 136.03/20.12 | | | | | | | |
% 136.03/20.12 | | | | | | | | (51) all_57_14 = e1 & op(e0, e1) = e1
% 136.03/20.12 | | | | | | | |
% 136.03/20.12 | | | | | | | | REF_CLOSE: (25), (28), (51) are inconsistent by sub-proof #247.
% 136.03/20.12 | | | | | | | |
% 136.03/20.12 | | | | | | | Case 2:
% 136.03/20.12 | | | | | | | |
% 136.03/20.12 | | | | | | | | (52) all_57_15 = e1 & op(e0, e0) = e1
% 136.03/20.12 | | | | | | | |
% 136.03/20.12 | | | | | | | | ALPHA: (52) implies:
% 136.03/20.12 | | | | | | | | (53) all_57_15 = e1
% 136.03/20.12 | | | | | | | | (54) op(e0, e0) = e1
% 136.03/20.12 | | | | | | | |
% 136.03/20.12 | | | | | | | | BETA: splitting (31) gives:
% 136.03/20.12 | | | | | | | |
% 136.03/20.12 | | | | | | | | Case 1:
% 136.03/20.12 | | | | | | | | |
% 136.03/20.12 | | | | | | | | | (55) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 &
% 136.03/20.12 | | | | | | | | | op(e2, e2) = e0)
% 136.03/20.12 | | | | | | | | |
% 136.03/20.12 | | | | | | | | | BETA: splitting (55) gives:
% 136.03/20.12 | | | | | | | | |
% 136.03/20.12 | | | | | | | | | Case 1:
% 136.03/20.12 | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | | (56) all_57_2 = e0 & op(e2, e3) = e0
% 136.03/20.12 | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | | REF_CLOSE: (29), (45), (56) are inconsistent by sub-proof
% 136.03/20.12 | | | | | | | | | | #272.
% 136.03/20.12 | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | Case 2:
% 136.03/20.12 | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | | (57) all_57_3 = e0 & op(e2, e2) = e0
% 136.03/20.12 | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | | REF_CLOSE: (12), (26), (57) are inconsistent by sub-proof
% 136.03/20.12 | | | | | | | | | | #302.
% 136.03/20.12 | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | End of split
% 136.03/20.12 | | | | | | | | |
% 136.03/20.12 | | | | | | | | Case 2:
% 136.03/20.12 | | | | | | | | |
% 136.03/20.12 | | | | | | | | | (58) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 &
% 136.03/20.12 | | | | | | | | | op(e2, e0) = e0)
% 136.03/20.12 | | | | | | | | |
% 136.03/20.12 | | | | | | | | | BETA: splitting (58) gives:
% 136.03/20.12 | | | | | | | | |
% 136.03/20.12 | | | | | | | | | Case 1:
% 136.03/20.12 | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | | (59) all_57_5 = e0 & op(e2, e1) = e0
% 136.03/20.12 | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | | REF_CLOSE: (4), (39), (59) are inconsistent by sub-proof
% 136.03/20.12 | | | | | | | | | | #277.
% 136.03/20.12 | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | Case 2:
% 136.03/20.12 | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | | (60) all_57_10 = e0 & op(e2, e0) = e0
% 136.03/20.12 | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | | ALPHA: (60) implies:
% 136.03/20.12 | | | | | | | | | | (61) all_57_10 = e0
% 136.03/20.12 | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | | BETA: splitting (23) gives:
% 136.03/20.12 | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | | Case 1:
% 136.03/20.12 | | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | | | (62) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 136.03/20.12 | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 136.03/20.12 | | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | | | BETA: splitting (62) gives:
% 136.03/20.12 | | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | | | Case 1:
% 136.03/20.12 | | | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | | | | (63) all_57_9 = e2 & op(e3, e0) = e2
% 136.03/20.12 | | | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | | | | ALPHA: (63) implies:
% 136.03/20.12 | | | | | | | | | | | | (64) all_57_9 = e2
% 136.03/20.12 | | | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | | | | REF_CLOSE: (3), (4), (6), (10), (11), (12), (14), (19), (24),
% 136.03/20.12 | | | | | | | | | | | | (28), (29), (32), (33), (64) are inconsistent by
% 136.03/20.12 | | | | | | | | | | | | sub-proof #250.
% 136.03/20.12 | | | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | | | Case 2:
% 136.03/20.12 | | | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | | | | (65) all_57_10 = e2 & op(e2, e0) = e2
% 136.03/20.12 | | | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | | | | ALPHA: (65) implies:
% 136.03/20.12 | | | | | | | | | | | | (66) all_57_10 = e2
% 136.03/20.12 | | | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | | | | REF_CLOSE: (4), (12), (26), (29), (31), (39), (45), (66) are
% 136.03/20.12 | | | | | | | | | | | | inconsistent by sub-proof #271.
% 136.03/20.12 | | | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | | | End of split
% 136.03/20.12 | | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | | Case 2:
% 136.03/20.12 | | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | | | (67) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 136.03/20.12 | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 136.03/20.12 | | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | | | BETA: splitting (67) gives:
% 136.03/20.12 | | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | | | Case 1:
% 136.03/20.12 | | | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | | | | (68) all_57_11 = e2 & op(e1, e0) = e2
% 136.03/20.12 | | | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | | | | ALPHA: (68) implies:
% 136.03/20.12 | | | | | | | | | | | | (69) all_57_11 = e2
% 136.03/20.12 | | | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | | | | BETA: splitting (30) gives:
% 136.03/20.12 | | | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | | | | Case 1:
% 136.03/20.12 | | | | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | | | | | (70) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 136.03/20.12 | | | | | | | | | | | | | & op(e2, e2) = e1)
% 136.03/20.12 | | | | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | | | | | BETA: splitting (70) gives:
% 136.03/20.12 | | | | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | | | | | Case 1:
% 136.03/20.12 | | | | | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | | | | | |
% 136.03/20.12 | | | | | | | | | | | | | | ALPHA: (40) implies:
% 136.03/20.12 | | | | | | | | | | | | | | (71) all_57_12 = e0
% 136.03/20.12 | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with e1, e3, e0, e0,
% 136.14/20.12 | | | | | | | | | | | | | | simplifying with (2), (54) gives:
% 136.14/20.12 | | | | | | | | | | | | | | (72) e3 = e1
% 136.14/20.12 | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | COMBINE_EQS: (15), (72) imply:
% 136.14/20.12 | | | | | | | | | | | | | | (73) all_57_6 = e1
% 136.14/20.12 | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | BETA: splitting (17) gives:
% 136.14/20.12 | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | Case 1:
% 136.14/20.12 | | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | | (74) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 136.14/20.12 | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 136.14/20.12 | | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | | BETA: splitting (74) gives:
% 136.14/20.12 | | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | | Case 1:
% 136.14/20.12 | | | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | | | (75) all_57_0 = e3 & op(e3, e3) = e3
% 136.14/20.12 | | | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | | | ALPHA: (75) implies:
% 136.14/20.12 | | | | | | | | | | | | | | | | (76) op(e3, e3) = e3
% 136.14/20.12 | | | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | | | REF_CLOSE: (3), (10), (14), (76) are inconsistent by
% 136.14/20.12 | | | | | | | | | | | | | | | | sub-proof #778.
% 136.14/20.12 | | | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | | Case 2:
% 136.14/20.12 | | | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | | | (77) all_57_2 = e3 & op(e2, e3) = e3
% 136.14/20.12 | | | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | | | ALPHA: (77) implies:
% 136.14/20.12 | | | | | | | | | | | | | | | | (78) all_57_2 = e3
% 136.14/20.12 | | | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | | | REF_CLOSE: (11), (26), (28), (29), (30), (39), (61), (78) are
% 136.14/20.12 | | | | | | | | | | | | | | | | inconsistent by sub-proof #369.
% 136.14/20.12 | | | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | | End of split
% 136.14/20.12 | | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | Case 2:
% 136.14/20.12 | | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | | (79) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 136.14/20.12 | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 136.14/20.12 | | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 136.14/20.12 | | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | | Case 1:
% 136.14/20.12 | | | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | | | (80) all_57_6 = e3 & op(e1, e3) = e3
% 136.14/20.12 | | | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | | | REF_CLOSE: (15), (28), (73) are inconsistent by sub-proof
% 136.14/20.12 | | | | | | | | | | | | | | | | #575.
% 136.14/20.12 | | | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | | Case 2:
% 136.14/20.12 | | | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | | | (81) all_57_12 = e3 & op(e0, e3) = e3
% 136.14/20.12 | | | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | | | ALPHA: (81) implies:
% 136.14/20.12 | | | | | | | | | | | | | | | | (82) all_57_12 = e3
% 136.14/20.12 | | | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | | | REF_CLOSE: (12), (71), (82) are inconsistent by sub-proof
% 136.14/20.12 | | | | | | | | | | | | | | | | #492.
% 136.14/20.12 | | | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | | End of split
% 136.14/20.12 | | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | End of split
% 136.14/20.12 | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | Case 2:
% 136.14/20.12 | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | (83) all_57_3 = e1 & op(e2, e2) = e1
% 136.14/20.12 | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | ALPHA: (83) implies:
% 136.14/20.12 | | | | | | | | | | | | | | (84) op(e2, e2) = e1
% 136.14/20.12 | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | REF_CLOSE: (10), (16), (28), (84) are inconsistent by
% 136.14/20.12 | | | | | | | | | | | | | | sub-proof #325.
% 136.14/20.12 | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | End of split
% 136.14/20.12 | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | Case 2:
% 136.14/20.12 | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | (85) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 136.14/20.12 | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 136.14/20.12 | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | BETA: splitting (85) gives:
% 136.14/20.12 | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | Case 1:
% 136.14/20.12 | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | (86) all_57_5 = e1 & op(e2, e1) = e1
% 136.14/20.12 | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | REF_CLOSE: (11), (39), (86) are inconsistent by sub-proof
% 136.14/20.12 | | | | | | | | | | | | | | #500.
% 136.14/20.12 | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | Case 2:
% 136.14/20.12 | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | (87) all_57_10 = e1 & op(e2, e0) = e1
% 136.14/20.12 | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | ALPHA: (87) implies:
% 136.14/20.12 | | | | | | | | | | | | | | (88) all_57_10 = e1
% 136.14/20.12 | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | BETA: splitting (27) gives:
% 136.14/20.12 | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | Case 1:
% 136.14/20.12 | | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | | (89) all_57_15 = e0 & op(e0, e0) = e0
% 136.14/20.12 | | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | | REF_CLOSE: (29), (53), (89) are inconsistent by sub-proof
% 136.14/20.12 | | | | | | | | | | | | | | | #412.
% 136.14/20.12 | | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | Case 2:
% 136.14/20.12 | | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | | (90) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 136.14/20.12 | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 136.14/20.12 | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 136.14/20.12 | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 136.14/20.12 | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 136.14/20.12 | | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | | REF_CLOSE: (4), (12), (13), (29), (69), (88), (90) are
% 136.14/20.12 | | | | | | | | | | | | | | | inconsistent by sub-proof #637.
% 136.14/20.12 | | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | | End of split
% 136.14/20.12 | | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | | End of split
% 136.14/20.12 | | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | End of split
% 136.14/20.12 | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | Case 2:
% 136.14/20.12 | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | (91) all_57_15 = e2 & op(e0, e0) = e2
% 136.14/20.12 | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | ALPHA: (91) implies:
% 136.14/20.12 | | | | | | | | | | | | (92) op(e0, e0) = e2
% 136.14/20.12 | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | | REF_CLOSE: (10), (11), (54), (92) are inconsistent by
% 136.14/20.12 | | | | | | | | | | | | sub-proof #636.
% 136.14/20.12 | | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | | End of split
% 136.14/20.12 | | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | | End of split
% 136.14/20.12 | | | | | | | | | |
% 136.14/20.12 | | | | | | | | | End of split
% 136.14/20.12 | | | | | | | | |
% 136.14/20.12 | | | | | | | | End of split
% 136.14/20.12 | | | | | | | |
% 136.14/20.12 | | | | | | | End of split
% 136.14/20.12 | | | | | | |
% 136.14/20.12 | | | | | | End of split
% 136.14/20.12 | | | | | |
% 136.14/20.12 | | | | | End of split
% 136.14/20.12 | | | | |
% 136.14/20.12 | | | | Case 2:
% 136.14/20.12 | | | | |
% 136.14/20.12 | | | | | (93) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0,
% 136.14/20.12 | | | | | e3) = e1)
% 136.14/20.12 | | | | |
% 136.14/20.12 | | | | | BETA: splitting (93) gives:
% 136.14/20.12 | | | | |
% 136.14/20.12 | | | | | Case 1:
% 136.14/20.12 | | | | | |
% 136.14/20.12 | | | | | | (94) all_57_6 = e1 & op(e1, e3) = e1
% 136.14/20.12 | | | | | |
% 136.14/20.12 | | | | | | REF_CLOSE: (15), (28), (94) are inconsistent by sub-proof #645.
% 136.14/20.12 | | | | | |
% 136.14/20.12 | | | | | Case 2:
% 136.14/20.12 | | | | | |
% 136.14/20.12 | | | | | | (95) all_57_12 = e1 & op(e0, e3) = e1
% 136.14/20.12 | | | | | |
% 136.14/20.12 | | | | | | ALPHA: (95) implies:
% 136.14/20.12 | | | | | | (96) all_57_12 = e1
% 136.14/20.12 | | | | | |
% 136.14/20.12 | | | | | | REF_CLOSE: (4), (5), (12), (22), (25), (29), (96) are inconsistent
% 136.14/20.12 | | | | | | by sub-proof #399.
% 136.14/20.12 | | | | | |
% 136.14/20.12 | | | | | End of split
% 136.14/20.12 | | | | |
% 136.14/20.12 | | | | End of split
% 136.14/20.12 | | | |
% 136.14/20.12 | | | Case 2:
% 136.14/20.12 | | | |
% 136.14/20.12 | | | | (97) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 136.14/20.12 | | | | e1) = e0)
% 136.14/20.12 | | | |
% 136.14/20.12 | | | | BETA: splitting (97) gives:
% 136.14/20.12 | | | |
% 136.14/20.12 | | | | Case 1:
% 136.14/20.12 | | | | |
% 136.14/20.12 | | | | | (98) all_57_13 = e0 & op(e0, e2) = e0
% 136.14/20.12 | | | | |
% 136.14/20.12 | | | | | REF_CLOSE: (4), (22), (98) are inconsistent by sub-proof #411.
% 136.14/20.12 | | | | |
% 136.14/20.12 | | | | Case 2:
% 136.14/20.12 | | | | |
% 136.14/20.12 | | | | | (99) all_57_14 = e0 & op(e0, e1) = e0
% 136.14/20.12 | | | | |
% 136.14/20.12 | | | | | REF_CLOSE: (12), (25), (99) are inconsistent by sub-proof #252.
% 136.14/20.12 | | | | |
% 136.14/20.12 | | | | End of split
% 136.14/20.12 | | | |
% 136.14/20.12 | | | End of split
% 136.14/20.12 | | |
% 136.14/20.12 | | End of split
% 136.14/20.12 | |
% 136.14/20.12 | Case 2:
% 136.14/20.12 | |
% 136.14/20.12 | | (100) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 136.14/20.12 | | e2)
% 136.14/20.12 | |
% 136.14/20.12 | | REF_CLOSE: (1), (3), (4), (6), (7), (9), (10), (11), (12), (13), (14), (18),
% 136.14/20.12 | | (19), (20), (21), (22), (24), (27), (28), (29), (32), (33), (100)
% 136.14/20.12 | | are inconsistent by sub-proof #249.
% 136.14/20.12 | |
% 136.14/20.12 | End of split
% 136.14/20.12 |
% 136.14/20.12 End of proof
% 136.14/20.12
% 136.14/20.12 Sub-proof #247 shows that the following formulas are inconsistent:
% 136.14/20.12 ----------------------------------------------------------------
% 136.14/20.12 (1) all_57_14 = e1 & op(e0, e1) = e1
% 136.14/20.12 (2) all_57_14 = e3
% 136.14/20.12 (3) ~ (e3 = e1)
% 136.14/20.12
% 136.14/20.12 Begin of proof
% 136.14/20.12 |
% 136.14/20.12 | ALPHA: (1) implies:
% 136.14/20.12 | (4) all_57_14 = e1
% 136.14/20.12 |
% 136.14/20.12 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.12 | (5) e3 = e1
% 136.14/20.12 |
% 136.14/20.12 | REDUCE: (3), (5) imply:
% 136.14/20.12 | (6) $false
% 136.14/20.12 |
% 136.14/20.12 | CLOSE: (6) is inconsistent.
% 136.14/20.12 |
% 136.14/20.12 End of proof
% 136.14/20.12
% 136.14/20.12 Sub-proof #248 shows that the following formulas are inconsistent:
% 136.14/20.12 ----------------------------------------------------------------
% 136.14/20.12 (1) all_57_13 = e1 & op(e0, e2) = e1
% 136.14/20.12 (2) all_57_13 = e2
% 136.14/20.12 (3) ~ (e2 = e1)
% 136.14/20.12
% 136.14/20.12 Begin of proof
% 136.14/20.12 |
% 136.14/20.12 | ALPHA: (1) implies:
% 136.14/20.12 | (4) all_57_13 = e1
% 136.14/20.12 |
% 136.14/20.12 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.12 | (5) e2 = e1
% 136.14/20.12 |
% 136.14/20.12 | REDUCE: (3), (5) imply:
% 136.14/20.12 | (6) $false
% 136.14/20.12 |
% 136.14/20.12 | CLOSE: (6) is inconsistent.
% 136.14/20.12 |
% 136.14/20.12 End of proof
% 136.14/20.12
% 136.14/20.12 Sub-proof #249 shows that the following formulas are inconsistent:
% 136.14/20.12 ----------------------------------------------------------------
% 136.14/20.12 (1) op(e1, e1) = all_6_2
% 136.14/20.12 (2) op(e3, e3) = e2
% 136.14/20.12 (3) ~ (e2 = e0)
% 136.14/20.12 (4) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 136.14/20.12 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 136.14/20.12 (5) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 136.14/20.12 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 136.14/20.12 (6) ~ (all_52_7 = e3)
% 136.14/20.12 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.12 (8) ~ (e2 = e1)
% 136.14/20.12 (9) ~ (e3 = e0)
% 136.14/20.12 (10) all_57_9 = e3
% 136.14/20.12 (11) ~ (e3 = e2)
% 136.14/20.12 (12) op(e0, e2) = all_52_7
% 136.14/20.12 (13) ~ (all_52_4 = e3)
% 136.14/20.12 (14) ~ (all_6_2 = e2)
% 136.14/20.12 (15) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 136.14/20.12 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 136.14/20.12 e1)
% 136.14/20.12 (16) all_57_13 = e2
% 136.14/20.12 (17) op(e3, e2) = all_52_4
% 136.14/20.12 (18) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 136.14/20.12 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 136.14/20.12 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 136.14/20.12 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 136.14/20.12 (19) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 136.14/20.12 (20) ~ (e3 = e1)
% 136.14/20.12 (21) ~ (e1 = e0)
% 136.14/20.12 (22) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 136.14/20.12 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 136.14/20.12 (23) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 136.14/20.12 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 136.14/20.12
% 136.14/20.12 Begin of proof
% 136.14/20.12 |
% 136.14/20.12 | BETA: splitting (19) gives:
% 136.14/20.12 |
% 136.14/20.12 | Case 1:
% 136.14/20.12 | |
% 136.14/20.12 | | (24) all_57_8 = e2 & op(e1, e1) = e2
% 136.14/20.12 | |
% 136.14/20.12 | | ALPHA: (24) implies:
% 136.14/20.12 | | (25) op(e1, e1) = e2
% 136.14/20.12 | |
% 136.14/20.12 | | REF_CLOSE: (1), (7), (14), (25) are inconsistent by sub-proof #767.
% 136.14/20.12 | |
% 136.14/20.12 | Case 2:
% 136.14/20.12 | |
% 136.14/20.12 | | (26) all_57_14 = e2 & op(e0, e1) = e2
% 136.14/20.12 | |
% 136.14/20.12 | | ALPHA: (26) implies:
% 136.14/20.12 | | (27) all_57_14 = e2
% 136.14/20.12 | |
% 136.14/20.12 | | BETA: splitting (5) gives:
% 136.14/20.12 | |
% 136.14/20.12 | | Case 1:
% 136.14/20.12 | | |
% 136.14/20.12 | | | (28) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2)
% 136.14/20.12 | | | = e3)
% 136.14/20.12 | | |
% 136.14/20.12 | | | BETA: splitting (28) gives:
% 136.14/20.12 | | |
% 136.14/20.12 | | | Case 1:
% 136.14/20.12 | | | |
% 136.14/20.12 | | | | (29) all_57_12 = e3 & op(e0, e3) = e3
% 136.14/20.12 | | | |
% 136.14/20.12 | | | | ALPHA: (29) implies:
% 136.14/20.12 | | | | (30) all_57_12 = e3
% 136.14/20.12 | | | |
% 136.14/20.12 | | | | REF_CLOSE: (3), (8), (9), (15), (16), (18), (20), (21), (27), (30) are
% 136.14/20.12 | | | | inconsistent by sub-proof #409.
% 136.14/20.12 | | | |
% 136.14/20.12 | | | Case 2:
% 136.14/20.12 | | | |
% 136.14/20.12 | | | | (31) all_57_13 = e3 & op(e0, e2) = e3
% 136.14/20.12 | | | |
% 136.14/20.12 | | | | REF_CLOSE: (6), (7), (12), (31) are inconsistent by sub-proof #556.
% 136.14/20.12 | | | |
% 136.14/20.12 | | | End of split
% 136.14/20.12 | | |
% 136.14/20.12 | | Case 2:
% 136.14/20.12 | | |
% 136.14/20.12 | | | (32) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0)
% 136.14/20.12 | | | = e3)
% 136.14/20.12 | | |
% 136.14/20.12 | | | BETA: splitting (32) gives:
% 136.14/20.12 | | |
% 136.14/20.12 | | | Case 1:
% 136.14/20.12 | | | |
% 136.14/20.12 | | | | (33) all_57_14 = e3 & op(e0, e1) = e3
% 136.14/20.12 | | | |
% 136.14/20.12 | | | | ALPHA: (33) implies:
% 136.14/20.12 | | | | (34) all_57_14 = e3
% 136.14/20.12 | | | |
% 136.14/20.12 | | | | COMBINE_EQS: (27), (34) imply:
% 136.14/20.12 | | | | (35) e3 = e2
% 136.14/20.12 | | | |
% 136.14/20.12 | | | | SIMP: (35) implies:
% 136.14/20.12 | | | | (36) e3 = e2
% 136.14/20.12 | | | |
% 136.14/20.12 | | | | COMBINE_EQS: (10), (36) imply:
% 136.14/20.12 | | | | (37) all_57_9 = e2
% 136.14/20.12 | | | |
% 136.14/20.12 | | | | REF_CLOSE: (2), (3), (4), (7), (8), (9), (11), (13), (17), (20), (21),
% 136.14/20.12 | | | | (22), (23), (37) are inconsistent by sub-proof #250.
% 136.14/20.12 | | | |
% 136.14/20.12 | | | Case 2:
% 136.14/20.12 | | | |
% 136.14/20.12 | | | | (38) all_57_15 = e3 & op(e0, e0) = e3
% 136.14/20.12 | | | |
% 136.14/20.12 | | | | REF_CLOSE: (3), (8), (9), (15), (16), (18), (20), (21), (27), (38) are
% 136.14/20.12 | | | | inconsistent by sub-proof #402.
% 136.14/20.12 | | | |
% 136.14/20.12 | | | End of split
% 136.14/20.12 | | |
% 136.14/20.12 | | End of split
% 136.14/20.12 | |
% 136.14/20.12 | End of split
% 136.14/20.12 |
% 136.14/20.12 End of proof
% 136.14/20.12
% 136.14/20.12 Sub-proof #250 shows that the following formulas are inconsistent:
% 136.14/20.12 ----------------------------------------------------------------
% 136.14/20.12 (1) op(e3, e3) = e2
% 136.14/20.12 (2) ~ (e2 = e0)
% 136.14/20.12 (3) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 136.14/20.12 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 136.14/20.12 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.12 (5) ~ (e2 = e1)
% 136.14/20.12 (6) ~ (e3 = e0)
% 136.14/20.12 (7) ~ (e3 = e2)
% 136.14/20.12 (8) all_57_9 = e2
% 136.14/20.12 (9) ~ (all_52_4 = e3)
% 136.14/20.12 (10) op(e3, e2) = all_52_4
% 136.14/20.12 (11) ~ (e3 = e1)
% 136.14/20.12 (12) ~ (e1 = e0)
% 136.14/20.12 (13) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 136.14/20.12 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 136.14/20.12 (14) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 136.14/20.12 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 136.14/20.12
% 136.14/20.12 Begin of proof
% 136.14/20.12 |
% 136.14/20.12 | BETA: splitting (13) gives:
% 136.14/20.12 |
% 136.14/20.12 | Case 1:
% 136.14/20.12 | |
% 136.14/20.12 | | (15) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 136.14/20.12 | | e3)
% 136.14/20.12 | |
% 136.14/20.12 | | REF_CLOSE: (1), (4), (7), (9), (10), (15) are inconsistent by sub-proof
% 136.14/20.12 | | #282.
% 136.14/20.12 | |
% 136.14/20.12 | Case 2:
% 136.14/20.12 | |
% 136.14/20.12 | | (16) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 136.14/20.12 | | e3)
% 136.14/20.12 | |
% 136.14/20.12 | | BETA: splitting (16) gives:
% 136.14/20.12 | |
% 136.14/20.12 | | Case 1:
% 136.14/20.12 | | |
% 136.14/20.12 | | | (17) all_57_4 = e3 & op(e3, e1) = e3
% 136.14/20.12 | | |
% 136.14/20.12 | | | ALPHA: (17) implies:
% 136.14/20.12 | | | (18) all_57_4 = e3
% 136.14/20.12 | | |
% 136.14/20.12 | | | BETA: splitting (3) gives:
% 136.14/20.12 | | |
% 136.14/20.12 | | | Case 1:
% 136.14/20.12 | | | |
% 136.14/20.12 | | | | (19) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2)
% 136.14/20.12 | | | | = e0)
% 136.14/20.12 | | | |
% 136.14/20.12 | | | | BETA: splitting (19) gives:
% 136.14/20.12 | | | |
% 136.14/20.12 | | | | Case 1:
% 136.14/20.12 | | | | |
% 136.14/20.12 | | | | | (20) all_57_0 = e0 & op(e3, e3) = e0
% 136.14/20.12 | | | | |
% 136.14/20.12 | | | | | ALPHA: (20) implies:
% 136.14/20.12 | | | | | (21) op(e3, e3) = e0
% 136.14/20.12 | | | | |
% 136.14/20.12 | | | | | REF_CLOSE: (1), (2), (4), (21) are inconsistent by sub-proof #495.
% 136.14/20.12 | | | | |
% 136.14/20.12 | | | | Case 2:
% 136.14/20.12 | | | | |
% 136.14/20.12 | | | | | (22) all_57_1 = e0 & op(e3, e2) = e0
% 136.14/20.12 | | | | |
% 136.14/20.12 | | | | | ALPHA: (22) implies:
% 136.14/20.12 | | | | | (23) all_57_1 = e0
% 136.14/20.12 | | | | |
% 136.14/20.12 | | | | | BETA: splitting (14) gives:
% 136.14/20.12 | | | | |
% 136.14/20.12 | | | | | Case 1:
% 136.14/20.12 | | | | | |
% 136.14/20.12 | | | | | | (24) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3,
% 136.14/20.12 | | | | | | e2) = e1)
% 136.14/20.12 | | | | | |
% 136.14/20.12 | | | | | | REF_CLOSE: (1), (4), (5), (12), (23), (24) are inconsistent by
% 136.14/20.12 | | | | | | sub-proof #281.
% 136.14/20.12 | | | | | |
% 136.14/20.12 | | | | | Case 2:
% 136.14/20.12 | | | | | |
% 136.14/20.12 | | | | | | (25) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3,
% 136.14/20.12 | | | | | | e0) = e1)
% 136.14/20.12 | | | | | |
% 136.14/20.12 | | | | | | BETA: splitting (25) gives:
% 136.14/20.12 | | | | | |
% 136.14/20.12 | | | | | | Case 1:
% 136.14/20.12 | | | | | | |
% 136.14/20.12 | | | | | | | (26) all_57_4 = e1 & op(e3, e1) = e1
% 136.14/20.12 | | | | | | |
% 136.14/20.12 | | | | | | | REF_CLOSE: (11), (18), (26) are inconsistent by sub-proof #382.
% 136.14/20.12 | | | | | | |
% 136.14/20.12 | | | | | | Case 2:
% 136.14/20.12 | | | | | | |
% 136.14/20.12 | | | | | | | (27) all_57_9 = e1 & op(e3, e0) = e1
% 136.14/20.12 | | | | | | |
% 136.14/20.12 | | | | | | | ALPHA: (27) implies:
% 136.14/20.12 | | | | | | | (28) all_57_9 = e1
% 136.14/20.12 | | | | | | |
% 136.14/20.12 | | | | | | | COMBINE_EQS: (8), (28) imply:
% 136.14/20.12 | | | | | | | (29) e2 = e1
% 136.14/20.12 | | | | | | |
% 136.14/20.12 | | | | | | | REDUCE: (5), (29) imply:
% 136.14/20.12 | | | | | | | (30) $false
% 136.14/20.12 | | | | | | |
% 136.14/20.12 | | | | | | | CLOSE: (30) is inconsistent.
% 136.14/20.12 | | | | | | |
% 136.14/20.12 | | | | | | End of split
% 136.14/20.12 | | | | | |
% 136.14/20.12 | | | | | End of split
% 136.14/20.12 | | | | |
% 136.14/20.12 | | | | End of split
% 136.14/20.12 | | | |
% 136.14/20.12 | | | Case 2:
% 136.14/20.12 | | | |
% 136.14/20.12 | | | | (31) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0)
% 136.14/20.12 | | | | = e0)
% 136.14/20.12 | | | |
% 136.14/20.12 | | | | BETA: splitting (31) gives:
% 136.14/20.12 | | | |
% 136.14/20.12 | | | | Case 1:
% 136.14/20.12 | | | | |
% 136.14/20.12 | | | | | (32) all_57_4 = e0 & op(e3, e1) = e0
% 136.14/20.12 | | | | |
% 136.14/20.12 | | | | | REF_CLOSE: (6), (18), (32) are inconsistent by sub-proof #384.
% 136.14/20.12 | | | | |
% 136.14/20.12 | | | | Case 2:
% 136.14/20.12 | | | | |
% 136.14/20.12 | | | | | (33) all_57_9 = e0 & op(e3, e0) = e0
% 136.14/20.12 | | | | |
% 136.14/20.12 | | | | | REF_CLOSE: (2), (8), (33) are inconsistent by sub-proof #657.
% 136.14/20.12 | | | | |
% 136.14/20.12 | | | | End of split
% 136.14/20.12 | | | |
% 136.14/20.12 | | | End of split
% 136.14/20.12 | | |
% 136.14/20.12 | | Case 2:
% 136.14/20.12 | | |
% 136.14/20.12 | | | (34) all_57_9 = e3 & op(e3, e0) = e3
% 136.14/20.12 | | |
% 136.14/20.12 | | | REF_CLOSE: (7), (8), (34) are inconsistent by sub-proof #612.
% 136.14/20.12 | | |
% 136.14/20.12 | | End of split
% 136.14/20.12 | |
% 136.14/20.12 | End of split
% 136.14/20.12 |
% 136.14/20.12 End of proof
% 136.14/20.12
% 136.14/20.12 Sub-proof #251 shows that the following formulas are inconsistent:
% 136.14/20.12 ----------------------------------------------------------------
% 136.14/20.12 (1) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 136.14/20.12 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 136.14/20.12 (2) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 136.14/20.12 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 136.14/20.12 (3) all_57_4 = e3 & op(e3, e1) = e3
% 136.14/20.12 (4) op(e1, e1) = all_6_2
% 136.14/20.12 (5) op(e3, e3) = e2
% 136.14/20.12 (6) ~ (e2 = e0)
% 136.14/20.12 (7) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 136.14/20.12 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 136.14/20.12 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.12 (9) ~ (e2 = e1)
% 136.14/20.12 (10) ~ (e3 = e0)
% 136.14/20.12 (11) ~ (e3 = e2)
% 136.14/20.12 (12) ~ (all_52_4 = e3)
% 136.14/20.12 (13) ~ (all_6_2 = e2)
% 136.14/20.12 (14) op(e3, e2) = all_52_4
% 136.14/20.12 (15) all_57_14 = e3
% 136.14/20.12 (16) ~ (e3 = e1)
% 136.14/20.12 (17) ~ (e1 = e0)
% 136.14/20.12 (18) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 136.14/20.12 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 136.14/20.12 (19) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 136.14/20.12 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 136.14/20.12 (20) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 136.14/20.12 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 136.14/20.12
% 136.14/20.12 Begin of proof
% 136.14/20.12 |
% 136.14/20.12 | ALPHA: (3) implies:
% 136.14/20.12 | (21) all_57_4 = e3
% 136.14/20.12 |
% 136.14/20.12 | BETA: splitting (20) gives:
% 136.14/20.12 |
% 136.14/20.12 | Case 1:
% 136.14/20.12 | |
% 136.14/20.12 | | (22) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 136.14/20.12 | | e2)
% 136.14/20.12 | |
% 136.14/20.12 | | BETA: splitting (22) gives:
% 136.14/20.12 | |
% 136.14/20.12 | | Case 1:
% 136.14/20.12 | | |
% 136.14/20.12 | | | (23) all_57_4 = e2 & op(e3, e1) = e2
% 136.14/20.12 | | |
% 136.14/20.12 | | | ALPHA: (23) implies:
% 136.14/20.12 | | | (24) all_57_4 = e2
% 136.14/20.12 | | |
% 136.14/20.12 | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (14), (16), (17),
% 136.14/20.12 | | | (18), (19), (24) are inconsistent by sub-proof #278.
% 136.14/20.12 | | |
% 136.14/20.12 | | Case 2:
% 136.14/20.12 | | |
% 136.14/20.12 | | | (25) all_57_5 = e2 & op(e2, e1) = e2
% 136.14/20.12 | | |
% 136.14/20.12 | | | ALPHA: (25) implies:
% 136.14/20.12 | | | (26) all_57_5 = e2
% 136.14/20.12 | | |
% 136.14/20.12 | | | BETA: splitting (2) gives:
% 136.14/20.12 | | |
% 136.14/20.12 | | | Case 1:
% 136.14/20.12 | | | |
% 136.14/20.13 | | | | (27) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1)
% 136.14/20.13 | | | | = e0)
% 136.14/20.13 | | | |
% 136.14/20.13 | | | | BETA: splitting (27) gives:
% 136.14/20.13 | | | |
% 136.14/20.13 | | | | Case 1:
% 136.14/20.13 | | | | |
% 136.14/20.13 | | | | | (28) all_57_4 = e0 & op(e3, e1) = e0
% 136.14/20.13 | | | | |
% 136.14/20.13 | | | | | REF_CLOSE: (10), (21), (28) are inconsistent by sub-proof #384.
% 136.14/20.13 | | | | |
% 136.14/20.13 | | | | Case 2:
% 136.14/20.13 | | | | |
% 136.14/20.13 | | | | | (29) all_57_5 = e0 & op(e2, e1) = e0
% 136.14/20.13 | | | | |
% 136.14/20.13 | | | | | REF_CLOSE: (6), (26), (29) are inconsistent by sub-proof #277.
% 136.14/20.13 | | | | |
% 136.14/20.13 | | | | End of split
% 136.14/20.13 | | | |
% 136.14/20.13 | | | Case 2:
% 136.14/20.13 | | | |
% 136.14/20.13 | | | | (30) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1)
% 136.14/20.13 | | | | = e0)
% 136.14/20.13 | | | |
% 136.14/20.13 | | | | BETA: splitting (30) gives:
% 136.14/20.13 | | | |
% 136.14/20.13 | | | | Case 1:
% 136.14/20.13 | | | | |
% 136.14/20.13 | | | | | (31) all_57_8 = e0 & op(e1, e1) = e0
% 136.14/20.13 | | | | |
% 136.14/20.13 | | | | | ALPHA: (31) implies:
% 136.14/20.13 | | | | | (32) op(e1, e1) = e0
% 136.14/20.13 | | | | |
% 136.14/20.13 | | | | | BETA: splitting (1) gives:
% 136.14/20.13 | | | | |
% 136.14/20.13 | | | | | Case 1:
% 136.14/20.13 | | | | | |
% 136.14/20.13 | | | | | | (33) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2,
% 136.14/20.13 | | | | | | e1) = e1)
% 136.14/20.13 | | | | | |
% 136.14/20.13 | | | | | | BETA: splitting (33) gives:
% 136.14/20.13 | | | | | |
% 136.14/20.13 | | | | | | Case 1:
% 136.14/20.13 | | | | | | |
% 136.14/20.13 | | | | | | | (34) all_57_4 = e1 & op(e3, e1) = e1
% 136.14/20.13 | | | | | | |
% 136.14/20.13 | | | | | | | REF_CLOSE: (16), (21), (34) are inconsistent by sub-proof #382.
% 136.14/20.13 | | | | | | |
% 136.14/20.13 | | | | | | Case 2:
% 136.14/20.13 | | | | | | |
% 136.14/20.13 | | | | | | | (35) all_57_5 = e1 & op(e2, e1) = e1
% 136.14/20.13 | | | | | | |
% 136.14/20.13 | | | | | | | ALPHA: (35) implies:
% 136.14/20.13 | | | | | | | (36) all_57_5 = e1
% 136.14/20.13 | | | | | | |
% 136.14/20.13 | | | | | | | REF_CLOSE: (9), (26), (36) are inconsistent by sub-proof #418.
% 136.14/20.13 | | | | | | |
% 136.14/20.13 | | | | | | End of split
% 136.14/20.13 | | | | | |
% 136.14/20.13 | | | | | Case 2:
% 136.14/20.13 | | | | | |
% 136.14/20.13 | | | | | | (37) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0,
% 136.14/20.13 | | | | | | e1) = e1)
% 136.14/20.13 | | | | | |
% 136.14/20.13 | | | | | | BETA: splitting (37) gives:
% 136.14/20.13 | | | | | |
% 136.14/20.13 | | | | | | Case 1:
% 136.14/20.13 | | | | | | |
% 136.14/20.13 | | | | | | | (38) all_57_8 = e1 & op(e1, e1) = e1
% 136.14/20.13 | | | | | | |
% 136.14/20.13 | | | | | | | ALPHA: (38) implies:
% 136.14/20.13 | | | | | | | (39) op(e1, e1) = e1
% 136.14/20.13 | | | | | | |
% 136.14/20.13 | | | | | | | REF_CLOSE: (8), (17), (32), (39) are inconsistent by sub-proof
% 136.14/20.13 | | | | | | | #721.
% 136.14/20.13 | | | | | | |
% 136.14/20.13 | | | | | | Case 2:
% 136.14/20.13 | | | | | | |
% 136.14/20.13 | | | | | | | (40) all_57_14 = e1 & op(e0, e1) = e1
% 136.14/20.13 | | | | | | |
% 136.14/20.13 | | | | | | | ALPHA: (40) implies:
% 136.14/20.13 | | | | | | | (41) all_57_14 = e1
% 136.14/20.13 | | | | | | |
% 136.14/20.13 | | | | | | | REF_CLOSE: (15), (16), (41) are inconsistent by sub-proof #561.
% 136.14/20.13 | | | | | | |
% 136.14/20.13 | | | | | | End of split
% 136.14/20.13 | | | | | |
% 136.14/20.13 | | | | | End of split
% 136.14/20.13 | | | | |
% 136.14/20.13 | | | | Case 2:
% 136.14/20.13 | | | | |
% 136.14/20.13 | | | | | (42) all_57_14 = e0 & op(e0, e1) = e0
% 136.14/20.13 | | | | |
% 136.14/20.13 | | | | | REF_CLOSE: (10), (15), (42) are inconsistent by sub-proof #252.
% 136.14/20.13 | | | | |
% 136.14/20.13 | | | | End of split
% 136.14/20.13 | | | |
% 136.14/20.13 | | | End of split
% 136.14/20.13 | | |
% 136.14/20.13 | | End of split
% 136.14/20.13 | |
% 136.14/20.13 | Case 2:
% 136.14/20.13 | |
% 136.14/20.13 | | (43) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 136.14/20.13 | | e2)
% 136.14/20.13 | |
% 136.14/20.13 | | BETA: splitting (43) gives:
% 136.14/20.13 | |
% 136.14/20.13 | | Case 1:
% 136.14/20.13 | | |
% 136.14/20.13 | | | (44) all_57_8 = e2 & op(e1, e1) = e2
% 136.14/20.13 | | |
% 136.14/20.13 | | | ALPHA: (44) implies:
% 136.14/20.13 | | | (45) op(e1, e1) = e2
% 136.14/20.13 | | |
% 136.14/20.13 | | | REF_CLOSE: (4), (8), (13), (45) are inconsistent by sub-proof #767.
% 136.14/20.13 | | |
% 136.14/20.13 | | Case 2:
% 136.14/20.13 | | |
% 136.14/20.13 | | | (46) all_57_14 = e2 & op(e0, e1) = e2
% 136.14/20.13 | | |
% 136.14/20.13 | | | ALPHA: (46) implies:
% 136.14/20.13 | | | (47) all_57_14 = e2
% 136.14/20.13 | | |
% 136.14/20.13 | | | COMBINE_EQS: (15), (47) imply:
% 136.14/20.13 | | | (48) e3 = e2
% 136.14/20.13 | | |
% 136.14/20.13 | | | COMBINE_EQS: (21), (48) imply:
% 136.14/20.13 | | | (49) all_57_4 = e2
% 136.14/20.13 | | |
% 136.14/20.13 | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (14), (16), (17),
% 136.14/20.13 | | | (18), (19), (49) are inconsistent by sub-proof #278.
% 136.14/20.13 | | |
% 136.14/20.13 | | End of split
% 136.14/20.13 | |
% 136.14/20.13 | End of split
% 136.14/20.13 |
% 136.14/20.13 End of proof
% 136.14/20.13
% 136.14/20.13 Sub-proof #252 shows that the following formulas are inconsistent:
% 136.14/20.13 ----------------------------------------------------------------
% 136.14/20.13 (1) all_57_14 = e0 & op(e0, e1) = e0
% 136.14/20.13 (2) all_57_14 = e3
% 136.14/20.13 (3) ~ (e3 = e0)
% 136.14/20.13
% 136.14/20.13 Begin of proof
% 136.14/20.13 |
% 136.14/20.13 | ALPHA: (1) implies:
% 136.14/20.13 | (4) all_57_14 = e0
% 136.14/20.13 |
% 136.14/20.13 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.13 | (5) e3 = e0
% 136.14/20.13 |
% 136.14/20.13 | REDUCE: (3), (5) imply:
% 136.14/20.13 | (6) $false
% 136.14/20.13 |
% 136.14/20.13 | CLOSE: (6) is inconsistent.
% 136.14/20.13 |
% 136.14/20.13 End of proof
% 136.14/20.13
% 136.14/20.13 Sub-proof #253 shows that the following formulas are inconsistent:
% 136.14/20.13 ----------------------------------------------------------------
% 136.14/20.13 (1) all_56_31 = e3
% 136.14/20.13 (2) all_56_31 = e1
% 136.14/20.13 (3) ~ (e3 = e1)
% 136.14/20.13
% 136.14/20.13 Begin of proof
% 136.14/20.13 |
% 136.14/20.13 | COMBINE_EQS: (1), (2) imply:
% 136.14/20.13 | (4) e3 = e1
% 136.14/20.13 |
% 136.14/20.13 | SIMP: (4) implies:
% 136.14/20.13 | (5) e3 = e1
% 136.14/20.13 |
% 136.14/20.13 | REDUCE: (3), (5) imply:
% 136.14/20.13 | (6) $false
% 136.14/20.13 |
% 136.14/20.13 | CLOSE: (6) is inconsistent.
% 136.14/20.13 |
% 136.14/20.13 End of proof
% 136.14/20.13
% 136.14/20.13 Sub-proof #254 shows that the following formulas are inconsistent:
% 136.14/20.13 ----------------------------------------------------------------
% 136.14/20.13 (1) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2)
% 136.14/20.13 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3,
% 136.14/20.13 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 136.14/20.13 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 136.14/20.13 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 136.14/20.13 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.14/20.13 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) =
% 136.14/20.13 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.14/20.13 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 136.14/20.13 $i(all_56_21) & $i(all_56_29))
% 136.14/20.13 (2) op(e3, e3) = e2
% 136.14/20.13 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.13 (4) ~ (e2 = e1)
% 136.14/20.13 (5) ~ (all_52_4 = e3)
% 136.14/20.13 (6) op(e3, e2) = all_52_4
% 136.14/20.13
% 136.14/20.13 Begin of proof
% 136.14/20.13 |
% 136.14/20.13 | BETA: splitting (1) gives:
% 136.14/20.13 |
% 136.14/20.13 | Case 1:
% 136.14/20.13 | |
% 136.14/20.13 | | (7) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 136.14/20.13 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 136.14/20.13 | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 136.14/20.13 | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 136.14/20.13 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)
% 136.14/20.13 | |
% 136.14/20.13 | | ALPHA: (7) implies:
% 136.14/20.13 | | (8) op(e3, e2) = e3
% 136.14/20.13 | |
% 136.14/20.13 | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #738.
% 136.14/20.13 | |
% 136.14/20.13 | Case 2:
% 136.14/20.13 | |
% 136.14/20.13 | | (9) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 136.14/20.13 | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 136.14/20.13 | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 136.14/20.13 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 136.14/20.13 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 136.14/20.13 | |
% 136.14/20.13 | | ALPHA: (9) implies:
% 136.14/20.13 | | (10) op(e3, e3) = e1
% 136.14/20.13 | |
% 136.14/20.13 | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #743.
% 136.14/20.13 | |
% 136.14/20.13 | End of split
% 136.14/20.13 |
% 136.14/20.13 End of proof
% 136.14/20.13
% 136.14/20.13 Sub-proof #255 shows that the following formulas are inconsistent:
% 136.14/20.13 ----------------------------------------------------------------
% 136.14/20.13 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.13 (2) ~ (e3 = e0)
% 136.14/20.13 (3) ~ (e3 = e2)
% 136.14/20.13 (4) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 136.14/20.13 (5) op(e0, e0) = e2
% 136.14/20.13 (6) all_57_11 = e0
% 136.14/20.13
% 136.14/20.13 Begin of proof
% 136.14/20.13 |
% 136.14/20.13 | BETA: splitting (4) gives:
% 136.14/20.13 |
% 136.14/20.13 | Case 1:
% 136.14/20.13 | |
% 136.14/20.13 | | (7) all_57_11 = e3 & op(e1, e0) = e3
% 136.14/20.13 | |
% 136.14/20.13 | | REF_CLOSE: (2), (6), (7) are inconsistent by sub-proof #256.
% 136.14/20.13 | |
% 136.14/20.13 | Case 2:
% 136.14/20.13 | |
% 136.14/20.13 | | (8) all_57_15 = e3 & op(e0, e0) = e3
% 136.14/20.13 | |
% 136.14/20.13 | | ALPHA: (8) implies:
% 136.14/20.13 | | (9) op(e0, e0) = e3
% 136.14/20.13 | |
% 136.14/20.13 | | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #634.
% 136.14/20.13 | |
% 136.14/20.13 | End of split
% 136.14/20.13 |
% 136.14/20.13 End of proof
% 136.14/20.13
% 136.14/20.13 Sub-proof #256 shows that the following formulas are inconsistent:
% 136.14/20.13 ----------------------------------------------------------------
% 136.14/20.13 (1) all_57_11 = e3 & op(e1, e0) = e3
% 136.14/20.13 (2) all_57_11 = e0
% 136.14/20.13 (3) ~ (e3 = e0)
% 136.14/20.13
% 136.14/20.13 Begin of proof
% 136.14/20.13 |
% 136.14/20.13 | ALPHA: (1) implies:
% 136.14/20.13 | (4) all_57_11 = e3
% 136.14/20.13 |
% 136.14/20.13 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.13 | (5) e3 = e0
% 136.14/20.13 |
% 136.14/20.13 | REDUCE: (3), (5) imply:
% 136.14/20.13 | (6) $false
% 136.14/20.13 |
% 136.14/20.13 | CLOSE: (6) is inconsistent.
% 136.14/20.13 |
% 136.14/20.13 End of proof
% 136.14/20.13
% 136.14/20.13 Sub-proof #257 shows that the following formulas are inconsistent:
% 136.14/20.13 ----------------------------------------------------------------
% 136.14/20.13 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.13 (2) ~ (e2 = e1)
% 136.14/20.13 (3) all_57_9 = e3
% 136.14/20.13 (4) op(e2, e0) = e0
% 136.14/20.13 (5) op(e0, e0) = e2
% 136.14/20.13 (6) all_57_11 = e0
% 136.14/20.13 (7) ~ (e3 = e1)
% 136.14/20.13 (8) ~ (e1 = e0)
% 136.14/20.13 (9) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 136.14/20.13 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 136.14/20.13
% 136.14/20.13 Begin of proof
% 136.14/20.13 |
% 136.14/20.13 | BETA: splitting (9) gives:
% 136.14/20.13 |
% 136.14/20.13 | Case 1:
% 136.14/20.13 | |
% 136.14/20.13 | | (10) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 136.14/20.13 | | e1)
% 136.14/20.13 | |
% 136.14/20.13 | | BETA: splitting (10) gives:
% 136.14/20.13 | |
% 136.14/20.13 | | Case 1:
% 136.14/20.13 | | |
% 136.14/20.13 | | | (11) all_57_9 = e1 & op(e3, e0) = e1
% 136.14/20.13 | | |
% 136.14/20.13 | | | ALPHA: (11) implies:
% 136.14/20.13 | | | (12) all_57_9 = e1
% 136.14/20.13 | | |
% 136.14/20.13 | | | REF_CLOSE: (3), (7), (12) are inconsistent by sub-proof #690.
% 136.14/20.13 | | |
% 136.14/20.13 | | Case 2:
% 136.14/20.13 | | |
% 136.14/20.13 | | | (13) all_57_10 = e1 & op(e2, e0) = e1
% 136.14/20.13 | | |
% 136.14/20.13 | | | ALPHA: (13) implies:
% 136.14/20.13 | | | (14) op(e2, e0) = e1
% 136.14/20.13 | | |
% 136.14/20.13 | | | REF_CLOSE: (1), (4), (8), (14) are inconsistent by sub-proof #695.
% 136.14/20.13 | | |
% 136.14/20.13 | | End of split
% 136.14/20.13 | |
% 136.14/20.13 | Case 2:
% 136.14/20.13 | |
% 136.14/20.13 | | (15) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 136.14/20.13 | | e1)
% 136.14/20.13 | |
% 136.14/20.13 | | BETA: splitting (15) gives:
% 136.14/20.13 | |
% 136.14/20.13 | | Case 1:
% 136.14/20.13 | | |
% 136.14/20.13 | | | (16) all_57_11 = e1 & op(e1, e0) = e1
% 136.14/20.13 | | |
% 136.14/20.13 | | | ALPHA: (16) implies:
% 136.14/20.13 | | | (17) all_57_11 = e1
% 136.14/20.13 | | |
% 136.14/20.13 | | | COMBINE_EQS: (6), (17) imply:
% 136.14/20.13 | | | (18) e1 = e0
% 136.14/20.13 | | |
% 136.14/20.13 | | | SIMP: (18) implies:
% 136.14/20.13 | | | (19) e1 = e0
% 136.14/20.13 | | |
% 136.14/20.13 | | | REDUCE: (8), (19) imply:
% 136.14/20.13 | | | (20) $false
% 136.14/20.13 | | |
% 136.14/20.13 | | | CLOSE: (20) is inconsistent.
% 136.14/20.13 | | |
% 136.14/20.13 | | Case 2:
% 136.14/20.13 | | |
% 136.14/20.13 | | | (21) all_57_15 = e1 & op(e0, e0) = e1
% 136.14/20.13 | | |
% 136.14/20.13 | | | ALPHA: (21) implies:
% 136.14/20.13 | | | (22) op(e0, e0) = e1
% 136.14/20.13 | | |
% 136.14/20.13 | | | REF_CLOSE: (1), (2), (5), (22) are inconsistent by sub-proof #636.
% 136.14/20.13 | | |
% 136.14/20.13 | | End of split
% 136.14/20.13 | |
% 136.14/20.13 | End of split
% 136.14/20.13 |
% 136.14/20.13 End of proof
% 136.14/20.13
% 136.14/20.13 Sub-proof #258 shows that the following formulas are inconsistent:
% 136.14/20.13 ----------------------------------------------------------------
% 136.14/20.13 (1) all_54_11 = all_52_14
% 136.14/20.13 (2) all_54_11 = e0
% 136.14/20.13 (3) ~ (all_52_14 = e0)
% 136.14/20.13
% 136.14/20.13 Begin of proof
% 136.14/20.13 |
% 136.14/20.13 | COMBINE_EQS: (1), (2) imply:
% 136.14/20.13 | (4) all_52_14 = e0
% 136.14/20.13 |
% 136.14/20.13 | SIMP: (4) implies:
% 136.14/20.13 | (5) all_52_14 = e0
% 136.14/20.13 |
% 136.14/20.13 | REDUCE: (3), (5) imply:
% 136.14/20.13 | (6) $false
% 136.14/20.13 |
% 136.14/20.13 | CLOSE: (6) is inconsistent.
% 136.14/20.13 |
% 136.14/20.13 End of proof
% 136.14/20.13
% 136.14/20.13 Sub-proof #259 shows that the following formulas are inconsistent:
% 136.14/20.13 ----------------------------------------------------------------
% 136.14/20.13 (1) all_54_11 = all_52_14
% 136.14/20.13 (2) all_54_11 = e2
% 136.14/20.13 (3) ~ (all_52_14 = e2)
% 136.14/20.13
% 136.14/20.13 Begin of proof
% 136.14/20.13 |
% 136.14/20.13 | COMBINE_EQS: (1), (2) imply:
% 136.14/20.13 | (4) all_52_14 = e2
% 136.14/20.13 |
% 136.14/20.13 | SIMP: (4) implies:
% 136.14/20.13 | (5) all_52_14 = e2
% 136.14/20.13 |
% 136.14/20.13 | REDUCE: (3), (5) imply:
% 136.14/20.13 | (6) $false
% 136.14/20.13 |
% 136.14/20.13 | CLOSE: (6) is inconsistent.
% 136.14/20.13 |
% 136.14/20.13 End of proof
% 136.14/20.13
% 136.14/20.13 Sub-proof #260 shows that the following formulas are inconsistent:
% 136.14/20.13 ----------------------------------------------------------------
% 136.14/20.13 (1) all_54_11 = all_52_14
% 136.14/20.13 (2) all_54_11 = e3
% 136.14/20.13 (3) ~ (all_52_14 = e3)
% 136.14/20.13
% 136.14/20.13 Begin of proof
% 136.14/20.13 |
% 136.14/20.13 | COMBINE_EQS: (1), (2) imply:
% 136.14/20.13 | (4) all_52_14 = e3
% 136.14/20.13 |
% 136.14/20.13 | SIMP: (4) implies:
% 136.14/20.13 | (5) all_52_14 = e3
% 136.14/20.13 |
% 136.14/20.13 | REDUCE: (3), (5) imply:
% 136.14/20.13 | (6) $false
% 136.14/20.13 |
% 136.14/20.13 | CLOSE: (6) is inconsistent.
% 136.14/20.13 |
% 136.14/20.13 End of proof
% 136.14/20.13
% 136.14/20.13 Sub-proof #261 shows that the following formulas are inconsistent:
% 136.14/20.13 ----------------------------------------------------------------
% 136.14/20.13 (1) ~ (all_52_12 = e1)
% 136.14/20.13 (2) all_54_0 = all_10_2
% 136.14/20.13 (3) op(e1, e1) = all_6_2
% 136.14/20.13 (4) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 136.14/20.13 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 136.14/20.13 (5) ~ (all_52_9 = all_6_2)
% 136.14/20.13 (6) op(e2, e0) = all_52_13
% 136.14/20.13 (7) ~ (all_40_2 = e0) | ( ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 &
% 136.14/20.13 $i(all_40_0)) | ( ~ (all_40_1 = e2) & op(e0, e0) = all_40_1 &
% 136.14/20.13 $i(all_40_1))
% 136.14/20.13 (8) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 136.14/20.13 (9) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 136.14/20.13 (10) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 136.14/20.13 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 136.14/20.13 (11) ~ (all_52_11 = e2)
% 136.14/20.13 (12) ~ (e2 = e0)
% 136.14/20.13 (13) ~ (all_52_4 = all_52_12)
% 136.14/20.13 (14) ~ (all_52_1 = all_52_2)
% 136.14/20.13 (15) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 136.14/20.13 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 136.14/20.13 (16) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 136.14/20.13 | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 136.14/20.13 e3)
% 136.14/20.13 (17) all_40_2 = all_6_2
% 136.14/20.13 (18) ( ~ (all_22_0 = e0) & op(e3, e2) = all_22_0 & $i(all_22_0)) | ( ~
% 136.14/20.13 (all_22_1 = e1) & op(e3, e3) = all_22_1 & $i(all_22_1))
% 136.14/20.13 (19) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 136.14/20.13 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 136.14/20.13 (20) ~ (all_52_7 = e3)
% 136.14/20.13 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.13 (22) ~ (e2 = e1)
% 136.14/20.13 (23) op(e2, e0) = all_26_0
% 136.14/20.13 (24) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 136.14/20.13 (25) ~ (all_52_1 = all_52_13)
% 136.14/20.13 (26) ~ (all_52_2 = e1)
% 136.14/20.13 (27) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 136.14/20.13 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 136.14/20.13 e2)
% 136.14/20.13 (28) op(e2, e2) = e3
% 136.14/20.13 (29) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 136.14/20.13 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 136.14/20.13 (30) all_54_3 = all_52_12
% 136.14/20.13 (31) ~ (all_52_1 = all_52_9)
% 136.14/20.13 (32) ~ (all_52_12 = e0)
% 136.14/20.13 (33) ~ (all_52_11 = all_6_2)
% 136.14/20.13 (34) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 136.14/20.13 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 136.14/20.13 (35) op(e0, e1) = all_52_11
% 136.14/20.13 (36) op(e0, e2) = all_52_7
% 136.14/20.13 (37) ~ (all_52_12 = all_10_2)
% 136.14/20.13 (38) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 136.14/20.13 (39) ~ (all_10_2 = e0)
% 136.14/20.13 (40) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 136.14/20.13 (41) ~ (all_6_2 = e2)
% 136.14/20.13 (42) ~ (all_52_13 = e2)
% 136.14/20.13 (43) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 136.14/20.13 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 136.14/20.13 op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 136.14/20.13 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 136.14/20.13 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 136.14/20.13 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.14/20.13 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 136.14/20.13 = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.14/20.13 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 136.14/20.13 $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~
% 136.14/20.13 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 136.14/20.13 (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) =
% 136.14/20.13 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0,
% 136.14/20.13 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 136.14/20.13 $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3)
% 136.14/20.13 & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 136.14/20.13 op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17
% 136.14/20.13 & op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 136.14/20.13 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.14/20.13 (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.14/20.13 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.14/20.13 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0)
% 136.14/20.13 = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) &
% 136.14/20.13 $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 &
% 136.14/20.13 all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.14/20.13 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 136.14/20.13 = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.14/20.13 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 136.14/20.13 $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~
% 136.14/20.13 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 136.14/20.13 (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 136.14/20.13 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0,
% 136.14/20.13 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 136.14/20.13 $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3)
% 136.14/20.13 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.14/20.13 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.14/20.13 all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2
% 136.14/20.13 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.14/20.13 (op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 =
% 136.14/20.13 e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 136.14/20.13 & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) =
% 136.14/20.13 all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 136.14/20.13 op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 136.14/20.13 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 136.14/20.13 e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 136.14/20.13 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 136.14/20.13 e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.14/20.13 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.14/20.13 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.14/20.13 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.14/20.13 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 136.14/20.13 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 136.14/20.13 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 136.14/20.13 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 136.14/20.13 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 136.14/20.13 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 136.14/20.13 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.14/20.13 $i(all_56_29))))
% 136.14/20.13 (44) ~ (all_26_0 = e1)
% 136.14/20.13 (45) op(e2, e0) = e0
% 136.14/20.13 (46) op(e3, e3) = all_10_2
% 136.14/20.13 (47) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 136.14/20.13 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 136.14/20.13 (48) ~ (all_52_9 = e3)
% 136.14/20.13 (49) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 136.14/20.13 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 136.14/20.13 e1)
% 136.14/20.13 (50) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 136.14/20.13 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 136.14/20.13 (51) op(e2, e1) = all_52_9
% 136.14/20.13 (52) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 136.14/20.13 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 136.14/20.13 (53) op(e1, e3) = all_52_2
% 136.14/20.13 (54) ~ (all_52_8 = all_52_12)
% 136.14/20.13 (55) op(e3, e2) = all_52_4
% 136.14/20.13 (56) ~ (all_52_12 = e2)
% 136.14/20.13 (57) ~ (all_52_13 = e3)
% 136.14/20.13 (58) all_57_10 = e0
% 136.14/20.13 (59) ~ (all_52_1 = e3)
% 136.14/20.13 (60) op(e0, e0) = e2
% 136.14/20.13 (61) ~ (all_10_2 = e2)
% 136.14/20.13 (62) all_57_3 = e3
% 136.14/20.13 (63) op(e2, e3) = all_52_1
% 136.14/20.13 (64) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 136.14/20.13 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 136.14/20.13 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 136.14/20.13 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 136.14/20.13 (65) all_54_7 = all_52_13
% 136.14/20.13 (66) op(e3, e1) = all_52_8
% 136.14/20.13 (67) ~ (all_52_9 = all_52_11)
% 136.14/20.13 (68) all_54_14 = all_52_11
% 136.14/20.13 (69) ~ (e1 = e0)
% 136.14/20.13 (70) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 136.14/20.13 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 136.14/20.13 (71) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 136.14/20.13 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 136.14/20.13 (72) all_54_4 = all_52_1
% 136.14/20.13 (73) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 136.14/20.13 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 136.14/20.13 (74) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 136.14/20.13 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 136.14/20.13 (75) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 136.14/20.13 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 136.14/20.13 (76) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 136.14/20.13 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 136.14/20.13
% 136.14/20.13 Begin of proof
% 136.14/20.13 |
% 136.14/20.13 | BETA: splitting (24) gives:
% 136.14/20.13 |
% 136.14/20.13 | Case 1:
% 136.14/20.13 | |
% 136.14/20.13 | | (77) all_54_3 = e3
% 136.14/20.13 | |
% 136.14/20.13 | | COMBINE_EQS: (30), (77) imply:
% 136.14/20.13 | | (78) all_52_12 = e3
% 136.14/20.13 | |
% 136.14/20.13 | | REDUCE: (13), (78) imply:
% 136.14/20.13 | | (79) ~ (all_52_4 = e3)
% 136.14/20.13 | |
% 136.14/20.13 | | REDUCE: (37), (78) imply:
% 136.14/20.13 | | (80) ~ (all_10_2 = e3)
% 136.14/20.13 | |
% 136.14/20.13 | | SIMP: (80) implies:
% 136.14/20.13 | | (81) ~ (all_10_2 = e3)
% 136.14/20.13 | |
% 136.14/20.13 | | REDUCE: (56), (78) imply:
% 136.14/20.13 | | (82) ~ (e3 = e2)
% 136.14/20.13 | |
% 136.14/20.13 | | REDUCE: (1), (78) imply:
% 136.14/20.13 | | (83) ~ (e3 = e1)
% 136.14/20.13 | |
% 136.14/20.13 | | REDUCE: (32), (78) imply:
% 136.14/20.13 | | (84) ~ (e3 = e0)
% 136.14/20.13 | |
% 136.14/20.13 | | BETA: splitting (40) gives:
% 136.14/20.13 | |
% 136.14/20.13 | | Case 1:
% 136.14/20.13 | | |
% 136.14/20.13 | | | (85) all_54_0 = e3
% 136.14/20.13 | | |
% 136.14/20.13 | | | COMBINE_EQS: (2), (85) imply:
% 136.14/20.13 | | | (86) all_10_2 = e3
% 136.14/20.13 | | |
% 136.14/20.13 | | | REDUCE: (81), (86) imply:
% 136.14/20.13 | | | (87) $false
% 136.14/20.13 | | |
% 136.14/20.13 | | | CLOSE: (87) is inconsistent.
% 136.14/20.13 | | |
% 136.14/20.13 | | Case 2:
% 136.14/20.13 | | |
% 136.14/20.13 | | | (88) ~ (all_54_0 = e3)
% 136.14/20.13 | | | (89) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 136.14/20.13 | | |
% 136.14/20.13 | | | BETA: splitting (89) gives:
% 136.14/20.13 | | |
% 136.14/20.13 | | | Case 1:
% 136.14/20.13 | | | |
% 136.14/20.13 | | | | (90) all_54_0 = e2
% 136.14/20.13 | | | |
% 136.14/20.13 | | | | COMBINE_EQS: (2), (90) imply:
% 136.14/20.13 | | | | (91) all_10_2 = e2
% 136.14/20.13 | | | |
% 136.14/20.13 | | | | REDUCE: (61), (91) imply:
% 136.14/20.13 | | | | (92) $false
% 136.14/20.13 | | | |
% 136.14/20.13 | | | | CLOSE: (92) is inconsistent.
% 136.14/20.13 | | | |
% 136.14/20.13 | | | Case 2:
% 136.14/20.13 | | | |
% 136.14/20.13 | | | | (93) ~ (all_54_0 = e2)
% 136.14/20.13 | | | | (94) all_54_0 = e1 | all_54_0 = e0
% 136.14/20.13 | | | |
% 136.14/20.13 | | | | BETA: splitting (43) gives:
% 136.14/20.13 | | | |
% 136.14/20.13 | | | | Case 1:
% 136.14/20.13 | | | | |
% 136.14/20.14 | | | | | (95) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~
% 136.14/20.14 | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0)
% 136.14/20.14 | | | | | & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = all_56_3
% 136.14/20.14 | | | | | & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 136.14/20.14 | | | | | e0) = all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 136.14/20.14 | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & all_56_17
% 136.14/20.14 | | | | | = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.14/20.14 | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 136.14/20.14 | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 136.14/20.14 | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29
% 136.14/20.14 | | | | | & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.14/20.14 | | | | | $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~
% 136.14/20.14 | | | | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 136.14/20.14 | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 &
% 136.14/20.14 | | | | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1)
% 136.14/20.14 | | | | | = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.14/20.14 | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 =
% 136.14/20.14 | | | | | e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.14/20.14 | | | | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3,
% 136.14/20.14 | | | | | e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) =
% 136.14/20.14 | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 136.14/20.14 | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 136.14/20.14 | | | | | $i(all_56_17) & $i(all_56_25))
% 136.14/20.14 | | | | |
% 136.14/20.14 | | | | | BETA: splitting (95) gives:
% 136.14/20.14 | | | | |
% 136.14/20.14 | | | | | Case 1:
% 136.14/20.14 | | | | | |
% 136.14/20.14 | | | | | | (96) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~
% 136.14/20.14 | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 =
% 136.14/20.14 | | | | | | e0) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) =
% 136.14/20.14 | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 136.14/20.14 | | | | | | & op(e2, e0) = all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 136.14/20.14 | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 136.14/20.14 | | | | | | all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2)
% 136.14/20.14 | | | | | | & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) =
% 136.14/20.14 | | | | | | e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2)
% 136.14/20.14 | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 136.14/20.14 | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.14/20.14 | | | | | | $i(all_56_29))
% 136.14/20.14 | | | | | |
% 136.14/20.14 | | | | | | BETA: splitting (96) gives:
% 136.14/20.14 | | | | | |
% 136.14/20.14 | | | | | | Case 1:
% 136.14/20.14 | | | | | | |
% 136.14/20.14 | | | | | | | (97) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~
% 136.14/20.14 | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 =
% 136.14/20.14 | | | | | | | e0) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) =
% 136.14/20.14 | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 136.14/20.14 | | | | | | | & op(e2, e0) = all_56_27 & $i(all_56_3) & $i(all_56_11) &
% 136.14/20.14 | | | | | | | $i(all_56_19) & $i(all_56_27)
% 136.14/20.14 | | | | | | |
% 136.14/20.14 | | | | | | | ALPHA: (97) implies:
% 136.14/20.14 | | | | | | | (98) op(e3, e3) = e2
% 136.14/20.14 | | | | | | |
% 136.14/20.14 | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (12), (14),
% 136.14/20.14 | | | | | | | (15), (16), (17), (19), (20), (21), (22), (23), (25),
% 136.14/20.14 | | | | | | | (27), (28), (29), (31), (33), (34), (35), (36), (38),
% 136.14/20.14 | | | | | | | (41), (42), (43), (44), (47), (48), (49), (50), (51),
% 136.14/20.14 | | | | | | | (52), (53), (55), (57), (59), (60), (62), (63), (64),
% 136.14/20.14 | | | | | | | (65), (67), (68), (69), (70), (71), (72), (73), (74),
% 136.14/20.14 | | | | | | | (75), (76), (79), (82), (83), (84), (98) are
% 136.14/20.14 | | | | | | | inconsistent by sub-proof #267.
% 136.14/20.14 | | | | | | |
% 136.14/20.14 | | | | | | Case 2:
% 136.14/20.14 | | | | | | |
% 136.14/20.14 | | | | | | | (99) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~
% 136.14/20.14 | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 =
% 136.14/20.14 | | | | | | | e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) =
% 136.14/20.14 | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21
% 136.14/20.14 | | | | | | | & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 136.14/20.14 | | | | | | | $i(all_56_21) & $i(all_56_29)
% 136.14/20.14 | | | | | | |
% 136.14/20.14 | | | | | | | ALPHA: (99) implies:
% 136.14/20.14 | | | | | | | (100) op(e3, e1) = e3
% 136.14/20.14 | | | | | | |
% 136.14/20.14 | | | | | | | REF_CLOSE: (1), (21), (24), (30), (32), (54), (56), (66), (100)
% 136.14/20.14 | | | | | | | are inconsistent by sub-proof #319.
% 136.14/20.14 | | | | | | |
% 136.14/20.14 | | | | | | End of split
% 136.14/20.14 | | | | | |
% 136.14/20.14 | | | | | Case 2:
% 136.14/20.14 | | | | | |
% 136.14/20.14 | | | | | | (101) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~
% 136.14/20.14 | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 =
% 136.14/20.14 | | | | | | e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) =
% 136.14/20.14 | | | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) =
% 136.14/20.14 | | | | | | all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.14/20.14 | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 136.14/20.14 | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~
% 136.14/20.14 | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 =
% 136.14/20.14 | | | | | | e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 &
% 136.14/20.14 | | | | | | op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e2,
% 136.14/20.14 | | | | | | e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) &
% 136.14/20.14 | | | | | | $i(all_56_9) & $i(all_56_17) & $i(all_56_25))
% 136.14/20.14 | | | | | |
% 136.14/20.14 | | | | | | BETA: splitting (101) gives:
% 136.14/20.14 | | | | | |
% 136.14/20.14 | | | | | | Case 1:
% 136.14/20.14 | | | | | | |
% 136.14/20.14 | | | | | | | (102) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~
% 136.14/20.14 | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 =
% 136.14/20.14 | | | | | | | e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) =
% 136.14/20.14 | | | | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) =
% 136.14/20.14 | | | | | | | all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.14/20.14 | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)
% 136.14/20.14 | | | | | | |
% 136.14/20.14 | | | | | | | ALPHA: (102) implies:
% 136.14/20.14 | | | | | | | (103) op(e3, e3) = e0
% 136.14/20.14 | | | | | | |
% 136.14/20.14 | | | | | | | REF_CLOSE: (2), (21), (39), (46), (94), (103) are inconsistent by
% 136.14/20.14 | | | | | | | sub-proof #263.
% 136.14/20.14 | | | | | | |
% 136.14/20.14 | | | | | | Case 2:
% 136.14/20.14 | | | | | | |
% 136.14/20.14 | | | | | | | (104) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~
% 136.14/20.14 | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 =
% 136.14/20.14 | | | | | | | e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 &
% 136.14/20.14 | | | | | | | op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e2,
% 136.14/20.14 | | | | | | | e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) &
% 136.14/20.14 | | | | | | | $i(all_56_9) & $i(all_56_17) & $i(all_56_25)
% 136.14/20.14 | | | | | | |
% 136.14/20.14 | | | | | | | ALPHA: (104) implies:
% 136.14/20.14 | | | | | | | (105) op(e2, e3) = e2
% 136.14/20.14 | | | | | | |
% 136.14/20.14 | | | | | | | BETA: splitting (94) gives:
% 136.14/20.14 | | | | | | |
% 136.14/20.14 | | | | | | | Case 1:
% 136.14/20.14 | | | | | | | |
% 136.14/20.14 | | | | | | | | (106) all_54_0 = e1
% 136.14/20.14 | | | | | | | |
% 136.14/20.14 | | | | | | | | COMBINE_EQS: (2), (106) imply:
% 136.14/20.14 | | | | | | | | (107) all_10_2 = e1
% 136.14/20.14 | | | | | | | |
% 136.14/20.14 | | | | | | | | SIMP: (107) implies:
% 136.14/20.14 | | | | | | | | (108) all_10_2 = e1
% 136.14/20.14 | | | | | | | |
% 136.14/20.14 | | | | | | | | REDUCE: (81), (108) imply:
% 136.14/20.14 | | | | | | | | (109) ~ (e3 = e1)
% 136.14/20.14 | | | | | | | |
% 136.14/20.14 | | | | | | | | REDUCE: (61), (108) imply:
% 136.14/20.14 | | | | | | | | (110) ~ (e2 = e1)
% 136.14/20.14 | | | | | | | |
% 136.14/20.14 | | | | | | | | REDUCE: (46), (108) imply:
% 136.14/20.14 | | | | | | | | (111) op(e3, e3) = e1
% 136.14/20.14 | | | | | | | |
% 136.14/20.14 | | | | | | | | BETA: splitting (70) gives:
% 136.14/20.14 | | | | | | | |
% 136.14/20.14 | | | | | | | | Case 1:
% 136.14/20.14 | | | | | | | | |
% 136.14/20.14 | | | | | | | | | (112) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 &
% 136.14/20.14 | | | | | | | | | op(e2, e2) = e1)
% 136.14/20.14 | | | | | | | | |
% 136.14/20.14 | | | | | | | | | REF_CLOSE: (21), (22), (28), (83), (105), (112) are
% 136.14/20.14 | | | | | | | | | inconsistent by sub-proof #292.
% 136.14/20.14 | | | | | | | | |
% 136.14/20.14 | | | | | | | | Case 2:
% 136.14/20.14 | | | | | | | | |
% 136.14/20.14 | | | | | | | | | (113) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 &
% 136.14/20.14 | | | | | | | | | op(e2, e0) = e1)
% 136.14/20.14 | | | | | | | | |
% 136.14/20.14 | | | | | | | | | BETA: splitting (113) gives:
% 136.14/20.14 | | | | | | | | |
% 136.14/20.14 | | | | | | | | | Case 1:
% 136.14/20.14 | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | (114) all_57_5 = e1 & op(e2, e1) = e1
% 136.14/20.14 | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | ALPHA: (114) implies:
% 136.14/20.14 | | | | | | | | | | (115) all_57_5 = e1
% 136.14/20.14 | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | BETA: splitting (76) gives:
% 136.14/20.14 | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | Case 1:
% 136.14/20.14 | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | (116) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 136.14/20.14 | | | | | | | | | | | & op(e2, e1) = e2)
% 136.14/20.14 | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | BETA: splitting (116) gives:
% 136.14/20.14 | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | Case 1:
% 136.14/20.14 | | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | | (117) all_57_4 = e2 & op(e3, e1) = e2
% 136.14/20.14 | | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | | ALPHA: (117) implies:
% 136.14/20.14 | | | | | | | | | | | | (118) all_57_4 = e2
% 136.14/20.14 | | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | | BETA: splitting (18) gives:
% 136.14/20.14 | | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | | Case 1:
% 136.14/20.14 | | | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | | | (119) ~ (all_22_0 = e0) & op(e3, e2) = all_22_0 &
% 136.14/20.14 | | | | | | | | | | | | | $i(all_22_0)
% 136.14/20.14 | | | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | | | ALPHA: (119) implies:
% 136.14/20.14 | | | | | | | | | | | | | (120) ~ (all_22_0 = e0)
% 136.14/20.14 | | | | | | | | | | | | | (121) op(e3, e2) = all_22_0
% 136.14/20.14 | | | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | | | BETA: splitting (15) gives:
% 136.14/20.14 | | | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | | | Case 1:
% 136.14/20.14 | | | | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | | | | (122) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 136.14/20.14 | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 136.14/20.14 | | | | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | | | | REF_CLOSE: (21), (69), (111), (120), (121), (122) are
% 136.14/20.14 | | | | | | | | | | | | | | inconsistent by sub-proof #307.
% 136.14/20.14 | | | | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | | | Case 2:
% 136.14/20.14 | | | | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | | | | (123) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 136.14/20.14 | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 136.14/20.14 | | | | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | | | | BETA: splitting (123) gives:
% 136.14/20.14 | | | | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | | | | Case 1:
% 136.14/20.14 | | | | | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | | | | | (124) all_57_4 = e0 & op(e3, e1) = e0
% 136.14/20.14 | | | | | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | | | | | REF_CLOSE: (12), (118), (124) are inconsistent by sub-proof
% 136.14/20.14 | | | | | | | | | | | | | | | #647.
% 136.14/20.14 | | | | | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | | | | Case 2:
% 136.14/20.14 | | | | | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | | | | | (125) all_57_9 = e0 & op(e3, e0) = e0
% 136.14/20.14 | | | | | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | | | | | ALPHA: (125) implies:
% 136.14/20.14 | | | | | | | | | | | | | | | (126) all_57_9 = e0
% 136.14/20.14 | | | | | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | | | | | REF_CLOSE: (6), (21), (22), (47), (57), (58), (60), (69),
% 136.14/20.14 | | | | | | | | | | | | | | | (75), (82), (83), (84), (126) are inconsistent by
% 136.14/20.14 | | | | | | | | | | | | | | | sub-proof #294.
% 136.14/20.14 | | | | | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | | | | End of split
% 136.14/20.14 | | | | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | | | End of split
% 136.14/20.14 | | | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | | Case 2:
% 136.14/20.14 | | | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | | | (127) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 &
% 136.14/20.14 | | | | | | | | | | | | | $i(all_22_1)
% 136.14/20.14 | | | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | | | REF_CLOSE: (21), (111), (127) are inconsistent by sub-proof
% 136.14/20.14 | | | | | | | | | | | | | #305.
% 136.14/20.14 | | | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | | End of split
% 136.14/20.14 | | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | Case 2:
% 136.14/20.14 | | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | | (128) all_57_5 = e2 & op(e2, e1) = e2
% 136.14/20.14 | | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | | ALPHA: (128) implies:
% 136.14/20.14 | | | | | | | | | | | | (129) all_57_5 = e2
% 136.14/20.14 | | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | | REF_CLOSE: (22), (115), (129) are inconsistent by sub-proof
% 136.14/20.14 | | | | | | | | | | | | #418.
% 136.14/20.14 | | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | End of split
% 136.14/20.14 | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | Case 2:
% 136.14/20.14 | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | (130) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 136.14/20.14 | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 136.14/20.14 | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | | REF_CLOSE: (3), (12), (16), (20), (21), (22), (36), (41),
% 136.14/20.14 | | | | | | | | | | | (49), (60), (64), (69), (82), (83), (84), (130)
% 136.14/20.14 | | | | | | | | | | | are inconsistent by sub-proof #262.
% 136.14/20.14 | | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | End of split
% 136.14/20.14 | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | Case 2:
% 136.14/20.14 | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | (131) all_57_10 = e1 & op(e2, e0) = e1
% 136.14/20.14 | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | ALPHA: (131) implies:
% 136.14/20.14 | | | | | | | | | | (132) op(e2, e0) = e1
% 136.14/20.14 | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | | REF_CLOSE: (21), (45), (69), (132) are inconsistent by
% 136.14/20.14 | | | | | | | | | | sub-proof #695.
% 136.14/20.14 | | | | | | | | | |
% 136.14/20.14 | | | | | | | | | End of split
% 136.14/20.14 | | | | | | | | |
% 136.14/20.14 | | | | | | | | End of split
% 136.14/20.14 | | | | | | | |
% 136.14/20.14 | | | | | | | Case 2:
% 136.14/20.14 | | | | | | | |
% 136.14/20.14 | | | | | | | | (133) all_54_0 = e0
% 136.14/20.14 | | | | | | | |
% 136.14/20.14 | | | | | | | | REF_CLOSE: (2), (39), (133) are inconsistent by sub-proof #264.
% 136.14/20.14 | | | | | | | |
% 136.14/20.14 | | | | | | | End of split
% 136.14/20.14 | | | | | | |
% 136.14/20.14 | | | | | | End of split
% 136.14/20.14 | | | | | |
% 136.14/20.14 | | | | | End of split
% 136.14/20.14 | | | | |
% 136.14/20.14 | | | | Case 2:
% 136.14/20.14 | | | | |
% 136.14/20.14 | | | | | (134) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~
% 136.14/20.14 | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0)
% 136.14/20.14 | | | | | & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 136.14/20.14 | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e1, e3) =
% 136.14/20.14 | | | | | e1 & op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 136.14/20.14 | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 &
% 136.14/20.14 | | | | | all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) &
% 136.14/20.14 | | | | | ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1
% 136.14/20.14 | | | | | & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 136.14/20.14 | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29
% 136.14/20.14 | | | | | & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.14/20.14 | | | | | $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~
% 136.14/20.14 | | | | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 136.14/20.14 | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 &
% 136.14/20.14 | | | | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1)
% 136.14/20.14 | | | | | = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.14/20.14 | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_13
% 136.14/20.14 | | | | | = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11
% 136.14/20.14 | | | | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.14/20.14 | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1)
% 136.14/20.14 | | | | | = all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 136.14/20.14 | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 136.14/20.14 | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = all_56_31 &
% 136.14/20.14 | | | | | $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~
% 136.14/20.14 | | | | | (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 136.14/20.14 | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 136.14/20.14 | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.14/20.14 | | | | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) &
% 136.14/20.14 | | | | | $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.14/20.14 | | | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 136.14/20.14 | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 136.14/20.14 | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 136.14/20.14 | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 136.14/20.14 | | | | | all_56_27 & op(e0, e2) = e0 & $i(all_56_3) &
% 136.14/20.14 | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.14/20.14 | | | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 136.14/20.14 | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 136.14/20.14 | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 136.14/20.14 | | | | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0,
% 136.14/20.14 | | | | | e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 136.14/20.14 | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 & ~
% 136.14/20.14 | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 136.14/20.14 | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 136.14/20.14 | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 136.14/20.14 | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5)
% 136.14/20.14 | | | | | & $i(all_56_13) & $i(all_56_21) & $i(all_56_29))))
% 136.14/20.14 | | | | |
% 136.14/20.14 | | | | | BETA: splitting (134) gives:
% 136.14/20.14 | | | | |
% 136.14/20.14 | | | | | Case 1:
% 136.14/20.14 | | | | | |
% 136.14/20.14 | | | | | | (135) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~
% 136.14/20.14 | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 =
% 136.14/20.14 | | | | | | e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 &
% 136.14/20.14 | | | | | | op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e1,
% 136.14/20.14 | | | | | | e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) &
% 136.14/20.14 | | | | | | $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.14/20.14 | | | | | | (all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 136.14/20.14 | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 =
% 136.14/20.14 | | | | | | e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 136.14/20.14 | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.14/20.14 | | | | | | all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 136.14/20.14 | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 136.14/20.14 | | | | | |
% 136.14/20.14 | | | | | | REF_CLOSE: (21), (26), (28), (53), (83), (135) are inconsistent by
% 136.14/20.14 | | | | | | sub-proof #304.
% 136.14/20.14 | | | | | |
% 136.14/20.14 | | | | | Case 2:
% 136.14/20.14 | | | | | |
% 136.14/20.14 | | | | | | (136) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 136.14/20.14 | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 =
% 136.14/20.14 | | | | | | e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 136.14/20.14 | | | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) =
% 136.14/20.14 | | | | | | all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.14/20.14 | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 136.14/20.14 | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 136.14/20.14 | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 =
% 136.14/20.14 | | | | | | e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 136.14/20.14 | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e1,
% 136.14/20.14 | | | | | | e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 136.14/20.14 | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (op(e0,
% 136.14/20.14 | | | | | | e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 136.14/20.14 | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.14/20.14 | | | | | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 136.14/20.14 | | | | | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 &
% 136.14/20.14 | | | | | | op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 136.14/20.14 | | | | | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 136.14/20.14 | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 &
% 136.14/20.14 | | | | | | all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 136.14/20.14 | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.14/20.14 | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 136.14/20.14 | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 136.14/20.14 | | | | | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 136.14/20.14 | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 &
% 136.14/20.14 | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.14/20.14 | | | | | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.14/20.14 | | | | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 136.14/20.14 | | | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) =
% 136.14/20.14 | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 136.14/20.14 | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 &
% 136.14/20.14 | | | | | | ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.14/20.14 | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 136.14/20.14 | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.14/20.14 | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0
% 136.14/20.14 | | | | | | & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.14/20.14 | | | | | | $i(all_56_29))))
% 136.14/20.14 | | | | | |
% 136.14/20.14 | | | | | | REF_CLOSE: (3), (7), (11), (17), (21), (22), (28), (33), (35), (38),
% 136.14/20.14 | | | | | | (41), (45), (60), (68), (82), (84), (136) are
% 136.14/20.14 | | | | | | inconsistent by sub-proof #265.
% 136.14/20.14 | | | | | |
% 136.14/20.14 | | | | | End of split
% 136.14/20.14 | | | | |
% 136.14/20.14 | | | | End of split
% 136.14/20.14 | | | |
% 136.14/20.14 | | | End of split
% 136.14/20.14 | | |
% 136.14/20.14 | | End of split
% 136.14/20.14 | |
% 136.14/20.14 | Case 2:
% 136.14/20.14 | |
% 136.14/20.14 | | (137) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 136.14/20.14 | |
% 136.14/20.14 | | REF_CLOSE: (1), (30), (32), (56), (137) are inconsistent by sub-proof #320.
% 136.14/20.14 | |
% 136.14/20.14 | End of split
% 136.14/20.14 |
% 136.14/20.14 End of proof
% 136.14/20.14
% 136.14/20.14 Sub-proof #262 shows that the following formulas are inconsistent:
% 136.14/20.14 ----------------------------------------------------------------
% 136.14/20.14 (1) op(e1, e1) = all_6_2
% 136.14/20.14 (2) ~ (e2 = e0)
% 136.14/20.14 (3) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 136.14/20.14 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 136.14/20.14 (4) ~ (all_52_7 = e3)
% 136.14/20.14 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.14 (6) ~ (e2 = e1)
% 136.14/20.14 (7) ~ (e3 = e0)
% 136.14/20.14 (8) ~ (e3 = e2)
% 136.14/20.14 (9) op(e0, e2) = all_52_7
% 136.14/20.14 (10) ~ (all_6_2 = e2)
% 136.14/20.14 (11) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 136.14/20.14 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 136.14/20.14 e1)
% 136.14/20.14 (12) op(e0, e0) = e2
% 136.14/20.14 (13) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 136.14/20.14 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 136.14/20.14 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 136.14/20.14 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 136.14/20.14 (14) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 136.14/20.14 (15) ~ (e3 = e1)
% 136.14/20.14 (16) ~ (e1 = e0)
% 136.14/20.14
% 136.14/20.14 Begin of proof
% 136.14/20.14 |
% 136.14/20.14 | BETA: splitting (14) gives:
% 136.14/20.14 |
% 136.14/20.14 | Case 1:
% 136.14/20.14 | |
% 136.14/20.14 | | (17) all_57_8 = e2 & op(e1, e1) = e2
% 136.14/20.14 | |
% 136.14/20.14 | | ALPHA: (17) implies:
% 136.14/20.14 | | (18) op(e1, e1) = e2
% 136.14/20.14 | |
% 136.14/20.14 | | REF_CLOSE: (1), (5), (10), (18) are inconsistent by sub-proof #767.
% 136.14/20.14 | |
% 136.14/20.14 | Case 2:
% 136.14/20.14 | |
% 136.14/20.14 | | (19) all_57_14 = e2 & op(e0, e1) = e2
% 136.14/20.14 | |
% 136.14/20.14 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), (15),
% 136.14/20.14 | | (16), (19) are inconsistent by sub-proof #283.
% 136.14/20.14 | |
% 136.14/20.14 | End of split
% 136.14/20.14 |
% 136.14/20.14 End of proof
% 136.14/20.14
% 136.14/20.14 Sub-proof #263 shows that the following formulas are inconsistent:
% 136.14/20.14 ----------------------------------------------------------------
% 136.14/20.14 (1) all_54_0 = all_10_2
% 136.14/20.14 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.14 (3) ~ (all_10_2 = e0)
% 136.14/20.14 (4) op(e3, e3) = all_10_2
% 136.14/20.14 (5) all_54_0 = e1 | all_54_0 = e0
% 136.14/20.14 (6) op(e3, e3) = e0
% 136.14/20.14
% 136.14/20.14 Begin of proof
% 136.14/20.14 |
% 136.14/20.14 | BETA: splitting (5) gives:
% 136.14/20.14 |
% 136.14/20.14 | Case 1:
% 136.14/20.14 | |
% 136.14/20.14 | | (7) all_54_0 = e1
% 136.14/20.14 | |
% 136.14/20.14 | | COMBINE_EQS: (1), (7) imply:
% 136.14/20.14 | | (8) all_10_2 = e1
% 136.14/20.14 | |
% 136.14/20.14 | | SIMP: (8) implies:
% 136.14/20.14 | | (9) all_10_2 = e1
% 136.14/20.14 | |
% 136.14/20.14 | | REDUCE: (3), (9) imply:
% 136.14/20.14 | | (10) ~ (e1 = e0)
% 136.14/20.14 | |
% 136.14/20.14 | | REDUCE: (4), (9) imply:
% 136.14/20.14 | | (11) op(e3, e3) = e1
% 136.14/20.14 | |
% 136.14/20.14 | | REF_CLOSE: (2), (6), (10), (11) are inconsistent by sub-proof #717.
% 136.14/20.14 | |
% 136.14/20.14 | Case 2:
% 136.14/20.14 | |
% 136.14/20.14 | | (12) all_54_0 = e0
% 136.14/20.14 | |
% 136.14/20.14 | | REF_CLOSE: (1), (3), (12) are inconsistent by sub-proof #264.
% 136.14/20.14 | |
% 136.14/20.14 | End of split
% 136.14/20.14 |
% 136.14/20.14 End of proof
% 136.14/20.14
% 136.14/20.14 Sub-proof #264 shows that the following formulas are inconsistent:
% 136.14/20.14 ----------------------------------------------------------------
% 136.14/20.14 (1) all_54_0 = all_10_2
% 136.14/20.14 (2) all_54_0 = e0
% 136.14/20.14 (3) ~ (all_10_2 = e0)
% 136.14/20.14
% 136.14/20.14 Begin of proof
% 136.14/20.14 |
% 136.14/20.14 | COMBINE_EQS: (1), (2) imply:
% 136.14/20.14 | (4) all_10_2 = e0
% 136.14/20.14 |
% 136.14/20.14 | SIMP: (4) implies:
% 136.14/20.14 | (5) all_10_2 = e0
% 136.14/20.14 |
% 136.14/20.14 | REDUCE: (3), (5) imply:
% 136.14/20.14 | (6) $false
% 136.14/20.14 |
% 136.14/20.14 | CLOSE: (6) is inconsistent.
% 136.14/20.14 |
% 136.14/20.14 End of proof
% 136.14/20.14
% 136.14/20.14 Sub-proof #265 shows that the following formulas are inconsistent:
% 136.14/20.14 ----------------------------------------------------------------
% 136.14/20.14 (1) op(e1, e1) = all_6_2
% 136.14/20.14 (2) ~ (all_40_2 = e0) | ( ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 &
% 136.14/20.14 $i(all_40_0)) | ( ~ (all_40_1 = e2) & op(e0, e0) = all_40_1 &
% 136.14/20.14 $i(all_40_1))
% 136.14/20.14 (3) ~ (all_52_11 = e2)
% 136.14/20.14 (4) all_40_2 = all_6_2
% 136.14/20.14 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.14 (6) ~ (e2 = e1)
% 136.14/20.14 (7) ~ (e3 = e0)
% 136.14/20.14 (8) ~ (e3 = e2)
% 136.14/20.14 (9) op(e2, e2) = e3
% 136.14/20.14 (10) ~ (all_52_11 = all_6_2)
% 136.14/20.14 (11) op(e0, e1) = all_52_11
% 136.14/20.14 (12) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 136.14/20.14 (13) ~ (all_6_2 = e2)
% 136.14/20.14 (14) op(e2, e0) = e0
% 136.14/20.14 (15) op(e0, e0) = e2
% 136.14/20.14 (16) all_54_14 = all_52_11
% 136.14/20.14 (17) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.14/20.14 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 136.14/20.14 op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.14/20.14 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.14/20.14 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 &
% 136.14/20.14 all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~
% 136.14/20.14 (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 136.14/20.14 op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 136.14/20.14 all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 136.14/20.14 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 136.14/20.14 all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~
% 136.14/20.14 (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 136.14/20.14 (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 &
% 136.14/20.14 op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0
% 136.14/20.14 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.14/20.14 (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 136.14/20.14 (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.14/20.14 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.14/20.14 all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.14/20.14 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.14/20.14 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.14/20.14 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.14/20.14 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 136.14/20.14 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 136.14/20.14 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 136.14/20.14 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 136.14/20.14 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 136.14/20.14 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 136.14/20.14 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.14/20.14 $i(all_56_29))))
% 136.14/20.14
% 136.14/20.14 Begin of proof
% 136.14/20.14 |
% 136.14/20.14 | BETA: splitting (17) gives:
% 136.14/20.14 |
% 136.14/20.14 | Case 1:
% 136.14/20.14 | |
% 136.14/20.14 | | (18) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ (all_56_15
% 136.14/20.14 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e2, e2) =
% 136.14/20.14 | | e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 136.14/20.14 | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 &
% 136.14/20.14 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31)
% 136.14/20.14 | |
% 136.14/20.14 | | ALPHA: (18) implies:
% 136.14/20.14 | | (19) op(e2, e2) = e0
% 136.14/20.14 | |
% 136.14/20.14 | | REF_CLOSE: (5), (7), (9), (19) are inconsistent by sub-proof #641.
% 136.14/20.14 | |
% 136.14/20.14 | Case 2:
% 136.14/20.14 | |
% 136.14/20.14 | | (20) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 136.14/20.14 | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.14/20.14 | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.14/20.14 | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1)
% 136.14/20.14 | | = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 136.14/20.14 | | $i(all_56_27)) | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 136.14/20.14 | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 136.14/20.14 | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 136.14/20.14 | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) =
% 136.14/20.14 | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 136.14/20.14 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.14/20.14 | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 136.14/20.14 | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.14/20.14 | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.14/20.14 | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.14/20.14 | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27))
% 136.14/20.14 | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.14/20.14 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.14/20.14 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 136.14/20.14 | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7)
% 136.14/20.14 | | & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 136.14/20.14 | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.14/20.14 | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5
% 136.14/20.14 | | & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 136.14/20.14 | | = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 136.14/20.14 | | $i(all_56_21) & $i(all_56_29))))
% 136.14/20.14 | |
% 136.14/20.14 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (10), (11), (12), (13), (14),
% 136.14/20.14 | | (15), (16), (20) are inconsistent by sub-proof #266.
% 136.14/20.14 | |
% 136.14/20.14 | End of split
% 136.14/20.14 |
% 136.14/20.14 End of proof
% 136.14/20.14
% 136.14/20.14 Sub-proof #266 shows that the following formulas are inconsistent:
% 136.14/20.14 ----------------------------------------------------------------
% 136.14/20.14 (1) op(e1, e1) = all_6_2
% 136.14/20.14 (2) ~ (all_40_2 = e0) | ( ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 &
% 136.14/20.14 $i(all_40_0)) | ( ~ (all_40_1 = e2) & op(e0, e0) = all_40_1 &
% 136.14/20.14 $i(all_40_1))
% 136.14/20.14 (3) ~ (all_52_11 = e2)
% 136.14/20.14 (4) all_40_2 = all_6_2
% 136.14/20.14 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.14 (6) ~ (e2 = e1)
% 136.14/20.14 (7) ~ (e3 = e2)
% 136.14/20.14 (8) ~ (all_52_11 = all_6_2)
% 136.14/20.14 (9) op(e0, e1) = all_52_11
% 136.14/20.14 (10) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 136.14/20.14 (11) ~ (all_6_2 = e2)
% 136.14/20.14 (12) op(e2, e0) = e0
% 136.14/20.14 (13) op(e0, e0) = e2
% 136.14/20.15 (14) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 136.14/20.15 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 136.14/20.15 all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 136.14/20.15 e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 136.14/20.15 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 136.14/20.15 all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~
% 136.14/20.15 (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 136.14/20.15 (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 &
% 136.14/20.15 op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0
% 136.14/20.15 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.14/20.15 (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 136.14/20.15 (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.14/20.15 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.14/20.15 all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.14/20.15 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.14/20.15 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.14/20.15 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.14/20.15 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 136.14/20.15 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 136.14/20.15 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 136.14/20.15 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 136.14/20.15 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 136.14/20.15 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 136.14/20.15 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.14/20.15 $i(all_56_29))))
% 136.14/20.15 (15) all_54_14 = all_52_11
% 136.14/20.15
% 136.14/20.15 Begin of proof
% 136.14/20.15 |
% 136.14/20.15 | BETA: splitting (14) gives:
% 136.14/20.15 |
% 136.14/20.15 | Case 1:
% 136.14/20.15 | |
% 136.14/20.15 | | (16) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11
% 136.14/20.15 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 136.14/20.15 | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 136.14/20.15 | | e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3)
% 136.14/20.15 | | & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)
% 136.14/20.15 | |
% 136.14/20.15 | | ALPHA: (16) implies:
% 136.14/20.15 | | (17) op(e1, e1) = e2
% 136.14/20.15 | |
% 136.14/20.15 | | REF_CLOSE: (1), (5), (11), (17) are inconsistent by sub-proof #767.
% 136.14/20.15 | |
% 136.14/20.15 | Case 2:
% 136.14/20.15 | |
% 136.14/20.15 | | (18) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31
% 136.14/20.15 | | = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 136.14/20.15 | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2)
% 136.14/20.15 | | = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 136.14/20.15 | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 136.14/20.15 | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3
% 136.14/20.15 | | = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 136.14/20.15 | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 136.14/20.15 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 136.14/20.15 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 136.14/20.15 | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7
% 136.14/20.15 | | = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 136.14/20.15 | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 136.14/20.15 | | e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) =
% 136.14/20.15 | | all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 136.14/20.15 | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 136.14/20.15 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 136.14/20.15 | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.14/20.15 | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 136.14/20.15 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)))
% 136.14/20.15 | |
% 136.14/20.15 | | ALPHA: (18) implies:
% 136.14/20.15 | | (19) op(e0, e0) = all_56_31
% 136.14/20.15 | | (20) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 136.14/20.15 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.14/20.15 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.14/20.15 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9)
% 136.14/20.15 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 136.14/20.15 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 136.14/20.15 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 136.14/20.15 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 136.14/20.15 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 136.14/20.15 | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 136.14/20.15 | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31
% 136.14/20.15 | | = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 136.14/20.15 | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 136.14/20.15 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 &
% 136.14/20.15 | | all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.14/20.15 | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 136.14/20.15 | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 136.14/20.15 | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 136.14/20.15 | | $i(all_56_21) & $i(all_56_29))
% 136.14/20.15 | |
% 136.14/20.15 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 136.14/20.15 | | (15), (19), (20) are inconsistent by sub-proof #273.
% 136.14/20.15 | |
% 136.14/20.15 | End of split
% 136.14/20.15 |
% 136.14/20.15 End of proof
% 136.14/20.15
% 136.14/20.15 Sub-proof #267 shows that the following formulas are inconsistent:
% 136.14/20.15 ----------------------------------------------------------------
% 136.14/20.15 (1) op(e1, e1) = all_6_2
% 136.14/20.15 (2) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 136.14/20.15 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 136.14/20.15 (3) ~ (all_52_9 = all_6_2)
% 136.14/20.15 (4) op(e2, e0) = all_52_13
% 136.14/20.15 (5) ~ (all_40_2 = e0) | ( ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 &
% 136.14/20.15 $i(all_40_0)) | ( ~ (all_40_1 = e2) & op(e0, e0) = all_40_1 &
% 136.14/20.15 $i(all_40_1))
% 136.14/20.15 (6) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 136.14/20.15 (7) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 136.14/20.15 (8) op(e3, e3) = e2
% 136.14/20.15 (9) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 136.14/20.15 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 136.14/20.15 (10) ~ (e2 = e0)
% 136.14/20.15 (11) ~ (all_52_1 = all_52_2)
% 136.14/20.15 (12) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 136.14/20.15 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 136.14/20.15 (13) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 136.14/20.15 | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 136.14/20.15 e3)
% 136.14/20.15 (14) all_40_2 = all_6_2
% 136.14/20.15 (15) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 136.14/20.15 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 136.14/20.15 (16) ~ (all_52_7 = e3)
% 136.14/20.15 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.15 (18) ~ (e2 = e1)
% 136.14/20.15 (19) ~ (e3 = e0)
% 136.14/20.15 (20) op(e2, e0) = all_26_0
% 136.14/20.15 (21) ~ (all_52_1 = all_52_13)
% 136.14/20.15 (22) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 136.14/20.15 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 136.14/20.15 e2)
% 136.14/20.15 (23) ~ (e3 = e2)
% 136.14/20.15 (24) op(e2, e2) = e3
% 136.14/20.15 (25) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 136.14/20.15 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 136.14/20.15 (26) ~ (all_52_1 = all_52_9)
% 136.14/20.15 (27) ~ (all_52_11 = all_6_2)
% 136.14/20.15 (28) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 136.14/20.15 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 136.14/20.15 (29) op(e0, e1) = all_52_11
% 136.14/20.15 (30) op(e0, e2) = all_52_7
% 136.14/20.15 (31) ~ (all_52_4 = e3)
% 136.14/20.15 (32) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 136.14/20.15 (33) ~ (all_6_2 = e2)
% 136.14/20.15 (34) ~ (all_52_13 = e2)
% 136.14/20.15 (35) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 136.14/20.15 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 136.14/20.15 op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 136.14/20.15 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 136.14/20.15 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 136.14/20.15 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.14/20.15 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 136.14/20.15 = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.14/20.15 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 136.14/20.15 $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~
% 136.14/20.15 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 136.14/20.15 (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) =
% 136.14/20.15 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0,
% 136.14/20.15 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 136.14/20.15 $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3)
% 136.14/20.15 & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 136.14/20.15 op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17
% 136.14/20.15 & op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 136.14/20.15 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.14/20.15 (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.14/20.15 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.14/20.15 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0)
% 136.14/20.15 = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) &
% 136.14/20.15 $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 &
% 136.14/20.15 all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.14/20.15 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 136.14/20.15 = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.14/20.15 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 136.14/20.15 $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~
% 136.14/20.15 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 136.14/20.15 (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 136.14/20.15 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0,
% 136.14/20.15 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 136.14/20.15 $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3)
% 136.14/20.15 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.14/20.15 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.14/20.15 all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2
% 136.14/20.15 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.14/20.15 (op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 =
% 136.14/20.15 e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 136.14/20.15 & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) =
% 136.14/20.15 all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 136.14/20.15 op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 136.14/20.15 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 136.14/20.15 e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 136.14/20.15 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 136.14/20.15 e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.14/20.15 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.14/20.15 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.14/20.15 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.14/20.15 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 136.14/20.15 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 136.14/20.15 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 136.14/20.15 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 136.14/20.15 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 136.14/20.15 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 136.14/20.15 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.14/20.15 $i(all_56_29))))
% 136.14/20.15 (36) ~ (all_26_0 = e1)
% 136.14/20.15 (37) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 136.14/20.15 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 136.14/20.15 (38) ~ (all_52_9 = e3)
% 136.14/20.15 (39) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 136.14/20.15 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 136.14/20.15 e1)
% 136.14/20.15 (40) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 136.14/20.15 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 136.14/20.15 (41) op(e2, e1) = all_52_9
% 136.14/20.15 (42) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 136.14/20.15 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 136.14/20.15 (43) op(e1, e3) = all_52_2
% 136.14/20.15 (44) op(e3, e2) = all_52_4
% 136.14/20.15 (45) ~ (all_52_13 = e3)
% 136.14/20.15 (46) ~ (all_52_1 = e3)
% 136.14/20.15 (47) op(e0, e0) = e2
% 136.14/20.15 (48) all_57_3 = e3
% 136.14/20.15 (49) op(e2, e3) = all_52_1
% 136.14/20.15 (50) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 136.14/20.15 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 136.14/20.15 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 136.14/20.15 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 136.14/20.15 (51) all_54_7 = all_52_13
% 136.14/20.15 (52) ~ (all_52_9 = all_52_11)
% 136.14/20.15 (53) all_54_14 = all_52_11
% 136.14/20.15 (54) ~ (e3 = e1)
% 136.14/20.15 (55) ~ (e1 = e0)
% 136.14/20.15 (56) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 136.14/20.15 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 136.14/20.15 (57) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 136.14/20.15 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 136.14/20.15 (58) all_54_4 = all_52_1
% 136.14/20.15 (59) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 136.14/20.15 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 136.14/20.15 (60) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 136.14/20.15 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 136.14/20.15 (61) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 136.14/20.15 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 136.14/20.15 (62) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 136.14/20.15 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 136.14/20.15
% 136.14/20.15 Begin of proof
% 136.14/20.15 |
% 136.14/20.15 | BETA: splitting (28) gives:
% 136.14/20.15 |
% 136.14/20.15 | Case 1:
% 136.14/20.15 | |
% 136.14/20.15 | | (63) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) =
% 136.14/20.15 | | e2)
% 136.14/20.15 | |
% 136.14/20.15 | | BETA: splitting (63) gives:
% 136.14/20.15 | |
% 136.14/20.15 | | Case 1:
% 136.14/20.15 | | |
% 136.14/20.15 | | | (64) all_57_6 = e2 & op(e1, e3) = e2
% 136.14/20.15 | | |
% 136.14/20.15 | | | ALPHA: (64) implies:
% 136.14/20.15 | | | (65) all_57_6 = e2
% 136.14/20.15 | | |
% 136.14/20.15 | | | REF_CLOSE: (2), (8), (10), (15), (17), (18), (19), (23), (25), (42), (48),
% 136.14/20.15 | | | (54), (55), (56), (57), (65) are inconsistent by sub-proof
% 136.14/20.15 | | | #360.
% 136.14/20.15 | | |
% 136.14/20.15 | | Case 2:
% 136.14/20.15 | | |
% 136.14/20.15 | | | (66) all_57_7 = e2 & op(e1, e2) = e2
% 136.14/20.15 | | |
% 136.14/20.15 | | | ALPHA: (66) implies:
% 136.14/20.15 | | | (67) all_57_7 = e2
% 136.14/20.15 | | |
% 136.14/20.15 | | | BETA: splitting (2) gives:
% 136.14/20.15 | | |
% 136.14/20.15 | | | Case 1:
% 136.14/20.15 | | | |
% 136.14/20.15 | | | | (68) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2)
% 136.14/20.15 | | | | = e2)
% 136.14/20.15 | | | |
% 136.14/20.15 | | | | BETA: splitting (68) gives:
% 136.14/20.15 | | | |
% 136.14/20.15 | | | | Case 1:
% 136.14/20.15 | | | | |
% 136.14/20.15 | | | | | (69) all_57_2 = e2 & op(e2, e3) = e2
% 136.14/20.15 | | | | |
% 136.14/20.15 | | | | | ALPHA: (69) implies:
% 136.14/20.15 | | | | | (70) all_57_2 = e2
% 136.14/20.15 | | | | |
% 136.14/20.15 | | | | | BETA: splitting (22) gives:
% 136.14/20.15 | | | | |
% 136.14/20.15 | | | | | Case 1:
% 136.14/20.15 | | | | | |
% 136.14/20.15 | | | | | | (71) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 &
% 136.14/20.15 | | | | | | op(e0, e2) = e2)
% 136.14/20.15 | | | | | |
% 136.14/20.15 | | | | | | REF_CLOSE: (8), (9), (10), (15), (17), (18), (19), (23), (25), (40),
% 136.14/20.15 | | | | | | (42), (48), (54), (55), (67), (71) are inconsistent by
% 136.14/20.15 | | | | | | sub-proof #286.
% 136.14/20.15 | | | | | |
% 136.14/20.15 | | | | | Case 2:
% 136.14/20.15 | | | | | |
% 136.14/20.15 | | | | | | (72) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 &
% 136.14/20.15 | | | | | | op(e0, e0) = e2)
% 136.14/20.15 | | | | | |
% 136.14/20.15 | | | | | | BETA: splitting (72) gives:
% 136.14/20.15 | | | | | |
% 136.14/20.15 | | | | | | Case 1:
% 136.14/20.15 | | | | | | |
% 136.14/20.15 | | | | | | | (73) all_57_14 = e2 & op(e0, e1) = e2
% 136.14/20.15 | | | | | | |
% 136.14/20.15 | | | | | | | REF_CLOSE: (10), (13), (16), (17), (18), (19), (23), (30), (39),
% 136.14/20.15 | | | | | | | (47), (50), (54), (55), (73) are inconsistent by
% 136.14/20.15 | | | | | | | sub-proof #283.
% 136.14/20.15 | | | | | | |
% 136.14/20.15 | | | | | | Case 2:
% 136.14/20.15 | | | | | | |
% 136.14/20.15 | | | | | | | (74) all_57_15 = e2 & op(e0, e0) = e2
% 136.14/20.15 | | | | | | |
% 136.14/20.15 | | | | | | | ALPHA: (74) implies:
% 136.14/20.15 | | | | | | | (75) all_57_15 = e2
% 136.14/20.15 | | | | | | |
% 136.14/20.15 | | | | | | | BETA: splitting (62) gives:
% 136.14/20.15 | | | | | | |
% 136.14/20.15 | | | | | | | Case 1:
% 136.14/20.15 | | | | | | | |
% 136.14/20.15 | | | | | | | | (76) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 &
% 136.14/20.15 | | | | | | | | op(e2, e1) = e2)
% 136.14/20.15 | | | | | | | |
% 136.14/20.15 | | | | | | | | BETA: splitting (76) gives:
% 136.14/20.15 | | | | | | | |
% 136.14/20.15 | | | | | | | | Case 1:
% 136.14/20.15 | | | | | | | | |
% 136.14/20.15 | | | | | | | | | (77) all_57_4 = e2 & op(e3, e1) = e2
% 136.14/20.15 | | | | | | | | |
% 136.14/20.15 | | | | | | | | | ALPHA: (77) implies:
% 136.14/20.15 | | | | | | | | | (78) all_57_4 = e2
% 136.14/20.15 | | | | | | | | |
% 136.14/20.15 | | | | | | | | | REF_CLOSE: (8), (10), (12), (17), (18), (19), (23), (31),
% 136.14/20.15 | | | | | | | | | (44), (54), (55), (59), (60), (78) are inconsistent
% 136.14/20.15 | | | | | | | | | by sub-proof #278.
% 136.14/20.15 | | | | | | | | |
% 136.14/20.15 | | | | | | | | Case 2:
% 136.14/20.15 | | | | | | | | |
% 136.14/20.15 | | | | | | | | | (79) all_57_5 = e2 & op(e2, e1) = e2
% 136.14/20.15 | | | | | | | | |
% 136.14/20.15 | | | | | | | | | ALPHA: (79) implies:
% 136.14/20.15 | | | | | | | | | (80) all_57_5 = e2
% 136.14/20.15 | | | | | | | | |
% 136.14/20.15 | | | | | | | | | BETA: splitting (56) gives:
% 136.14/20.15 | | | | | | | | |
% 136.14/20.15 | | | | | | | | | Case 1:
% 136.14/20.15 | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | (81) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 &
% 136.14/20.15 | | | | | | | | | | op(e2, e2) = e1)
% 136.14/20.15 | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | BETA: splitting (81) gives:
% 136.14/20.15 | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | Case 1:
% 136.14/20.15 | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | (82) all_57_2 = e1 & op(e2, e3) = e1
% 136.14/20.15 | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | REF_CLOSE: (18), (70), (82) are inconsistent by sub-proof
% 136.14/20.15 | | | | | | | | | | | #497.
% 136.14/20.15 | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | Case 2:
% 136.14/20.15 | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | (83) all_57_3 = e1 & op(e2, e2) = e1
% 136.14/20.15 | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | REF_CLOSE: (48), (54), (83) are inconsistent by sub-proof
% 136.14/20.15 | | | | | | | | | | | #303.
% 136.14/20.15 | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | End of split
% 136.14/20.15 | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | Case 2:
% 136.14/20.15 | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | (84) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1
% 136.14/20.15 | | | | | | | | | | & op(e2, e0) = e1)
% 136.14/20.15 | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | BETA: splitting (84) gives:
% 136.14/20.15 | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | Case 1:
% 136.14/20.15 | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | (85) all_57_5 = e1 & op(e2, e1) = e1
% 136.14/20.15 | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | REF_CLOSE: (18), (80), (85) are inconsistent by sub-proof
% 136.14/20.15 | | | | | | | | | | | #500.
% 136.14/20.15 | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | Case 2:
% 136.14/20.15 | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | (86) all_57_10 = e1 & op(e2, e0) = e1
% 136.14/20.15 | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | ALPHA: (86) implies:
% 136.14/20.15 | | | | | | | | | | | (87) all_57_10 = e1
% 136.14/20.15 | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | BETA: splitting (57) gives:
% 136.14/20.15 | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | Case 1:
% 136.14/20.15 | | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | | (88) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 136.14/20.15 | | | | | | | | | | | | & op(e2, e2) = e0)
% 136.14/20.15 | | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | | BETA: splitting (88) gives:
% 136.14/20.15 | | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | | Case 1:
% 136.14/20.15 | | | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | | | (89) all_57_2 = e0 & op(e2, e3) = e0
% 136.14/20.15 | | | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | | | REF_CLOSE: (10), (70), (89) are inconsistent by sub-proof
% 136.14/20.15 | | | | | | | | | | | | | #494.
% 136.14/20.15 | | | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | | Case 2:
% 136.14/20.15 | | | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | | | (90) all_57_3 = e0 & op(e2, e2) = e0
% 136.14/20.15 | | | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | | | REF_CLOSE: (19), (48), (90) are inconsistent by sub-proof
% 136.14/20.15 | | | | | | | | | | | | | #302.
% 136.14/20.15 | | | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | | End of split
% 136.14/20.15 | | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | Case 2:
% 136.14/20.15 | | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | | (91) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 136.14/20.15 | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 136.14/20.15 | | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | | BETA: splitting (91) gives:
% 136.14/20.15 | | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | | Case 1:
% 136.14/20.15 | | | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | | | (92) all_57_5 = e0 & op(e2, e1) = e0
% 136.14/20.15 | | | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | | | REF_CLOSE: (10), (80), (92) are inconsistent by sub-proof
% 136.14/20.15 | | | | | | | | | | | | | #277.
% 136.14/20.15 | | | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | | Case 2:
% 136.14/20.15 | | | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | | | (93) all_57_10 = e0 & op(e2, e0) = e0
% 136.14/20.15 | | | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | | | ALPHA: (93) implies:
% 136.14/20.15 | | | | | | | | | | | | | (94) all_57_10 = e0
% 136.14/20.15 | | | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | | | REF_CLOSE: (55), (87), (94) are inconsistent by sub-proof
% 136.14/20.15 | | | | | | | | | | | | | #639.
% 136.14/20.15 | | | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | | End of split
% 136.14/20.15 | | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | End of split
% 136.14/20.15 | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | End of split
% 136.14/20.15 | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | End of split
% 136.14/20.15 | | | | | | | | |
% 136.14/20.15 | | | | | | | | End of split
% 136.14/20.15 | | | | | | | |
% 136.14/20.15 | | | | | | | Case 2:
% 136.14/20.15 | | | | | | | |
% 136.14/20.15 | | | | | | | | (95) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 &
% 136.14/20.15 | | | | | | | | op(e0, e1) = e2)
% 136.14/20.15 | | | | | | | |
% 136.14/20.15 | | | | | | | | REF_CLOSE: (1), (10), (13), (16), (17), (18), (19), (23), (30),
% 136.14/20.15 | | | | | | | | (33), (39), (50), (54), (55), (75), (95) are
% 136.14/20.15 | | | | | | | | inconsistent by sub-proof #276.
% 136.14/20.15 | | | | | | | |
% 136.14/20.15 | | | | | | | End of split
% 136.14/20.15 | | | | | | |
% 136.14/20.15 | | | | | | End of split
% 136.14/20.15 | | | | | |
% 136.14/20.15 | | | | | End of split
% 136.14/20.15 | | | | |
% 136.14/20.15 | | | | Case 2:
% 136.14/20.15 | | | | |
% 136.14/20.15 | | | | | (96) all_57_3 = e2 & op(e2, e2) = e2
% 136.14/20.15 | | | | |
% 136.14/20.15 | | | | | REF_CLOSE: (23), (48), (96) are inconsistent by sub-proof #375.
% 136.14/20.15 | | | | |
% 136.14/20.15 | | | | End of split
% 136.14/20.15 | | | |
% 136.14/20.15 | | | Case 2:
% 136.14/20.15 | | | |
% 136.14/20.15 | | | | (97) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0)
% 136.14/20.15 | | | | = e2)
% 136.14/20.15 | | | |
% 136.14/20.15 | | | | BETA: splitting (97) gives:
% 136.14/20.15 | | | |
% 136.14/20.15 | | | | Case 1:
% 136.14/20.15 | | | | |
% 136.14/20.15 | | | | | (98) all_57_5 = e2 & op(e2, e1) = e2
% 136.14/20.15 | | | | |
% 136.14/20.15 | | | | | ALPHA: (98) implies:
% 136.14/20.15 | | | | | (99) op(e2, e1) = e2
% 136.14/20.15 | | | | |
% 136.14/20.15 | | | | | GROUND_INST: instantiating (17) with all_52_13, all_26_0, e0, e2,
% 136.14/20.15 | | | | | simplifying with (4), (20) gives:
% 136.14/20.15 | | | | | (100) all_52_13 = all_26_0
% 136.14/20.15 | | | | |
% 136.14/20.15 | | | | | GROUND_INST: instantiating (17) with all_52_9, e2, e1, e2, simplifying
% 136.14/20.15 | | | | | with (41), (99) gives:
% 136.14/20.15 | | | | | (101) all_52_9 = e2
% 136.14/20.15 | | | | |
% 136.14/20.15 | | | | | COMBINE_EQS: (51), (100) imply:
% 136.14/20.15 | | | | | (102) all_54_7 = all_26_0
% 136.14/20.15 | | | | |
% 136.14/20.15 | | | | | REDUCE: (26), (101) imply:
% 136.14/20.15 | | | | | (103) ~ (all_52_1 = e2)
% 136.14/20.15 | | | | |
% 136.14/20.15 | | | | | REDUCE: (21), (100) imply:
% 136.14/20.15 | | | | | (104) ~ (all_52_1 = all_26_0)
% 136.14/20.15 | | | | |
% 136.14/20.15 | | | | | REDUCE: (52), (101) imply:
% 136.14/20.15 | | | | | (105) ~ (all_52_11 = e2)
% 136.14/20.15 | | | | |
% 136.14/20.15 | | | | | SIMP: (105) implies:
% 136.14/20.15 | | | | | (106) ~ (all_52_11 = e2)
% 136.14/20.15 | | | | |
% 136.14/20.15 | | | | | REDUCE: (3), (101) imply:
% 136.14/20.15 | | | | | (107) ~ (all_6_2 = e2)
% 136.14/20.15 | | | | |
% 136.14/20.15 | | | | | REDUCE: (38), (101) imply:
% 136.14/20.15 | | | | | (108) ~ (e3 = e2)
% 136.14/20.15 | | | | |
% 136.14/20.15 | | | | | REDUCE: (45), (100) imply:
% 136.14/20.15 | | | | | (109) ~ (all_26_0 = e3)
% 136.14/20.15 | | | | |
% 136.14/20.15 | | | | | REDUCE: (34), (100) imply:
% 136.14/20.15 | | | | | (110) ~ (all_26_0 = e2)
% 136.14/20.15 | | | | |
% 136.14/20.15 | | | | | BETA: splitting (7) gives:
% 136.14/20.15 | | | | |
% 136.14/20.15 | | | | | Case 1:
% 136.14/20.15 | | | | | |
% 136.14/20.15 | | | | | | (111) all_54_7 = e3
% 136.14/20.15 | | | | | |
% 136.14/20.15 | | | | | | COMBINE_EQS: (102), (111) imply:
% 136.14/20.15 | | | | | | (112) all_26_0 = e3
% 136.14/20.15 | | | | | |
% 136.14/20.15 | | | | | | SIMP: (112) implies:
% 136.14/20.15 | | | | | | (113) all_26_0 = e3
% 136.14/20.15 | | | | | |
% 136.14/20.15 | | | | | | REDUCE: (109), (113) imply:
% 136.14/20.15 | | | | | | (114) $false
% 136.14/20.15 | | | | | |
% 136.14/20.15 | | | | | | CLOSE: (114) is inconsistent.
% 136.14/20.15 | | | | | |
% 136.14/20.15 | | | | | Case 2:
% 136.14/20.15 | | | | | |
% 136.14/20.15 | | | | | | (115) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 136.14/20.15 | | | | | |
% 136.14/20.15 | | | | | | BETA: splitting (115) gives:
% 136.14/20.15 | | | | | |
% 136.14/20.15 | | | | | | Case 1:
% 136.14/20.15 | | | | | | |
% 136.14/20.15 | | | | | | | (116) all_54_7 = e2
% 136.14/20.15 | | | | | | |
% 136.14/20.15 | | | | | | | COMBINE_EQS: (102), (116) imply:
% 136.14/20.15 | | | | | | | (117) all_26_0 = e2
% 136.14/20.15 | | | | | | |
% 136.14/20.15 | | | | | | | SIMP: (117) implies:
% 136.14/20.15 | | | | | | | (118) all_26_0 = e2
% 136.14/20.15 | | | | | | |
% 136.14/20.15 | | | | | | | REDUCE: (110), (118) imply:
% 136.14/20.15 | | | | | | | (119) $false
% 136.14/20.15 | | | | | | |
% 136.14/20.15 | | | | | | | CLOSE: (119) is inconsistent.
% 136.14/20.15 | | | | | | |
% 136.14/20.15 | | | | | | Case 2:
% 136.14/20.15 | | | | | | |
% 136.14/20.15 | | | | | | | (120) ~ (all_54_7 = e2)
% 136.14/20.15 | | | | | | | (121) all_54_7 = e1 | all_54_7 = e0
% 136.14/20.15 | | | | | | |
% 136.14/20.15 | | | | | | | BETA: splitting (121) gives:
% 136.14/20.15 | | | | | | |
% 136.14/20.15 | | | | | | | Case 1:
% 136.14/20.15 | | | | | | | |
% 136.14/20.15 | | | | | | | | (122) all_54_7 = e1
% 136.14/20.15 | | | | | | | |
% 136.14/20.15 | | | | | | | | COMBINE_EQS: (102), (122) imply:
% 136.14/20.15 | | | | | | | | (123) all_26_0 = e1
% 136.14/20.15 | | | | | | | |
% 136.14/20.15 | | | | | | | | SIMP: (123) implies:
% 136.14/20.15 | | | | | | | | (124) all_26_0 = e1
% 136.14/20.15 | | | | | | | |
% 136.14/20.15 | | | | | | | | REDUCE: (36), (124) imply:
% 136.14/20.15 | | | | | | | | (125) $false
% 136.14/20.15 | | | | | | | |
% 136.14/20.15 | | | | | | | | CLOSE: (125) is inconsistent.
% 136.14/20.15 | | | | | | | |
% 136.14/20.15 | | | | | | | Case 2:
% 136.14/20.15 | | | | | | | |
% 136.14/20.15 | | | | | | | | (126) all_54_7 = e0
% 136.14/20.15 | | | | | | | |
% 136.14/20.15 | | | | | | | | COMBINE_EQS: (102), (126) imply:
% 136.14/20.15 | | | | | | | | (127) all_26_0 = e0
% 136.14/20.15 | | | | | | | |
% 136.14/20.15 | | | | | | | | SIMP: (127) implies:
% 136.14/20.15 | | | | | | | | (128) all_26_0 = e0
% 136.14/20.15 | | | | | | | |
% 136.14/20.15 | | | | | | | | REDUCE: (104), (128) imply:
% 136.14/20.15 | | | | | | | | (129) ~ (all_52_1 = e0)
% 136.14/20.15 | | | | | | | |
% 136.14/20.15 | | | | | | | | REDUCE: (110), (128) imply:
% 136.14/20.15 | | | | | | | | (130) ~ (e2 = e0)
% 136.14/20.15 | | | | | | | |
% 136.14/20.15 | | | | | | | | REDUCE: (20), (128) imply:
% 136.14/20.15 | | | | | | | | (131) op(e2, e0) = e0
% 136.14/20.15 | | | | | | | |
% 136.14/20.15 | | | | | | | | BETA: splitting (6) gives:
% 136.14/20.15 | | | | | | | |
% 136.14/20.15 | | | | | | | | Case 1:
% 136.14/20.15 | | | | | | | | |
% 136.14/20.15 | | | | | | | | | (132) all_54_4 = e3
% 136.14/20.15 | | | | | | | | |
% 136.14/20.15 | | | | | | | | | REF_CLOSE: (46), (58), (132) are inconsistent by sub-proof
% 136.14/20.15 | | | | | | | | | #481.
% 136.14/20.15 | | | | | | | | |
% 136.14/20.15 | | | | | | | | Case 2:
% 136.14/20.15 | | | | | | | | |
% 136.14/20.15 | | | | | | | | | (133) ~ (all_54_4 = e3)
% 136.14/20.15 | | | | | | | | | (134) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 136.14/20.15 | | | | | | | | |
% 136.14/20.15 | | | | | | | | | BETA: splitting (134) gives:
% 136.14/20.15 | | | | | | | | |
% 136.14/20.15 | | | | | | | | | Case 1:
% 136.14/20.15 | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | (135) all_54_4 = e2
% 136.14/20.15 | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | COMBINE_EQS: (58), (135) imply:
% 136.14/20.15 | | | | | | | | | | (136) all_52_1 = e2
% 136.14/20.15 | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | SIMP: (136) implies:
% 136.14/20.15 | | | | | | | | | | (137) all_52_1 = e2
% 136.14/20.15 | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | REDUCE: (103), (137) imply:
% 136.14/20.15 | | | | | | | | | | (138) $false
% 136.14/20.15 | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | CLOSE: (138) is inconsistent.
% 136.14/20.15 | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | Case 2:
% 136.14/20.15 | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | (139) ~ (all_54_4 = e2)
% 136.14/20.15 | | | | | | | | | | (140) all_54_4 = e1 | all_54_4 = e0
% 136.14/20.15 | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | BETA: splitting (140) gives:
% 136.14/20.15 | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | Case 1:
% 136.14/20.15 | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | (141) all_54_4 = e1
% 136.14/20.15 | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | COMBINE_EQS: (58), (141) imply:
% 136.14/20.15 | | | | | | | | | | | (142) all_52_1 = e1
% 136.14/20.15 | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | SIMP: (142) implies:
% 136.14/20.15 | | | | | | | | | | | (143) all_52_1 = e1
% 136.14/20.15 | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | REDUCE: (11), (143) imply:
% 136.14/20.15 | | | | | | | | | | | (144) ~ (all_52_2 = e1)
% 136.14/20.15 | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | SIMP: (144) implies:
% 136.14/20.15 | | | | | | | | | | | (145) ~ (all_52_2 = e1)
% 136.14/20.15 | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | REDUCE: (46), (143) imply:
% 136.14/20.15 | | | | | | | | | | | (146) ~ (e3 = e1)
% 136.14/20.15 | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | REDUCE: (103), (143) imply:
% 136.14/20.15 | | | | | | | | | | | (147) ~ (e2 = e1)
% 136.14/20.15 | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | REDUCE: (49), (143) imply:
% 136.14/20.15 | | | | | | | | | | | (148) op(e2, e3) = e1
% 136.14/20.15 | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | BETA: splitting (35) gives:
% 136.14/20.15 | | | | | | | | | | |
% 136.14/20.15 | | | | | | | | | | | Case 1:
% 136.14/20.15 | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | (149) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 136.14/20.16 | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 136.14/20.16 | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 136.14/20.16 | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 136.14/20.16 | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 136.14/20.16 | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 136.14/20.16 | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.14/20.16 | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 136.14/20.16 | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 136.14/20.16 | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 136.14/20.16 | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 136.14/20.16 | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 136.14/20.16 | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 136.14/20.16 | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 136.14/20.16 | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 136.14/20.16 | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 136.14/20.16 | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 136.14/20.16 | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 136.14/20.16 | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 136.14/20.16 | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.14/20.16 | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 136.14/20.16 | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 136.14/20.16 | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 136.14/20.16 | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 136.14/20.16 | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 136.14/20.16 | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 136.14/20.16 | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 136.14/20.16 | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 136.14/20.16 | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | BETA: splitting (149) gives:
% 136.14/20.16 | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | Case 1:
% 136.14/20.16 | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | (150) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 =
% 136.14/20.16 | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 136.14/20.16 | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 136.14/20.16 | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2,
% 136.14/20.16 | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 136.14/20.16 | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) &
% 136.14/20.16 | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.14/20.16 | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 =
% 136.14/20.16 | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 136.14/20.16 | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 136.14/20.16 | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1,
% 136.14/20.16 | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 &
% 136.14/20.16 | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) &
% 136.14/20.16 | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 136.14/20.16 | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | REF_CLOSE: (8), (17), (18), (131), (150) are inconsistent by
% 136.14/20.16 | | | | | | | | | | | | | sub-proof #274.
% 136.14/20.16 | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | Case 2:
% 136.14/20.16 | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | (151) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 136.14/20.16 | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 136.14/20.16 | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 136.14/20.16 | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0,
% 136.14/20.16 | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 136.14/20.16 | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.14/20.16 | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 136.14/20.16 | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 136.14/20.16 | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 136.14/20.16 | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 136.14/20.16 | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 136.14/20.16 | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 &
% 136.14/20.16 | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 136.14/20.16 | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25))
% 136.14/20.16 | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | BETA: splitting (151) gives:
% 136.14/20.16 | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | Case 1:
% 136.14/20.16 | | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | | (152) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 =
% 136.14/20.16 | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 136.14/20.16 | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3,
% 136.14/20.16 | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 136.14/20.16 | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 136.14/20.16 | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 136.14/20.16 | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 136.14/20.16 | | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | | ALPHA: (152) implies:
% 136.14/20.16 | | | | | | | | | | | | | | (153) op(e3, e3) = e0
% 136.14/20.16 | | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | | REF_CLOSE: (8), (10), (17), (153) are inconsistent by
% 136.14/20.16 | | | | | | | | | | | | | | sub-proof #495.
% 136.14/20.16 | | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | Case 2:
% 136.14/20.16 | | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | | (154) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 =
% 136.14/20.16 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) &
% 136.14/20.16 | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 136.14/20.16 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 136.14/20.16 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2,
% 136.14/20.16 | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 136.14/20.16 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)
% 136.14/20.16 | | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | | ALPHA: (154) implies:
% 136.14/20.16 | | | | | | | | | | | | | | (155) op(e2, e3) = e2
% 136.14/20.16 | | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with e1, e2, e3, e2,
% 136.14/20.16 | | | | | | | | | | | | | | simplifying with (148), (155) gives:
% 136.14/20.16 | | | | | | | | | | | | | | (156) e2 = e1
% 136.14/20.16 | | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | | REDUCE: (18), (156) imply:
% 136.14/20.16 | | | | | | | | | | | | | | (157) $false
% 136.14/20.16 | | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | | CLOSE: (157) is inconsistent.
% 136.14/20.16 | | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | End of split
% 136.14/20.16 | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | End of split
% 136.14/20.16 | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | Case 2:
% 136.14/20.16 | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | (158) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 136.14/20.16 | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 136.14/20.16 | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 136.14/20.16 | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 136.14/20.16 | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 136.14/20.16 | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 136.14/20.16 | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 136.14/20.16 | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 136.14/20.16 | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 136.14/20.16 | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 136.14/20.16 | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 136.14/20.16 | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 136.14/20.16 | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 136.14/20.16 | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0
% 136.14/20.16 | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 136.14/20.16 | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 136.14/20.16 | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 136.14/20.16 | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 136.14/20.16 | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0)
% 136.14/20.16 | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 136.14/20.16 | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1
% 136.14/20.16 | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 136.14/20.16 | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 136.14/20.16 | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 136.14/20.16 | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 136.14/20.16 | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 &
% 136.14/20.16 | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 136.14/20.16 | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 136.14/20.16 | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 136.14/20.16 | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 136.14/20.16 | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 136.14/20.16 | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 136.14/20.16 | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) =
% 136.14/20.16 | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 136.14/20.16 | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 136.14/20.16 | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15
% 136.14/20.16 | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) &
% 136.14/20.16 | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 136.14/20.16 | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 136.14/20.16 | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.14/20.16 | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 136.14/20.16 | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 136.14/20.16 | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 136.14/20.16 | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) &
% 136.14/20.16 | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 136.14/20.16 | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 136.14/20.16 | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 136.14/20.16 | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) =
% 136.14/20.16 | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 136.14/20.16 | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 136.14/20.16 | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 136.14/20.16 | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 136.14/20.16 | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 136.14/20.16 | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 136.14/20.16 | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 136.14/20.16 | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 136.14/20.16 | | | | | | | | | | | | & $i(all_56_29))))
% 136.14/20.16 | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | BETA: splitting (158) gives:
% 136.14/20.16 | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | Case 1:
% 136.14/20.16 | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | (159) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 =
% 136.14/20.16 | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 136.14/20.16 | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 136.14/20.16 | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 136.14/20.16 | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 &
% 136.14/20.16 | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 136.14/20.16 | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1
% 136.14/20.16 | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 136.14/20.16 | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 136.14/20.16 | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 136.14/20.16 | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 136.14/20.16 | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 136.14/20.16 | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 136.14/20.16 | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 136.14/20.16 | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | REF_CLOSE: (17), (24), (43), (54), (145), (159) are
% 136.14/20.16 | | | | | | | | | | | | | inconsistent by sub-proof #304.
% 136.14/20.16 | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | Case 2:
% 136.14/20.16 | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | (160) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 136.14/20.16 | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 136.14/20.16 | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 &
% 136.14/20.16 | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0,
% 136.14/20.16 | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 136.14/20.16 | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.14/20.16 | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 136.14/20.16 | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 136.14/20.16 | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 136.14/20.16 | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 136.14/20.16 | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.14/20.16 | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 136.14/20.16 | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 136.14/20.16 | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.14/20.16 | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 136.14/20.16 | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 136.14/20.16 | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 136.14/20.16 | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.14/20.16 | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 136.14/20.16 | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 136.14/20.16 | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 136.14/20.16 | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 136.14/20.16 | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 136.14/20.16 | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 136.14/20.16 | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 136.14/20.16 | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 136.14/20.16 | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 136.14/20.16 | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.14/20.16 | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 136.14/20.16 | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 136.14/20.16 | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.14/20.16 | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 136.14/20.16 | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 136.14/20.16 | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 136.14/20.16 | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 136.14/20.16 | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 136.14/20.16 | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 136.14/20.16 | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 136.14/20.16 | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 136.14/20.16 | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 136.14/20.16 | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 136.14/20.16 | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 136.14/20.16 | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 136.14/20.16 | | | | | | | | | | | | | & $i(all_56_29))))
% 136.14/20.16 | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | BETA: splitting (160) gives:
% 136.14/20.16 | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | Case 1:
% 136.14/20.16 | | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | | (161) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 136.14/20.16 | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 136.14/20.16 | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2,
% 136.14/20.16 | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 136.14/20.16 | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 136.14/20.16 | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 136.14/20.16 | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)
% 136.14/20.16 | | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | | ALPHA: (161) implies:
% 136.14/20.16 | | | | | | | | | | | | | | (162) op(e2, e0) = e2
% 136.14/20.16 | | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with e0, e2, e0, e2,
% 136.14/20.16 | | | | | | | | | | | | | | simplifying with (131), (162) gives:
% 136.14/20.16 | | | | | | | | | | | | | | (163) e2 = e0
% 136.14/20.16 | | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | | REDUCE: (10), (163) imply:
% 136.14/20.16 | | | | | | | | | | | | | | (164) $false
% 136.14/20.16 | | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | | CLOSE: (164) is inconsistent.
% 136.14/20.16 | | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | Case 2:
% 136.14/20.16 | | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | | (165) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 136.14/20.16 | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 136.14/20.16 | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 136.14/20.16 | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.14/20.16 | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2)
% 136.14/20.16 | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 136.14/20.16 | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.14/20.16 | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 136.14/20.16 | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 136.14/20.16 | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17
% 136.14/20.16 | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.14/20.16 | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3,
% 136.14/20.16 | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 136.14/20.16 | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) &
% 136.14/20.16 | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) &
% 136.14/20.16 | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 136.14/20.16 | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 136.14/20.16 | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 136.14/20.16 | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2)
% 136.14/20.16 | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 &
% 136.14/20.16 | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.14/20.16 | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 136.14/20.16 | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 &
% 136.14/20.16 | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.14/20.16 | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 136.14/20.16 | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 136.14/20.16 | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 136.14/20.16 | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 136.14/20.16 | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) &
% 136.14/20.16 | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31
% 136.14/20.16 | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 136.14/20.16 | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29
% 136.14/20.16 | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 136.14/20.16 | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 &
% 136.14/20.16 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 136.14/20.16 | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 136.14/20.16 | | | | | | | | | | | | | | & $i(all_56_29))))
% 136.14/20.16 | | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | | BETA: splitting (165) gives:
% 136.14/20.16 | | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | | Case 1:
% 136.14/20.16 | | | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | | | (166) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 =
% 136.14/20.16 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1)
% 136.14/20.16 | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 136.14/20.16 | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 136.14/20.16 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 136.14/20.16 | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 136.14/20.16 | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)
% 136.14/20.16 | | | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | | | ALPHA: (166) implies:
% 136.14/20.16 | | | | | | | | | | | | | | | (167) op(e1, e1) = e2
% 136.14/20.16 | | | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | | | REF_CLOSE: (1), (17), (33), (167) are inconsistent by
% 136.14/20.16 | | | | | | | | | | | | | | | sub-proof #767.
% 136.14/20.16 | | | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | | Case 2:
% 136.14/20.16 | | | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | | | (168) op(e0, e0) = all_56_31 & $i(all_56_31) &
% 136.14/20.16 | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 136.14/20.16 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 136.14/20.16 | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.14/20.16 | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 136.14/20.16 | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 136.14/20.16 | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 136.14/20.16 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 =
% 136.14/20.16 | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 136.14/20.16 | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 136.14/20.16 | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 136.14/20.16 | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.14/20.16 | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 136.14/20.16 | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 136.14/20.16 | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 136.14/20.16 | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.14/20.16 | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 136.14/20.16 | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1,
% 136.14/20.16 | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 136.14/20.16 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 136.14/20.16 | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 136.14/20.16 | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~
% 136.14/20.16 | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.14/20.16 | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 136.14/20.16 | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13
% 136.14/20.16 | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) =
% 136.14/20.16 | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 136.14/20.16 | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) &
% 136.14/20.16 | | | | | | | | | | | | | | | $i(all_56_29)))
% 136.14/20.16 | | | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | | | ALPHA: (168) implies:
% 136.14/20.16 | | | | | | | | | | | | | | | (169) op(e0, e0) = all_56_31
% 136.14/20.16 | | | | | | | | | | | | | | | (170) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 136.14/20.16 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 136.14/20.16 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 136.14/20.16 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 &
% 136.14/20.16 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 136.14/20.16 | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 136.14/20.16 | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 136.14/20.16 | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) &
% 136.14/20.16 | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.14/20.16 | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 136.14/20.16 | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27
% 136.14/20.16 | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 136.14/20.16 | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 =
% 136.14/20.16 | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.14/20.16 | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 136.14/20.16 | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 136.14/20.16 | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 136.14/20.16 | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 &
% 136.14/20.16 | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 136.14/20.16 | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 =
% 136.14/20.16 | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 136.14/20.16 | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 136.14/20.16 | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.14/20.16 | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1)
% 136.14/20.16 | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) &
% 136.14/20.16 | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29))
% 136.14/20.16 | | | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (14), (17), (18), (23), (27), (29),
% 136.14/20.16 | | | | | | | | | | | | | | | (32), (47), (53), (106), (131), (169), (170) are
% 136.14/20.16 | | | | | | | | | | | | | | | inconsistent by sub-proof #273.
% 136.14/20.16 | | | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | | End of split
% 136.14/20.16 | | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | | End of split
% 136.14/20.16 | | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | | End of split
% 136.14/20.16 | | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | End of split
% 136.14/20.16 | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | Case 2:
% 136.14/20.16 | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | (171) all_54_4 = e0
% 136.14/20.16 | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | COMBINE_EQS: (58), (171) imply:
% 136.14/20.16 | | | | | | | | | | | (172) all_52_1 = e0
% 136.14/20.16 | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | SIMP: (172) implies:
% 136.14/20.16 | | | | | | | | | | | (173) all_52_1 = e0
% 136.14/20.16 | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | REDUCE: (129), (173) imply:
% 136.14/20.16 | | | | | | | | | | | (174) $false
% 136.14/20.16 | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | | CLOSE: (174) is inconsistent.
% 136.14/20.16 | | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | | End of split
% 136.14/20.16 | | | | | | | | | |
% 136.14/20.16 | | | | | | | | | End of split
% 136.14/20.16 | | | | | | | | |
% 136.14/20.16 | | | | | | | | End of split
% 136.14/20.16 | | | | | | | |
% 136.14/20.16 | | | | | | | End of split
% 136.14/20.16 | | | | | | |
% 136.14/20.16 | | | | | | End of split
% 136.14/20.16 | | | | | |
% 136.14/20.16 | | | | | End of split
% 136.14/20.16 | | | | |
% 136.14/20.16 | | | | Case 2:
% 136.14/20.16 | | | | |
% 136.14/20.16 | | | | | (175) all_57_10 = e2 & op(e2, e0) = e2
% 136.14/20.16 | | | | |
% 136.14/20.16 | | | | | ALPHA: (175) implies:
% 136.14/20.16 | | | | | (176) all_57_10 = e2
% 136.14/20.16 | | | | |
% 136.14/20.16 | | | | | REF_CLOSE: (1), (8), (9), (10), (12), (13), (15), (16), (17), (18),
% 136.14/20.16 | | | | | (19), (22), (23), (25), (30), (31), (33), (39), (40), (42),
% 136.14/20.16 | | | | | (44), (47), (48), (50), (54), (55), (56), (57), (59), (60),
% 136.14/20.16 | | | | | (62), (67), (176) are inconsistent by sub-proof #269.
% 136.14/20.16 | | | | |
% 136.14/20.16 | | | | End of split
% 136.14/20.16 | | | |
% 136.14/20.16 | | | End of split
% 136.14/20.16 | | |
% 136.14/20.16 | | End of split
% 136.14/20.16 | |
% 136.14/20.16 | Case 2:
% 136.14/20.16 | |
% 136.14/20.16 | | (177) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) =
% 136.14/20.16 | | e2)
% 136.14/20.16 | |
% 136.14/20.16 | | REF_CLOSE: (1), (4), (10), (17), (18), (19), (23), (33), (37), (45), (47),
% 136.14/20.16 | | (50), (54), (55), (61), (177) are inconsistent by sub-proof #268.
% 136.14/20.16 | |
% 136.14/20.16 | End of split
% 136.14/20.16 |
% 136.14/20.16 End of proof
% 136.14/20.16
% 136.14/20.16 Sub-proof #268 shows that the following formulas are inconsistent:
% 136.14/20.16 ----------------------------------------------------------------
% 136.14/20.16 (1) op(e1, e1) = all_6_2
% 136.14/20.16 (2) op(e2, e0) = all_52_13
% 136.14/20.16 (3) ~ (e2 = e0)
% 136.14/20.16 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.16 (5) ~ (e2 = e1)
% 136.14/20.16 (6) ~ (e3 = e0)
% 136.14/20.16 (7) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 136.14/20.16 (8) ~ (e3 = e2)
% 136.14/20.16 (9) ~ (all_6_2 = e2)
% 136.14/20.16 (10) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 136.14/20.16 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 136.14/20.16 (11) ~ (all_52_13 = e3)
% 136.14/20.16 (12) op(e0, e0) = e2
% 136.14/20.16 (13) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 136.14/20.16 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 136.14/20.16 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 136.14/20.16 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 136.14/20.16 (14) ~ (e3 = e1)
% 136.14/20.16 (15) ~ (e1 = e0)
% 136.14/20.16 (16) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 136.14/20.16 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 136.14/20.16
% 136.14/20.16 Begin of proof
% 136.14/20.16 |
% 136.14/20.16 | BETA: splitting (7) gives:
% 136.14/20.16 |
% 136.14/20.16 | Case 1:
% 136.14/20.16 | |
% 136.14/20.16 | | (17) all_57_8 = e2 & op(e1, e1) = e2
% 136.14/20.16 | |
% 136.14/20.16 | | ALPHA: (17) implies:
% 136.14/20.16 | | (18) op(e1, e1) = e2
% 136.14/20.16 | |
% 136.14/20.16 | | REF_CLOSE: (1), (4), (9), (18) are inconsistent by sub-proof #767.
% 136.14/20.16 | |
% 136.14/20.16 | Case 2:
% 136.14/20.16 | |
% 136.14/20.16 | | (19) all_57_11 = e2 & op(e1, e0) = e2
% 136.14/20.16 | |
% 136.14/20.16 | | ALPHA: (19) implies:
% 136.14/20.16 | | (20) all_57_11 = e2
% 136.14/20.16 | |
% 136.14/20.16 | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (10), (11), (12), (13), (14), (15),
% 136.14/20.16 | | (16), (20) are inconsistent by sub-proof #633.
% 136.14/20.16 | |
% 136.14/20.16 | End of split
% 136.14/20.16 |
% 136.14/20.16 End of proof
% 136.14/20.16
% 136.14/20.16 Sub-proof #269 shows that the following formulas are inconsistent:
% 136.14/20.16 ----------------------------------------------------------------
% 136.14/20.16 (1) op(e1, e1) = all_6_2
% 136.14/20.16 (2) op(e3, e3) = e2
% 136.14/20.16 (3) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 136.14/20.16 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 136.14/20.16 (4) ~ (e2 = e0)
% 136.14/20.16 (5) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 136.14/20.16 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 136.14/20.16 (6) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 136.14/20.16 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 136.14/20.16 (7) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 136.14/20.16 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 136.14/20.16 (8) ~ (all_52_7 = e3)
% 136.14/20.16 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.16 (10) ~ (e2 = e1)
% 136.14/20.16 (11) ~ (e3 = e0)
% 136.14/20.16 (12) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 136.14/20.16 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 136.14/20.16 e2)
% 136.14/20.16 (13) ~ (e3 = e2)
% 136.14/20.16 (14) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 136.14/20.16 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 136.14/20.16 (15) op(e0, e2) = all_52_7
% 136.14/20.16 (16) ~ (all_52_4 = e3)
% 136.14/20.16 (17) ~ (all_6_2 = e2)
% 136.14/20.16 (18) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 136.14/20.16 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 136.14/20.16 e1)
% 136.14/20.16 (19) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 136.14/20.16 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 136.14/20.16 (20) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 136.14/20.16 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 136.14/20.16 (21) op(e3, e2) = all_52_4
% 136.14/20.16 (22) op(e0, e0) = e2
% 136.14/20.16 (23) all_57_3 = e3
% 136.14/20.16 (24) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 136.14/20.16 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 136.14/20.16 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 136.14/20.16 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 136.14/20.16 (25) ~ (e3 = e1)
% 136.14/20.16 (26) ~ (e1 = e0)
% 136.14/20.16 (27) all_57_7 = e2
% 136.14/20.16 (28) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 136.14/20.16 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 136.14/20.16 (29) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 136.14/20.16 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 136.14/20.16 (30) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 136.14/20.16 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 136.14/20.16 (31) all_57_10 = e2
% 136.14/20.16 (32) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 136.14/20.16 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 136.14/20.16 (33) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 136.14/20.16 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 136.14/20.16
% 136.14/20.16 Begin of proof
% 136.14/20.16 |
% 136.14/20.16 | BETA: splitting (12) gives:
% 136.14/20.16 |
% 136.14/20.16 | Case 1:
% 136.14/20.16 | |
% 136.14/20.16 | | (34) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 136.14/20.16 | | e2)
% 136.14/20.16 | |
% 136.14/20.16 | | REF_CLOSE: (2), (3), (4), (7), (9), (10), (11), (13), (14), (19), (20),
% 136.14/20.16 | | (23), (25), (26), (27), (34) are inconsistent by sub-proof #286.
% 136.14/20.16 | |
% 136.14/20.16 | Case 2:
% 136.14/20.16 | |
% 136.14/20.16 | | (35) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 136.14/20.16 | | e2)
% 136.14/20.16 | |
% 136.14/20.16 | | BETA: splitting (35) gives:
% 136.14/20.16 | |
% 136.14/20.16 | | Case 1:
% 136.14/20.16 | | |
% 136.14/20.16 | | | (36) all_57_14 = e2 & op(e0, e1) = e2
% 136.14/20.16 | | |
% 136.14/20.16 | | | REF_CLOSE: (4), (6), (8), (9), (10), (11), (13), (15), (18), (22), (24),
% 136.14/20.16 | | | (25), (26), (36) are inconsistent by sub-proof #283.
% 136.14/20.16 | | |
% 136.14/20.16 | | Case 2:
% 136.14/20.16 | | |
% 136.14/20.16 | | | (37) all_57_15 = e2 & op(e0, e0) = e2
% 136.14/20.16 | | |
% 136.14/20.16 | | | ALPHA: (37) implies:
% 136.14/20.16 | | | (38) all_57_15 = e2
% 136.14/20.16 | | |
% 136.14/20.16 | | | BETA: splitting (33) gives:
% 136.14/20.16 | | |
% 136.14/20.16 | | | Case 1:
% 136.14/20.16 | | | |
% 136.14/20.16 | | | | (39) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1)
% 136.14/20.16 | | | | = e2)
% 136.14/20.16 | | | |
% 136.14/20.16 | | | | BETA: splitting (39) gives:
% 136.14/20.16 | | | |
% 136.14/20.16 | | | | Case 1:
% 136.14/20.16 | | | | |
% 136.14/20.16 | | | | | (40) all_57_4 = e2 & op(e3, e1) = e2
% 136.14/20.16 | | | | |
% 136.14/20.16 | | | | | ALPHA: (40) implies:
% 136.14/20.16 | | | | | (41) all_57_4 = e2
% 136.14/20.16 | | | | |
% 136.14/20.16 | | | | | REF_CLOSE: (2), (4), (5), (9), (10), (11), (13), (16), (21), (25),
% 136.14/20.16 | | | | | (26), (30), (32), (41) are inconsistent by sub-proof #278.
% 136.14/20.16 | | | | |
% 136.14/20.16 | | | | Case 2:
% 136.14/20.16 | | | | |
% 136.14/20.16 | | | | | (42) all_57_5 = e2 & op(e2, e1) = e2
% 136.14/20.16 | | | | |
% 136.14/20.16 | | | | | ALPHA: (42) implies:
% 136.14/20.16 | | | | | (43) all_57_5 = e2
% 136.14/20.16 | | | | |
% 136.14/20.16 | | | | | BETA: splitting (28) gives:
% 136.14/20.16 | | | | |
% 136.14/20.16 | | | | | Case 1:
% 136.14/20.16 | | | | | |
% 136.14/20.16 | | | | | | (44) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2,
% 136.14/20.16 | | | | | | e2) = e1)
% 136.14/20.16 | | | | | |
% 136.14/20.16 | | | | | | BETA: splitting (44) gives:
% 136.14/20.16 | | | | | |
% 136.14/20.16 | | | | | | Case 1:
% 136.14/20.16 | | | | | | |
% 136.14/20.16 | | | | | | | (45) all_57_2 = e1 & op(e2, e3) = e1
% 136.14/20.16 | | | | | | |
% 136.14/20.16 | | | | | | | ALPHA: (45) implies:
% 136.14/20.16 | | | | | | | (46) all_57_2 = e1
% 136.14/20.16 | | | | | | |
% 136.14/20.16 | | | | | | | REF_CLOSE: (4), (11), (23), (26), (29), (31), (43), (46) are
% 136.14/20.16 | | | | | | | inconsistent by sub-proof #271.
% 136.14/20.16 | | | | | | |
% 136.14/20.16 | | | | | | Case 2:
% 136.14/20.16 | | | | | | |
% 136.14/20.17 | | | | | | | (47) all_57_3 = e1 & op(e2, e2) = e1
% 136.14/20.17 | | | | | | |
% 136.14/20.17 | | | | | | | REF_CLOSE: (23), (25), (47) are inconsistent by sub-proof #370.
% 136.14/20.17 | | | | | | |
% 136.14/20.17 | | | | | | End of split
% 136.14/20.17 | | | | | |
% 136.14/20.17 | | | | | Case 2:
% 136.14/20.17 | | | | | |
% 136.14/20.17 | | | | | | (48) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2,
% 136.14/20.17 | | | | | | e0) = e1)
% 136.14/20.17 | | | | | |
% 136.14/20.17 | | | | | | BETA: splitting (48) gives:
% 136.14/20.17 | | | | | |
% 136.14/20.17 | | | | | | Case 1:
% 136.14/20.17 | | | | | | |
% 136.14/20.17 | | | | | | | (49) all_57_5 = e1 & op(e2, e1) = e1
% 136.14/20.17 | | | | | | |
% 136.14/20.17 | | | | | | | REF_CLOSE: (10), (43), (49) are inconsistent by sub-proof #500.
% 136.14/20.17 | | | | | | |
% 136.14/20.17 | | | | | | Case 2:
% 136.14/20.17 | | | | | | |
% 136.14/20.17 | | | | | | | (50) all_57_10 = e1 & op(e2, e0) = e1
% 136.14/20.17 | | | | | | |
% 136.14/20.17 | | | | | | | REF_CLOSE: (10), (31), (50) are inconsistent by sub-proof #270.
% 136.14/20.17 | | | | | | |
% 136.14/20.17 | | | | | | End of split
% 136.14/20.17 | | | | | |
% 136.14/20.17 | | | | | End of split
% 136.14/20.17 | | | | |
% 136.14/20.17 | | | | End of split
% 136.14/20.17 | | | |
% 136.14/20.17 | | | Case 2:
% 136.14/20.17 | | | |
% 136.14/20.17 | | | | (51) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1)
% 136.14/20.17 | | | | = e2)
% 136.14/20.17 | | | |
% 136.14/20.17 | | | | REF_CLOSE: (1), (4), (6), (8), (9), (10), (11), (13), (15), (17), (18),
% 136.14/20.17 | | | | (24), (25), (26), (38), (51) are inconsistent by sub-proof
% 136.14/20.17 | | | | #276.
% 136.14/20.17 | | | |
% 136.14/20.17 | | | End of split
% 136.14/20.17 | | |
% 136.14/20.17 | | End of split
% 136.14/20.17 | |
% 136.14/20.17 | End of split
% 136.14/20.17 |
% 136.14/20.17 End of proof
% 136.14/20.17
% 136.14/20.17 Sub-proof #270 shows that the following formulas are inconsistent:
% 136.14/20.17 ----------------------------------------------------------------
% 136.14/20.17 (1) all_57_10 = e1 & op(e2, e0) = e1
% 136.14/20.17 (2) all_57_10 = e2
% 136.14/20.17 (3) ~ (e2 = e1)
% 136.14/20.17
% 136.14/20.17 Begin of proof
% 136.14/20.17 |
% 136.14/20.17 | ALPHA: (1) implies:
% 136.14/20.17 | (4) all_57_10 = e1
% 136.14/20.17 |
% 136.14/20.17 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.17 | (5) e2 = e1
% 136.14/20.17 |
% 136.14/20.17 | REDUCE: (3), (5) imply:
% 136.14/20.17 | (6) $false
% 136.14/20.17 |
% 136.14/20.17 | CLOSE: (6) is inconsistent.
% 136.14/20.17 |
% 136.14/20.17 End of proof
% 136.14/20.17
% 136.14/20.17 Sub-proof #271 shows that the following formulas are inconsistent:
% 136.14/20.17 ----------------------------------------------------------------
% 136.14/20.17 (1) all_57_2 = e1
% 136.14/20.17 (2) ~ (e2 = e0)
% 136.14/20.17 (3) all_57_5 = e2
% 136.14/20.17 (4) ~ (e3 = e0)
% 136.14/20.17 (5) all_57_3 = e3
% 136.14/20.17 (6) ~ (e1 = e0)
% 136.14/20.17 (7) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 136.14/20.17 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 136.14/20.17 (8) all_57_10 = e2
% 136.14/20.17
% 136.14/20.17 Begin of proof
% 136.14/20.17 |
% 136.14/20.17 | BETA: splitting (7) gives:
% 136.14/20.17 |
% 136.14/20.17 | Case 1:
% 136.14/20.17 | |
% 136.14/20.17 | | (9) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 136.14/20.17 | |
% 136.14/20.17 | | BETA: splitting (9) gives:
% 136.14/20.17 | |
% 136.14/20.17 | | Case 1:
% 136.14/20.17 | | |
% 136.14/20.17 | | | (10) all_57_2 = e0 & op(e2, e3) = e0
% 136.14/20.17 | | |
% 136.14/20.17 | | | REF_CLOSE: (1), (6), (10) are inconsistent by sub-proof #272.
% 136.14/20.17 | | |
% 136.14/20.17 | | Case 2:
% 136.14/20.17 | | |
% 136.14/20.17 | | | (11) all_57_3 = e0 & op(e2, e2) = e0
% 136.14/20.17 | | |
% 136.14/20.17 | | | REF_CLOSE: (4), (5), (11) are inconsistent by sub-proof #302.
% 136.14/20.17 | | |
% 136.14/20.17 | | End of split
% 136.14/20.17 | |
% 136.14/20.17 | Case 2:
% 136.14/20.17 | |
% 136.14/20.17 | | (12) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 136.14/20.17 | | e0)
% 136.14/20.17 | |
% 136.14/20.17 | | BETA: splitting (12) gives:
% 136.14/20.17 | |
% 136.14/20.17 | | Case 1:
% 136.14/20.17 | | |
% 136.14/20.17 | | | (13) all_57_5 = e0 & op(e2, e1) = e0
% 136.14/20.17 | | |
% 136.14/20.17 | | | REF_CLOSE: (2), (3), (13) are inconsistent by sub-proof #277.
% 136.14/20.17 | | |
% 136.14/20.17 | | Case 2:
% 136.14/20.17 | | |
% 136.14/20.17 | | | (14) all_57_10 = e0 & op(e2, e0) = e0
% 136.14/20.17 | | |
% 136.14/20.17 | | | REF_CLOSE: (2), (8), (14) are inconsistent by sub-proof #363.
% 136.14/20.17 | | |
% 136.14/20.17 | | End of split
% 136.14/20.17 | |
% 136.14/20.17 | End of split
% 136.14/20.17 |
% 136.14/20.17 End of proof
% 136.14/20.17
% 136.14/20.17 Sub-proof #272 shows that the following formulas are inconsistent:
% 136.14/20.17 ----------------------------------------------------------------
% 136.14/20.17 (1) all_57_2 = e0 & op(e2, e3) = e0
% 136.14/20.17 (2) all_57_2 = e1
% 136.14/20.17 (3) ~ (e1 = e0)
% 136.14/20.17
% 136.14/20.17 Begin of proof
% 136.14/20.17 |
% 136.14/20.17 | ALPHA: (1) implies:
% 136.14/20.17 | (4) all_57_2 = e0
% 136.14/20.17 |
% 136.14/20.17 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.17 | (5) e1 = e0
% 136.14/20.17 |
% 136.14/20.17 | REDUCE: (3), (5) imply:
% 136.14/20.17 | (6) $false
% 136.14/20.17 |
% 136.14/20.17 | CLOSE: (6) is inconsistent.
% 136.14/20.17 |
% 136.14/20.17 End of proof
% 136.14/20.17
% 136.14/20.17 Sub-proof #273 shows that the following formulas are inconsistent:
% 136.14/20.17 ----------------------------------------------------------------
% 136.14/20.17 (1) op(e1, e1) = all_6_2
% 136.14/20.17 (2) ~ (all_40_2 = e0) | ( ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 &
% 136.14/20.17 $i(all_40_0)) | ( ~ (all_40_1 = e2) & op(e0, e0) = all_40_1 &
% 136.14/20.17 $i(all_40_1))
% 136.14/20.17 (3) ~ (all_52_11 = e2)
% 136.14/20.17 (4) all_40_2 = all_6_2
% 136.14/20.17 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.17 (6) ~ (e2 = e1)
% 136.14/20.17 (7) ~ (e3 = e2)
% 136.14/20.17 (8) ~ (all_52_11 = all_6_2)
% 136.14/20.17 (9) op(e0, e1) = all_52_11
% 136.14/20.17 (10) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 136.14/20.17 (11) op(e2, e0) = e0
% 136.14/20.17 (12) op(e0, e0) = e2
% 136.14/20.17 (13) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.14/20.17 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.14/20.17 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0)
% 136.14/20.17 = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 136.14/20.17 $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~
% 136.14/20.17 (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 136.14/20.17 (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 136.14/20.17 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.14/20.17 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.14/20.17 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.14/20.17 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 136.14/20.17 op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.14/20.17 op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 136.14/20.17 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13
% 136.14/20.17 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 136.14/20.17 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1,
% 136.14/20.17 e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 136.14/20.17 $i(all_56_21) & $i(all_56_29))
% 136.14/20.17 (14) all_54_14 = all_52_11
% 136.14/20.17 (15) op(e0, e0) = all_56_31
% 136.14/20.17
% 136.14/20.17 Begin of proof
% 136.14/20.17 |
% 136.14/20.17 | GROUND_INST: instantiating (5) with e2, all_56_31, e0, e0, simplifying with
% 136.14/20.17 | (12), (15) gives:
% 136.14/20.17 | (16) all_56_31 = e2
% 136.14/20.17 |
% 136.14/20.17 | BETA: splitting (13) gives:
% 136.14/20.17 |
% 136.14/20.17 | Case 1:
% 136.14/20.17 | |
% 136.14/20.17 | | (17) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 136.14/20.17 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.14/20.17 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.14/20.17 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9)
% 136.14/20.17 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 136.14/20.17 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 136.14/20.17 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 136.14/20.17 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 136.14/20.17 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 136.14/20.17 | | $i(all_56_27))
% 136.14/20.17 | |
% 136.14/20.17 | | BETA: splitting (17) gives:
% 136.14/20.17 | |
% 136.14/20.17 | | Case 1:
% 136.14/20.17 | | |
% 136.14/20.17 | | | (18) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 136.14/20.17 | | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.14/20.17 | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.14/20.17 | | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9)
% 136.14/20.17 | | | & $i(all_56_17) & $i(all_56_25)
% 136.14/20.17 | | |
% 136.14/20.17 | | | ALPHA: (18) implies:
% 136.14/20.17 | | | (19) all_56_31 = e3
% 136.14/20.17 | | |
% 136.14/20.17 | | | REF_CLOSE: (7), (16), (19) are inconsistent by sub-proof #532.
% 136.14/20.17 | | |
% 136.14/20.17 | | Case 2:
% 136.14/20.17 | | |
% 136.14/20.17 | | | (20) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 136.14/20.17 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.14/20.17 | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.14/20.17 | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.14/20.17 | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)
% 136.14/20.17 | | |
% 136.14/20.17 | | | ALPHA: (20) implies:
% 136.14/20.17 | | | (21) ~ (all_56_27 = e0)
% 136.14/20.17 | | | (22) op(e2, e0) = all_56_27
% 136.14/20.17 | | |
% 136.14/20.17 | | | GROUND_INST: instantiating (5) with e0, all_56_27, e0, e2, simplifying
% 136.14/20.17 | | | with (11), (22) gives:
% 136.14/20.17 | | | (23) all_56_27 = e0
% 136.14/20.17 | | |
% 136.14/20.17 | | | REDUCE: (21), (23) imply:
% 136.14/20.17 | | | (24) $false
% 136.14/20.17 | | |
% 136.14/20.17 | | | CLOSE: (24) is inconsistent.
% 136.14/20.17 | | |
% 136.14/20.17 | | End of split
% 136.14/20.17 | |
% 136.14/20.17 | Case 2:
% 136.14/20.17 | |
% 136.14/20.17 | | (25) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.14/20.17 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.14/20.17 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 136.14/20.17 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 136.14/20.17 | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 136.14/20.17 | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 136.14/20.17 | | ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 136.14/20.17 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 136.14/20.17 | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.14/20.17 | | $i(all_56_29))
% 136.14/20.17 | |
% 136.14/20.17 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (12), (14), (16),
% 136.14/20.17 | | (25) are inconsistent by sub-proof #524.
% 136.14/20.17 | |
% 136.14/20.17 | End of split
% 136.14/20.17 |
% 136.14/20.17 End of proof
% 136.14/20.17
% 136.14/20.17 Sub-proof #274 shows that the following formulas are inconsistent:
% 136.14/20.17 ----------------------------------------------------------------
% 136.14/20.17 (1) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2)
% 136.14/20.17 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3,
% 136.14/20.17 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 136.14/20.17 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 136.14/20.17 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 136.14/20.17 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.14/20.17 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) =
% 136.14/20.17 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.14/20.17 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 136.14/20.17 $i(all_56_21) & $i(all_56_29))
% 136.14/20.17 (2) op(e3, e3) = e2
% 136.14/20.17 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.17 (4) ~ (e2 = e1)
% 136.14/20.17 (5) op(e2, e0) = e0
% 136.14/20.17
% 136.14/20.17 Begin of proof
% 136.14/20.17 |
% 136.14/20.17 | BETA: splitting (1) gives:
% 136.14/20.17 |
% 136.14/20.17 | Case 1:
% 136.14/20.17 | |
% 136.14/20.17 | | (6) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 136.14/20.17 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 136.14/20.17 | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 136.14/20.17 | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 136.14/20.17 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)
% 136.14/20.17 | |
% 136.14/20.17 | | ALPHA: (6) implies:
% 136.14/20.17 | | (7) ~ (all_56_27 = e0)
% 136.14/20.17 | | (8) op(e2, e0) = all_56_27
% 136.14/20.17 | |
% 136.14/20.17 | | REF_CLOSE: (3), (5), (7), (8) are inconsistent by sub-proof #275.
% 136.14/20.17 | |
% 136.14/20.17 | Case 2:
% 136.14/20.17 | |
% 136.14/20.17 | | (9) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 136.14/20.17 | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 136.14/20.17 | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 136.14/20.17 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 136.14/20.17 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 136.14/20.17 | |
% 136.14/20.17 | | ALPHA: (9) implies:
% 136.14/20.17 | | (10) op(e3, e3) = e1
% 136.14/20.17 | |
% 136.14/20.17 | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #743.
% 136.14/20.17 | |
% 136.14/20.17 | End of split
% 136.14/20.17 |
% 136.14/20.17 End of proof
% 136.14/20.17
% 136.14/20.17 Sub-proof #275 shows that the following formulas are inconsistent:
% 136.14/20.17 ----------------------------------------------------------------
% 136.14/20.17 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.17 (2) op(e2, e0) = all_56_27
% 136.14/20.17 (3) op(e2, e0) = e0
% 136.14/20.17 (4) ~ (all_56_27 = e0)
% 136.14/20.17
% 136.14/20.17 Begin of proof
% 136.14/20.17 |
% 136.14/20.17 | GROUND_INST: instantiating (1) with e0, all_56_27, e0, e2, simplifying with
% 136.14/20.17 | (2), (3) gives:
% 136.14/20.17 | (5) all_56_27 = e0
% 136.14/20.17 |
% 136.14/20.17 | REDUCE: (4), (5) imply:
% 136.14/20.17 | (6) $false
% 136.14/20.17 |
% 136.14/20.17 | CLOSE: (6) is inconsistent.
% 136.14/20.17 |
% 136.14/20.17 End of proof
% 136.14/20.17
% 136.14/20.17 Sub-proof #276 shows that the following formulas are inconsistent:
% 136.14/20.17 ----------------------------------------------------------------
% 136.14/20.17 (1) op(e1, e1) = all_6_2
% 136.14/20.17 (2) ~ (e2 = e0)
% 136.14/20.17 (3) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 136.14/20.17 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 136.14/20.17 (4) ~ (all_52_7 = e3)
% 136.14/20.17 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.17 (6) ~ (e2 = e1)
% 136.14/20.17 (7) ~ (e3 = e0)
% 136.14/20.17 (8) ~ (e3 = e2)
% 136.14/20.17 (9) op(e0, e2) = all_52_7
% 136.14/20.17 (10) ~ (all_6_2 = e2)
% 136.14/20.17 (11) all_57_15 = e2
% 136.14/20.17 (12) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 136.14/20.17 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 136.14/20.17 e1)
% 136.14/20.17 (13) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 136.14/20.17 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 136.14/20.17 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 136.14/20.17 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 136.14/20.17 (14) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 136.14/20.17 (15) ~ (e3 = e1)
% 136.14/20.17 (16) ~ (e1 = e0)
% 136.14/20.17
% 136.14/20.17 Begin of proof
% 136.14/20.17 |
% 136.14/20.17 | BETA: splitting (14) gives:
% 136.14/20.17 |
% 136.14/20.17 | Case 1:
% 136.14/20.17 | |
% 136.14/20.17 | | (17) all_57_8 = e2 & op(e1, e1) = e2
% 136.14/20.17 | |
% 136.14/20.17 | | ALPHA: (17) implies:
% 136.14/20.17 | | (18) op(e1, e1) = e2
% 136.14/20.17 | |
% 136.14/20.17 | | REF_CLOSE: (1), (5), (10), (18) are inconsistent by sub-proof #767.
% 136.14/20.17 | |
% 136.14/20.17 | Case 2:
% 136.14/20.17 | |
% 136.14/20.17 | | (19) all_57_14 = e2 & op(e0, e1) = e2
% 136.14/20.17 | |
% 136.14/20.17 | | ALPHA: (19) implies:
% 136.14/20.17 | | (20) all_57_14 = e2
% 136.14/20.17 | |
% 136.14/20.17 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), (15),
% 136.14/20.17 | | (16), (20) are inconsistent by sub-proof #433.
% 136.14/20.17 | |
% 136.14/20.17 | End of split
% 136.14/20.17 |
% 136.14/20.17 End of proof
% 136.14/20.17
% 136.14/20.17 Sub-proof #277 shows that the following formulas are inconsistent:
% 136.14/20.17 ----------------------------------------------------------------
% 136.14/20.17 (1) all_57_5 = e0 & op(e2, e1) = e0
% 136.14/20.17 (2) all_57_5 = e2
% 136.14/20.17 (3) ~ (e2 = e0)
% 136.14/20.17
% 136.14/20.17 Begin of proof
% 136.14/20.17 |
% 136.14/20.17 | ALPHA: (1) implies:
% 136.14/20.17 | (4) all_57_5 = e0
% 136.14/20.17 |
% 136.14/20.17 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.17 | (5) e2 = e0
% 136.14/20.17 |
% 136.14/20.17 | REDUCE: (3), (5) imply:
% 136.14/20.17 | (6) $false
% 136.14/20.17 |
% 136.14/20.17 | CLOSE: (6) is inconsistent.
% 136.14/20.17 |
% 136.14/20.17 End of proof
% 136.14/20.17
% 136.14/20.17 Sub-proof #278 shows that the following formulas are inconsistent:
% 136.14/20.17 ----------------------------------------------------------------
% 136.14/20.17 (1) op(e3, e3) = e2
% 136.14/20.17 (2) ~ (e2 = e0)
% 136.14/20.17 (3) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 136.14/20.17 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 136.14/20.17 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.17 (5) ~ (e2 = e1)
% 136.14/20.17 (6) ~ (e3 = e0)
% 136.14/20.17 (7) ~ (e3 = e2)
% 136.14/20.17 (8) ~ (all_52_4 = e3)
% 136.14/20.17 (9) all_57_4 = e2
% 136.14/20.17 (10) op(e3, e2) = all_52_4
% 136.14/20.17 (11) ~ (e3 = e1)
% 136.14/20.17 (12) ~ (e1 = e0)
% 136.14/20.17 (13) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 136.14/20.17 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 136.14/20.17 (14) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 136.14/20.17 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 136.14/20.17
% 136.14/20.17 Begin of proof
% 136.14/20.17 |
% 136.14/20.17 | BETA: splitting (13) gives:
% 136.14/20.17 |
% 136.14/20.17 | Case 1:
% 136.14/20.17 | |
% 136.14/20.17 | | (15) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 136.14/20.17 | | e3)
% 136.14/20.17 | |
% 136.14/20.17 | | REF_CLOSE: (1), (4), (7), (8), (10), (15) are inconsistent by sub-proof
% 136.14/20.17 | | #282.
% 136.14/20.17 | |
% 136.14/20.17 | Case 2:
% 136.14/20.17 | |
% 136.14/20.17 | | (16) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 136.14/20.17 | | e3)
% 136.14/20.17 | |
% 136.14/20.17 | | BETA: splitting (16) gives:
% 136.14/20.17 | |
% 136.14/20.17 | | Case 1:
% 136.14/20.17 | | |
% 136.14/20.17 | | | (17) all_57_4 = e3 & op(e3, e1) = e3
% 136.14/20.17 | | |
% 136.14/20.17 | | | REF_CLOSE: (7), (9), (17) are inconsistent by sub-proof #734.
% 136.14/20.17 | | |
% 136.14/20.17 | | Case 2:
% 136.14/20.17 | | |
% 136.14/20.17 | | | (18) all_57_9 = e3 & op(e3, e0) = e3
% 136.14/20.17 | | |
% 136.14/20.17 | | | ALPHA: (18) implies:
% 136.14/20.17 | | | (19) all_57_9 = e3
% 136.14/20.17 | | |
% 136.14/20.17 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (11), (12), (14), (19) are
% 136.14/20.17 | | | inconsistent by sub-proof #279.
% 136.14/20.17 | | |
% 136.14/20.17 | | End of split
% 136.14/20.17 | |
% 136.14/20.17 | End of split
% 136.14/20.17 |
% 136.14/20.17 End of proof
% 136.14/20.17
% 136.14/20.17 Sub-proof #279 shows that the following formulas are inconsistent:
% 136.14/20.17 ----------------------------------------------------------------
% 136.14/20.17 (1) op(e3, e3) = e2
% 136.14/20.17 (2) ~ (e2 = e0)
% 136.14/20.17 (3) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 136.14/20.17 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 136.14/20.17 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.17 (5) ~ (e2 = e1)
% 136.14/20.17 (6) ~ (e3 = e0)
% 136.14/20.17 (7) all_57_9 = e3
% 136.14/20.17 (8) all_57_4 = e2
% 136.14/20.17 (9) ~ (e3 = e1)
% 136.14/20.17 (10) ~ (e1 = e0)
% 136.14/20.17 (11) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 136.14/20.17 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 136.14/20.17
% 136.14/20.17 Begin of proof
% 136.14/20.17 |
% 136.14/20.17 | BETA: splitting (3) gives:
% 136.14/20.17 |
% 136.14/20.17 | Case 1:
% 136.14/20.17 | |
% 136.14/20.17 | | (12) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 136.14/20.17 | | e0)
% 136.14/20.17 | |
% 136.14/20.17 | | BETA: splitting (12) gives:
% 136.14/20.17 | |
% 136.14/20.17 | | Case 1:
% 136.14/20.17 | | |
% 136.14/20.17 | | | (13) all_57_0 = e0 & op(e3, e3) = e0
% 136.14/20.17 | | |
% 136.14/20.17 | | | ALPHA: (13) implies:
% 136.14/20.17 | | | (14) op(e3, e3) = e0
% 136.14/20.17 | | |
% 136.14/20.17 | | | REF_CLOSE: (1), (2), (4), (14) are inconsistent by sub-proof #495.
% 136.14/20.17 | | |
% 136.14/20.17 | | Case 2:
% 136.14/20.17 | | |
% 136.14/20.17 | | | (15) all_57_1 = e0 & op(e3, e2) = e0
% 136.14/20.17 | | |
% 136.14/20.17 | | | ALPHA: (15) implies:
% 136.14/20.17 | | | (16) all_57_1 = e0
% 136.14/20.17 | | |
% 136.14/20.17 | | | REF_CLOSE: (1), (4), (5), (7), (8), (9), (10), (11), (16) are inconsistent
% 136.14/20.17 | | | by sub-proof #280.
% 136.14/20.17 | | |
% 136.14/20.17 | | End of split
% 136.14/20.17 | |
% 136.14/20.17 | Case 2:
% 136.14/20.17 | |
% 136.14/20.17 | | (17) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 136.14/20.17 | | e0)
% 136.14/20.17 | |
% 136.14/20.17 | | BETA: splitting (17) gives:
% 136.14/20.17 | |
% 136.14/20.17 | | Case 1:
% 136.14/20.17 | | |
% 136.14/20.17 | | | (18) all_57_4 = e0 & op(e3, e1) = e0
% 136.14/20.17 | | |
% 136.14/20.17 | | | REF_CLOSE: (2), (8), (18) are inconsistent by sub-proof #647.
% 136.14/20.17 | | |
% 136.14/20.17 | | Case 2:
% 136.14/20.17 | | |
% 136.14/20.17 | | | (19) all_57_9 = e0 & op(e3, e0) = e0
% 136.14/20.17 | | |
% 136.14/20.17 | | | ALPHA: (19) implies:
% 136.14/20.17 | | | (20) all_57_9 = e0
% 136.14/20.17 | | |
% 136.14/20.17 | | | REF_CLOSE: (6), (7), (20) are inconsistent by sub-proof #670.
% 136.14/20.17 | | |
% 136.14/20.17 | | End of split
% 136.14/20.17 | |
% 136.14/20.17 | End of split
% 136.14/20.17 |
% 136.14/20.17 End of proof
% 136.14/20.17
% 136.14/20.17 Sub-proof #280 shows that the following formulas are inconsistent:
% 136.14/20.17 ----------------------------------------------------------------
% 136.14/20.17 (1) op(e3, e3) = e2
% 136.14/20.17 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.17 (3) ~ (e2 = e1)
% 136.14/20.17 (4) all_57_9 = e3
% 136.14/20.17 (5) all_57_4 = e2
% 136.14/20.17 (6) all_57_1 = e0
% 136.14/20.17 (7) ~ (e3 = e1)
% 136.14/20.17 (8) ~ (e1 = e0)
% 136.14/20.17 (9) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 136.14/20.17 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 136.14/20.17
% 136.14/20.17 Begin of proof
% 136.14/20.17 |
% 136.14/20.17 | BETA: splitting (9) gives:
% 136.14/20.17 |
% 136.14/20.17 | Case 1:
% 136.14/20.17 | |
% 136.14/20.17 | | (10) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 136.14/20.17 | | e1)
% 136.14/20.17 | |
% 136.14/20.17 | | REF_CLOSE: (1), (2), (3), (6), (8), (10) are inconsistent by sub-proof #281.
% 136.14/20.17 | |
% 136.14/20.17 | Case 2:
% 136.14/20.17 | |
% 136.14/20.17 | | (11) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 136.14/20.17 | | e1)
% 136.14/20.17 | |
% 136.14/20.17 | | BETA: splitting (11) gives:
% 136.14/20.17 | |
% 136.14/20.17 | | Case 1:
% 136.14/20.17 | | |
% 136.14/20.17 | | | (12) all_57_4 = e1 & op(e3, e1) = e1
% 136.14/20.17 | | |
% 136.14/20.17 | | | ALPHA: (12) implies:
% 136.14/20.17 | | | (13) all_57_4 = e1
% 136.14/20.17 | | |
% 136.14/20.17 | | | REF_CLOSE: (3), (5), (13) are inconsistent by sub-proof #669.
% 136.14/20.17 | | |
% 136.14/20.17 | | Case 2:
% 136.14/20.17 | | |
% 136.14/20.17 | | | (14) all_57_9 = e1 & op(e3, e0) = e1
% 136.14/20.17 | | |
% 136.14/20.17 | | | REF_CLOSE: (4), (7), (14) are inconsistent by sub-proof #640.
% 136.14/20.17 | | |
% 136.14/20.17 | | End of split
% 136.14/20.17 | |
% 136.14/20.17 | End of split
% 136.14/20.17 |
% 136.14/20.17 End of proof
% 136.14/20.17
% 136.14/20.17 Sub-proof #281 shows that the following formulas are inconsistent:
% 136.14/20.17 ----------------------------------------------------------------
% 136.14/20.17 (1) op(e3, e3) = e2
% 136.14/20.17 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.17 (3) ~ (e2 = e1)
% 136.14/20.17 (4) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1)
% 136.14/20.17 (5) all_57_1 = e0
% 136.14/20.17 (6) ~ (e1 = e0)
% 136.14/20.17
% 136.14/20.17 Begin of proof
% 136.14/20.17 |
% 136.14/20.17 | BETA: splitting (4) gives:
% 136.14/20.17 |
% 136.14/20.17 | Case 1:
% 136.14/20.17 | |
% 136.14/20.17 | | (7) all_57_0 = e1 & op(e3, e3) = e1
% 136.14/20.17 | |
% 136.14/20.17 | | ALPHA: (7) implies:
% 136.14/20.17 | | (8) op(e3, e3) = e1
% 136.14/20.17 | |
% 136.14/20.17 | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #743.
% 136.14/20.17 | |
% 136.14/20.17 | Case 2:
% 136.14/20.17 | |
% 136.14/20.17 | | (9) all_57_1 = e1 & op(e3, e2) = e1
% 136.14/20.17 | |
% 136.14/20.17 | | REF_CLOSE: (5), (6), (9) are inconsistent by sub-proof #289.
% 136.14/20.17 | |
% 136.14/20.17 | End of split
% 136.14/20.17 |
% 136.14/20.17 End of proof
% 136.14/20.17
% 136.14/20.17 Sub-proof #282 shows that the following formulas are inconsistent:
% 136.14/20.17 ----------------------------------------------------------------
% 136.14/20.17 (1) op(e3, e3) = e2
% 136.14/20.17 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.17 (3) ~ (e3 = e2)
% 136.14/20.17 (4) ~ (all_52_4 = e3)
% 136.14/20.17 (5) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3)
% 136.14/20.17 (6) op(e3, e2) = all_52_4
% 136.14/20.17
% 136.14/20.17 Begin of proof
% 136.14/20.17 |
% 136.14/20.17 | BETA: splitting (5) gives:
% 136.14/20.17 |
% 136.14/20.17 | Case 1:
% 136.14/20.17 | |
% 136.14/20.17 | | (7) all_57_0 = e3 & op(e3, e3) = e3
% 136.14/20.17 | |
% 136.14/20.17 | | ALPHA: (7) implies:
% 136.14/20.17 | | (8) op(e3, e3) = e3
% 136.14/20.17 | |
% 136.14/20.17 | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #778.
% 136.14/20.17 | |
% 136.14/20.17 | Case 2:
% 136.14/20.17 | |
% 136.14/20.17 | | (9) all_57_1 = e3 & op(e3, e2) = e3
% 136.14/20.17 | |
% 136.14/20.17 | | ALPHA: (9) implies:
% 136.14/20.17 | | (10) op(e3, e2) = e3
% 136.14/20.17 | |
% 136.14/20.17 | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #738.
% 136.14/20.17 | |
% 136.14/20.17 | End of split
% 136.14/20.17 |
% 136.14/20.17 End of proof
% 136.14/20.17
% 136.14/20.17 Sub-proof #283 shows that the following formulas are inconsistent:
% 136.14/20.17 ----------------------------------------------------------------
% 136.14/20.17 (1) all_57_14 = e2 & op(e0, e1) = e2
% 136.14/20.17 (2) ~ (e2 = e0)
% 136.14/20.17 (3) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 136.14/20.17 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 136.14/20.17 (4) ~ (all_52_7 = e3)
% 136.14/20.17 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.17 (6) ~ (e2 = e1)
% 136.14/20.17 (7) ~ (e3 = e0)
% 136.14/20.17 (8) ~ (e3 = e2)
% 136.14/20.17 (9) op(e0, e2) = all_52_7
% 136.14/20.17 (10) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 136.14/20.17 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 136.14/20.17 e1)
% 136.14/20.17 (11) op(e0, e0) = e2
% 136.14/20.17 (12) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 136.14/20.17 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 136.14/20.17 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 136.14/20.17 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 136.14/20.17 (13) ~ (e3 = e1)
% 136.14/20.17 (14) ~ (e1 = e0)
% 136.14/20.17
% 136.14/20.17 Begin of proof
% 136.14/20.17 |
% 136.14/20.17 | ALPHA: (1) implies:
% 136.14/20.17 | (15) all_57_14 = e2
% 136.14/20.17 |
% 136.14/20.17 | BETA: splitting (3) gives:
% 136.14/20.17 |
% 136.14/20.17 | Case 1:
% 136.14/20.17 | |
% 136.14/20.17 | | (16) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 136.14/20.17 | | e3)
% 136.14/20.17 | |
% 136.14/20.17 | | BETA: splitting (16) gives:
% 136.14/20.17 | |
% 136.14/20.17 | | Case 1:
% 136.14/20.17 | | |
% 136.14/20.17 | | | (17) all_57_12 = e3 & op(e0, e3) = e3
% 136.14/20.17 | | |
% 136.14/20.17 | | | ALPHA: (17) implies:
% 136.14/20.17 | | | (18) all_57_12 = e3
% 136.14/20.17 | | |
% 136.14/20.17 | | | BETA: splitting (12) gives:
% 136.14/20.17 | | |
% 136.14/20.17 | | | Case 1:
% 136.14/20.17 | | | |
% 136.14/20.17 | | | | (19) all_57_15 = e0 & op(e0, e0) = e0
% 136.14/20.17 | | | |
% 136.14/20.17 | | | | ALPHA: (19) implies:
% 136.14/20.17 | | | | (20) op(e0, e0) = e0
% 136.14/20.17 | | | |
% 136.14/20.17 | | | | REF_CLOSE: (2), (5), (11), (20) are inconsistent by sub-proof #714.
% 136.14/20.17 | | | |
% 136.14/20.17 | | | Case 2:
% 136.14/20.17 | | | |
% 136.14/20.17 | | | | (21) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 136.14/20.17 | | | | e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 136.14/20.17 | | | | ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 136.14/20.17 | | | | e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 136.14/20.17 | | | |
% 136.14/20.17 | | | | ALPHA: (21) implies:
% 136.14/20.17 | | | | (22) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 136.14/20.18 | | | | e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 136.14/20.18 | | | |
% 136.14/20.18 | | | | REF_CLOSE: (2), (5), (6), (7), (10), (11), (13), (14), (15), (18), (22)
% 136.14/20.18 | | | | are inconsistent by sub-proof #284.
% 136.14/20.18 | | | |
% 136.14/20.18 | | | End of split
% 136.14/20.18 | | |
% 136.14/20.18 | | Case 2:
% 136.14/20.18 | | |
% 136.14/20.18 | | | (23) all_57_13 = e3 & op(e0, e2) = e3
% 136.14/20.18 | | |
% 136.14/20.18 | | | REF_CLOSE: (4), (5), (9), (23) are inconsistent by sub-proof #556.
% 136.14/20.18 | | |
% 136.14/20.18 | | End of split
% 136.14/20.18 | |
% 136.14/20.18 | Case 2:
% 136.14/20.18 | |
% 136.14/20.18 | | (24) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 136.14/20.18 | | e3)
% 136.14/20.18 | |
% 136.14/20.18 | | BETA: splitting (24) gives:
% 136.14/20.18 | |
% 136.14/20.18 | | Case 1:
% 136.14/20.18 | | |
% 136.14/20.18 | | | (25) all_57_14 = e3 & op(e0, e1) = e3
% 136.14/20.18 | | |
% 136.14/20.18 | | | ALPHA: (25) implies:
% 136.14/20.18 | | | (26) all_57_14 = e3
% 136.14/20.18 | | |
% 136.14/20.18 | | | REF_CLOSE: (8), (15), (26) are inconsistent by sub-proof #407.
% 136.14/20.18 | | |
% 136.14/20.18 | | Case 2:
% 136.14/20.18 | | |
% 136.14/20.18 | | | (27) all_57_15 = e3 & op(e0, e0) = e3
% 136.14/20.18 | | |
% 136.14/20.18 | | | ALPHA: (27) implies:
% 136.14/20.18 | | | (28) op(e0, e0) = e3
% 136.14/20.18 | | |
% 136.14/20.18 | | | REF_CLOSE: (5), (8), (11), (28) are inconsistent by sub-proof #634.
% 136.14/20.18 | | |
% 136.14/20.18 | | End of split
% 136.14/20.18 | |
% 136.14/20.18 | End of split
% 136.14/20.18 |
% 136.14/20.18 End of proof
% 136.14/20.18
% 136.14/20.18 Sub-proof #284 shows that the following formulas are inconsistent:
% 136.14/20.18 ----------------------------------------------------------------
% 136.14/20.18 (1) ~ (e2 = e0)
% 136.14/20.18 (2) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 136.14/20.18 (all_57_14 = e0 & op(e0, e1) = e0)
% 136.14/20.18 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.18 (4) ~ (e2 = e1)
% 136.14/20.18 (5) ~ (e3 = e0)
% 136.14/20.18 (6) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 136.14/20.18 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 136.14/20.18 (7) all_57_12 = e3
% 136.14/20.18 (8) all_57_14 = e2
% 136.14/20.18 (9) op(e0, e0) = e2
% 136.14/20.18 (10) ~ (e3 = e1)
% 136.14/20.18 (11) ~ (e1 = e0)
% 136.14/20.18
% 136.14/20.18 Begin of proof
% 136.14/20.18 |
% 136.14/20.18 | BETA: splitting (6) gives:
% 136.14/20.18 |
% 136.14/20.18 | Case 1:
% 136.14/20.18 | |
% 136.14/20.18 | | (12) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 136.14/20.18 | | e1)
% 136.14/20.18 | |
% 136.14/20.18 | | BETA: splitting (12) gives:
% 136.14/20.18 | |
% 136.14/20.18 | | Case 1:
% 136.14/20.18 | | |
% 136.14/20.18 | | | (13) all_57_12 = e1 & op(e0, e3) = e1
% 136.14/20.18 | | |
% 136.14/20.18 | | | ALPHA: (13) implies:
% 136.14/20.18 | | | (14) all_57_12 = e1
% 136.14/20.18 | | |
% 136.14/20.18 | | | REF_CLOSE: (7), (10), (14) are inconsistent by sub-proof #591.
% 136.14/20.18 | | |
% 136.14/20.18 | | Case 2:
% 136.14/20.18 | | |
% 136.14/20.18 | | | (15) all_57_13 = e1 & op(e0, e2) = e1
% 136.14/20.18 | | |
% 136.14/20.18 | | | ALPHA: (15) implies:
% 136.14/20.18 | | | (16) all_57_13 = e1
% 136.14/20.18 | | |
% 136.14/20.18 | | | REF_CLOSE: (1), (2), (5), (7), (8), (11), (16) are inconsistent by
% 136.14/20.18 | | | sub-proof #285.
% 136.14/20.18 | | |
% 136.14/20.18 | | End of split
% 136.14/20.18 | |
% 136.14/20.18 | Case 2:
% 136.14/20.18 | |
% 136.14/20.18 | | (17) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 136.14/20.18 | | e1)
% 136.14/20.18 | |
% 136.14/20.18 | | BETA: splitting (17) gives:
% 136.14/20.18 | |
% 136.14/20.18 | | Case 1:
% 136.14/20.18 | | |
% 136.14/20.18 | | | (18) all_57_14 = e1 & op(e0, e1) = e1
% 136.14/20.18 | | |
% 136.14/20.18 | | | ALPHA: (18) implies:
% 136.14/20.18 | | | (19) all_57_14 = e1
% 136.14/20.18 | | |
% 136.14/20.18 | | | REF_CLOSE: (4), (8), (19) are inconsistent by sub-proof #560.
% 136.14/20.18 | | |
% 136.14/20.18 | | Case 2:
% 136.14/20.18 | | |
% 136.14/20.18 | | | (20) all_57_15 = e1 & op(e0, e0) = e1
% 136.14/20.18 | | |
% 136.14/20.18 | | | ALPHA: (20) implies:
% 136.14/20.18 | | | (21) op(e0, e0) = e1
% 136.14/20.18 | | |
% 136.14/20.18 | | | REF_CLOSE: (3), (4), (9), (21) are inconsistent by sub-proof #636.
% 136.14/20.18 | | |
% 136.14/20.18 | | End of split
% 136.14/20.18 | |
% 136.14/20.18 | End of split
% 136.14/20.18 |
% 136.14/20.18 End of proof
% 136.14/20.18
% 136.14/20.18 Sub-proof #285 shows that the following formulas are inconsistent:
% 136.14/20.18 ----------------------------------------------------------------
% 136.14/20.18 (1) ~ (e2 = e0)
% 136.14/20.18 (2) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 136.14/20.18 (all_57_14 = e0 & op(e0, e1) = e0)
% 136.14/20.18 (3) ~ (e3 = e0)
% 136.14/20.18 (4) all_57_13 = e1
% 136.14/20.18 (5) all_57_12 = e3
% 136.14/20.18 (6) all_57_14 = e2
% 136.14/20.18 (7) ~ (e1 = e0)
% 136.14/20.18
% 136.14/20.18 Begin of proof
% 136.14/20.18 |
% 136.14/20.18 | BETA: splitting (2) gives:
% 136.14/20.18 |
% 136.14/20.18 | Case 1:
% 136.14/20.18 | |
% 136.14/20.18 | | (8) all_57_12 = e0 & op(e0, e3) = e0
% 136.14/20.18 | |
% 136.14/20.18 | | REF_CLOSE: (3), (5), (8) are inconsistent by sub-proof #436.
% 136.14/20.18 | |
% 136.14/20.18 | Case 2:
% 136.14/20.18 | |
% 136.14/20.18 | | (9) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 136.14/20.18 | | e0)
% 136.14/20.18 | |
% 136.14/20.18 | | REF_CLOSE: (1), (4), (6), (7), (9) are inconsistent by sub-proof #579.
% 136.14/20.18 | |
% 136.14/20.18 | End of split
% 136.14/20.18 |
% 136.14/20.18 End of proof
% 136.14/20.18
% 136.14/20.18 Sub-proof #286 shows that the following formulas are inconsistent:
% 136.14/20.18 ----------------------------------------------------------------
% 136.14/20.18 (1) op(e3, e3) = e2
% 136.14/20.18 (2) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 136.14/20.18 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 136.14/20.18 (3) ~ (e2 = e0)
% 136.14/20.18 (4) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 136.14/20.18 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 136.14/20.18 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.18 (6) ~ (e2 = e1)
% 136.14/20.18 (7) ~ (e3 = e0)
% 136.14/20.18 (8) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 136.14/20.18 (9) ~ (e3 = e2)
% 136.14/20.18 (10) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 136.14/20.18 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 136.14/20.18 (11) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 136.14/20.18 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 136.14/20.18 (12) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 136.14/20.18 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 136.14/20.18 (13) all_57_3 = e3
% 136.14/20.18 (14) ~ (e3 = e1)
% 136.14/20.18 (15) ~ (e1 = e0)
% 136.14/20.18 (16) all_57_7 = e2
% 136.14/20.18
% 136.14/20.18 Begin of proof
% 136.14/20.18 |
% 136.14/20.18 | BETA: splitting (8) gives:
% 136.14/20.18 |
% 136.14/20.18 | Case 1:
% 136.14/20.18 | |
% 136.14/20.18 | | (17) all_57_12 = e2 & op(e0, e3) = e2
% 136.14/20.18 | |
% 136.14/20.18 | | ALPHA: (17) implies:
% 136.14/20.18 | | (18) all_57_12 = e2
% 136.14/20.18 | |
% 136.14/20.18 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (12), (14), (15), (18)
% 136.14/20.18 | | are inconsistent by sub-proof #290.
% 136.14/20.18 | |
% 136.14/20.18 | Case 2:
% 136.14/20.18 | |
% 136.14/20.18 | | (19) all_57_13 = e2 & op(e0, e2) = e2
% 136.14/20.18 | |
% 136.14/20.18 | | ALPHA: (19) implies:
% 136.14/20.18 | | (20) all_57_13 = e2
% 136.14/20.18 | |
% 136.14/20.18 | | REF_CLOSE: (2), (3), (6), (7), (11), (13), (14), (15), (16), (20) are
% 136.14/20.18 | | inconsistent by sub-proof #287.
% 136.14/20.18 | |
% 136.14/20.18 | End of split
% 136.14/20.18 |
% 136.14/20.18 End of proof
% 136.14/20.18
% 136.14/20.18 Sub-proof #287 shows that the following formulas are inconsistent:
% 136.14/20.18 ----------------------------------------------------------------
% 136.14/20.18 (1) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 136.14/20.18 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 136.14/20.18 (2) ~ (e2 = e0)
% 136.14/20.18 (3) ~ (e2 = e1)
% 136.14/20.18 (4) ~ (e3 = e0)
% 136.14/20.18 (5) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 136.14/20.18 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 136.14/20.18 (6) all_57_13 = e2
% 136.14/20.18 (7) all_57_3 = e3
% 136.14/20.18 (8) ~ (e3 = e1)
% 136.14/20.18 (9) ~ (e1 = e0)
% 136.14/20.18 (10) all_57_7 = e2
% 136.14/20.18
% 136.14/20.18 Begin of proof
% 136.14/20.18 |
% 136.14/20.18 | BETA: splitting (1) gives:
% 136.14/20.18 |
% 136.14/20.18 | Case 1:
% 136.14/20.18 | |
% 136.14/20.18 | | (11) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 136.14/20.18 | | e0)
% 136.14/20.18 | |
% 136.14/20.18 | | BETA: splitting (11) gives:
% 136.14/20.18 | |
% 136.14/20.18 | | Case 1:
% 136.14/20.18 | | |
% 136.14/20.18 | | | (12) all_57_1 = e0 & op(e3, e2) = e0
% 136.14/20.18 | | |
% 136.14/20.18 | | | ALPHA: (12) implies:
% 136.14/20.18 | | | (13) all_57_1 = e0
% 136.14/20.18 | | |
% 136.14/20.18 | | | BETA: splitting (5) gives:
% 136.14/20.18 | | |
% 136.14/20.18 | | | Case 1:
% 136.14/20.18 | | | |
% 136.14/20.18 | | | | (14) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2)
% 136.14/20.18 | | | | = e1)
% 136.14/20.18 | | | |
% 136.14/20.18 | | | | BETA: splitting (14) gives:
% 136.14/20.18 | | | |
% 136.14/20.18 | | | | Case 1:
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | (15) all_57_1 = e1 & op(e3, e2) = e1
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | REF_CLOSE: (9), (13), (15) are inconsistent by sub-proof #289.
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | Case 2:
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | (16) all_57_3 = e1 & op(e2, e2) = e1
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | REF_CLOSE: (7), (8), (16) are inconsistent by sub-proof #370.
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | End of split
% 136.14/20.18 | | | |
% 136.14/20.18 | | | Case 2:
% 136.14/20.18 | | | |
% 136.14/20.18 | | | | (17) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2)
% 136.14/20.18 | | | | = e1)
% 136.14/20.18 | | | |
% 136.14/20.18 | | | | BETA: splitting (17) gives:
% 136.14/20.18 | | | |
% 136.14/20.18 | | | | Case 1:
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | (18) all_57_7 = e1 & op(e1, e2) = e1
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | ALPHA: (18) implies:
% 136.14/20.18 | | | | | (19) all_57_7 = e1
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | REF_CLOSE: (3), (10), (19) are inconsistent by sub-proof #288.
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | Case 2:
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | (20) all_57_13 = e1 & op(e0, e2) = e1
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | ALPHA: (20) implies:
% 136.14/20.18 | | | | | (21) all_57_13 = e1
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | REF_CLOSE: (3), (6), (21) are inconsistent by sub-proof #567.
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | End of split
% 136.14/20.18 | | | |
% 136.14/20.18 | | | End of split
% 136.14/20.18 | | |
% 136.14/20.18 | | Case 2:
% 136.14/20.18 | | |
% 136.14/20.18 | | | (22) all_57_3 = e0 & op(e2, e2) = e0
% 136.14/20.18 | | |
% 136.14/20.18 | | | REF_CLOSE: (4), (7), (22) are inconsistent by sub-proof #374.
% 136.14/20.18 | | |
% 136.14/20.18 | | End of split
% 136.14/20.18 | |
% 136.14/20.18 | Case 2:
% 136.14/20.18 | |
% 136.14/20.18 | | (23) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 136.14/20.18 | | e0)
% 136.14/20.18 | |
% 136.14/20.18 | | BETA: splitting (23) gives:
% 136.14/20.18 | |
% 136.14/20.18 | | Case 1:
% 136.14/20.18 | | |
% 136.14/20.18 | | | (24) all_57_7 = e0 & op(e1, e2) = e0
% 136.14/20.18 | | |
% 136.14/20.18 | | | REF_CLOSE: (2), (10), (24) are inconsistent by sub-proof #664.
% 136.14/20.18 | | |
% 136.14/20.18 | | Case 2:
% 136.14/20.18 | | |
% 136.14/20.18 | | | (25) all_57_13 = e0 & op(e0, e2) = e0
% 136.14/20.18 | | |
% 136.14/20.18 | | | REF_CLOSE: (2), (6), (25) are inconsistent by sub-proof #411.
% 136.14/20.18 | | |
% 136.14/20.18 | | End of split
% 136.14/20.18 | |
% 136.14/20.18 | End of split
% 136.14/20.18 |
% 136.14/20.18 End of proof
% 136.14/20.18
% 136.14/20.18 Sub-proof #288 shows that the following formulas are inconsistent:
% 136.14/20.18 ----------------------------------------------------------------
% 136.14/20.18 (1) all_57_7 = e2
% 136.14/20.18 (2) all_57_7 = e1
% 136.14/20.18 (3) ~ (e2 = e1)
% 136.14/20.18
% 136.14/20.18 Begin of proof
% 136.14/20.18 |
% 136.14/20.18 | COMBINE_EQS: (1), (2) imply:
% 136.14/20.18 | (4) e2 = e1
% 136.14/20.18 |
% 136.14/20.18 | SIMP: (4) implies:
% 136.14/20.18 | (5) e2 = e1
% 136.14/20.18 |
% 136.14/20.18 | REDUCE: (3), (5) imply:
% 136.14/20.18 | (6) $false
% 136.14/20.18 |
% 136.14/20.18 | CLOSE: (6) is inconsistent.
% 136.14/20.18 |
% 136.14/20.18 End of proof
% 136.14/20.18
% 136.14/20.18 Sub-proof #289 shows that the following formulas are inconsistent:
% 136.14/20.18 ----------------------------------------------------------------
% 136.14/20.18 (1) all_57_1 = e1 & op(e3, e2) = e1
% 136.14/20.18 (2) all_57_1 = e0
% 136.14/20.18 (3) ~ (e1 = e0)
% 136.14/20.18
% 136.14/20.18 Begin of proof
% 136.14/20.18 |
% 136.14/20.18 | ALPHA: (1) implies:
% 136.14/20.18 | (4) all_57_1 = e1
% 136.14/20.18 |
% 136.14/20.18 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.18 | (5) e1 = e0
% 136.14/20.18 |
% 136.14/20.18 | SIMP: (5) implies:
% 136.14/20.18 | (6) e1 = e0
% 136.14/20.18 |
% 136.14/20.18 | REDUCE: (3), (6) imply:
% 136.14/20.18 | (7) $false
% 136.14/20.18 |
% 136.14/20.18 | CLOSE: (7) is inconsistent.
% 136.14/20.18 |
% 136.14/20.18 End of proof
% 136.14/20.18
% 136.14/20.18 Sub-proof #290 shows that the following formulas are inconsistent:
% 136.14/20.18 ----------------------------------------------------------------
% 136.14/20.18 (1) op(e3, e3) = e2
% 136.14/20.18 (2) ~ (e2 = e0)
% 136.14/20.18 (3) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 136.14/20.18 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 136.14/20.18 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.18 (5) ~ (e2 = e1)
% 136.14/20.18 (6) ~ (e3 = e0)
% 136.14/20.18 (7) ~ (e3 = e2)
% 136.14/20.18 (8) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 136.14/20.18 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 136.14/20.18 (9) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 136.14/20.18 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 136.14/20.18 (10) ~ (e3 = e1)
% 136.14/20.18 (11) ~ (e1 = e0)
% 136.14/20.18 (12) all_57_12 = e2
% 136.14/20.18
% 136.14/20.18 Begin of proof
% 136.14/20.18 |
% 136.14/20.18 | BETA: splitting (8) gives:
% 136.14/20.18 |
% 136.14/20.18 | Case 1:
% 136.14/20.18 | |
% 136.14/20.18 | | (13) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 136.14/20.18 | | e3)
% 136.14/20.18 | |
% 136.14/20.18 | | BETA: splitting (13) gives:
% 136.14/20.18 | |
% 136.14/20.18 | | Case 1:
% 136.14/20.18 | | |
% 136.14/20.18 | | | (14) all_57_0 = e3 & op(e3, e3) = e3
% 136.14/20.18 | | |
% 136.14/20.18 | | | ALPHA: (14) implies:
% 136.14/20.18 | | | (15) op(e3, e3) = e3
% 136.14/20.18 | | |
% 136.14/20.18 | | | REF_CLOSE: (1), (4), (7), (15) are inconsistent by sub-proof #778.
% 136.14/20.18 | | |
% 136.14/20.18 | | Case 2:
% 136.14/20.18 | | |
% 136.14/20.18 | | | (16) all_57_2 = e3 & op(e2, e3) = e3
% 136.14/20.18 | | |
% 136.14/20.18 | | | ALPHA: (16) implies:
% 136.14/20.18 | | | (17) all_57_2 = e3
% 136.14/20.18 | | |
% 136.14/20.18 | | | BETA: splitting (9) gives:
% 136.14/20.18 | | |
% 136.14/20.18 | | | Case 1:
% 136.14/20.18 | | | |
% 136.14/20.18 | | | | (18) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3)
% 136.14/20.18 | | | | = e0)
% 136.14/20.18 | | | |
% 136.14/20.18 | | | | REF_CLOSE: (1), (2), (4), (6), (17), (18) are inconsistent by sub-proof
% 136.14/20.18 | | | | #426.
% 136.14/20.18 | | | |
% 136.14/20.18 | | | Case 2:
% 136.14/20.18 | | | |
% 136.14/20.18 | | | | (19) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3)
% 136.14/20.18 | | | | = e0)
% 136.14/20.18 | | | |
% 136.14/20.18 | | | | BETA: splitting (19) gives:
% 136.14/20.18 | | | |
% 136.14/20.18 | | | | Case 1:
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | (20) all_57_6 = e0 & op(e1, e3) = e0
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | ALPHA: (20) implies:
% 136.14/20.18 | | | | | (21) all_57_6 = e0
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | BETA: splitting (3) gives:
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | Case 1:
% 136.14/20.18 | | | | | |
% 136.14/20.18 | | | | | | (22) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2,
% 136.14/20.18 | | | | | | e3) = e1)
% 136.14/20.18 | | | | | |
% 136.14/20.18 | | | | | | REF_CLOSE: (1), (4), (5), (10), (17), (22) are inconsistent by
% 136.14/20.18 | | | | | | sub-proof #356.
% 136.14/20.18 | | | | | |
% 136.14/20.18 | | | | | Case 2:
% 136.14/20.18 | | | | | |
% 136.14/20.18 | | | | | | (23) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0,
% 136.14/20.18 | | | | | | e3) = e1)
% 136.14/20.18 | | | | | |
% 136.14/20.18 | | | | | | REF_CLOSE: (5), (11), (12), (21), (23) are inconsistent by sub-proof
% 136.14/20.18 | | | | | | #417.
% 136.14/20.18 | | | | | |
% 136.14/20.18 | | | | | End of split
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | Case 2:
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | (24) all_57_12 = e0 & op(e0, e3) = e0
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | REF_CLOSE: (2), (12), (24) are inconsistent by sub-proof #578.
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | End of split
% 136.14/20.18 | | | |
% 136.14/20.18 | | | End of split
% 136.14/20.18 | | |
% 136.14/20.18 | | End of split
% 136.14/20.18 | |
% 136.14/20.18 | Case 2:
% 136.14/20.18 | |
% 136.14/20.18 | | (25) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 136.14/20.18 | | e3)
% 136.14/20.18 | |
% 136.14/20.18 | | BETA: splitting (25) gives:
% 136.14/20.18 | |
% 136.14/20.18 | | Case 1:
% 136.14/20.18 | | |
% 136.14/20.18 | | | (26) all_57_6 = e3 & op(e1, e3) = e3
% 136.14/20.18 | | |
% 136.14/20.18 | | | ALPHA: (26) implies:
% 136.14/20.18 | | | (27) all_57_6 = e3
% 136.14/20.18 | | |
% 136.14/20.18 | | | BETA: splitting (9) gives:
% 136.14/20.18 | | |
% 136.14/20.18 | | | Case 1:
% 136.14/20.18 | | | |
% 136.14/20.18 | | | | (28) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3)
% 136.14/20.18 | | | | = e0)
% 136.14/20.18 | | | |
% 136.14/20.18 | | | | BETA: splitting (28) gives:
% 136.14/20.18 | | | |
% 136.14/20.18 | | | | Case 1:
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | (29) all_57_0 = e0 & op(e3, e3) = e0
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | ALPHA: (29) implies:
% 136.14/20.18 | | | | | (30) op(e3, e3) = e0
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | REF_CLOSE: (1), (2), (4), (30) are inconsistent by sub-proof #495.
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | Case 2:
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | (31) all_57_2 = e0 & op(e2, e3) = e0
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | ALPHA: (31) implies:
% 136.14/20.18 | | | | | (32) all_57_2 = e0
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | REF_CLOSE: (1), (3), (4), (5), (10), (11), (12), (27), (32) are
% 136.14/20.18 | | | | | inconsistent by sub-proof #643.
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | End of split
% 136.14/20.18 | | | |
% 136.14/20.18 | | | Case 2:
% 136.14/20.18 | | | |
% 136.14/20.18 | | | | (33) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3)
% 136.14/20.18 | | | | = e0)
% 136.14/20.18 | | | |
% 136.14/20.18 | | | | REF_CLOSE: (2), (6), (12), (27), (33) are inconsistent by sub-proof
% 136.14/20.18 | | | | #577.
% 136.14/20.18 | | | |
% 136.14/20.18 | | | End of split
% 136.14/20.18 | | |
% 136.14/20.18 | | Case 2:
% 136.14/20.18 | | |
% 136.14/20.18 | | | (34) all_57_12 = e3 & op(e0, e3) = e3
% 136.14/20.18 | | |
% 136.14/20.18 | | | ALPHA: (34) implies:
% 136.14/20.18 | | | (35) all_57_12 = e3
% 136.14/20.18 | | |
% 136.14/20.18 | | | REF_CLOSE: (7), (12), (35) are inconsistent by sub-proof #518.
% 136.14/20.18 | | |
% 136.14/20.18 | | End of split
% 136.14/20.18 | |
% 136.14/20.18 | End of split
% 136.14/20.18 |
% 136.14/20.18 End of proof
% 136.14/20.18
% 136.14/20.18 Sub-proof #291 shows that the following formulas are inconsistent:
% 136.14/20.18 ----------------------------------------------------------------
% 136.14/20.18 (1) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 136.14/20.18 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 136.14/20.18 (2) op(e2, e0) = all_52_13
% 136.14/20.18 (3) ~ (e2 = e0)
% 136.14/20.18 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.18 (5) ~ (e2 = e1)
% 136.14/20.18 (6) ~ (e3 = e0)
% 136.14/20.18 (7) ~ (e3 = e2)
% 136.14/20.18 (8) op(e2, e2) = e3
% 136.14/20.18 (9) op(e2, e0) = e0
% 136.14/20.18 (10) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 136.14/20.18 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 136.14/20.18 (11) ~ (all_52_13 = e3)
% 136.14/20.18 (12) op(e0, e0) = e2
% 136.14/20.18 (13) all_57_3 = e3
% 136.14/20.18 (14) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 136.14/20.18 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 136.14/20.18 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 136.14/20.18 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 136.14/20.18 (15) ~ (e3 = e1)
% 136.14/20.18 (16) ~ (e1 = e0)
% 136.14/20.18 (17) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 136.14/20.18 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 136.14/20.18 (18) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 136.14/20.18 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 136.14/20.18 (19) all_57_9 = e0
% 136.14/20.18 (20) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 136.14/20.18 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 136.14/20.18
% 136.14/20.18 Begin of proof
% 136.14/20.18 |
% 136.14/20.18 | BETA: splitting (18) gives:
% 136.14/20.18 |
% 136.14/20.18 | Case 1:
% 136.14/20.18 | |
% 136.14/20.18 | | (21) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 136.14/20.18 | | e0)
% 136.14/20.18 | |
% 136.14/20.18 | | BETA: splitting (21) gives:
% 136.14/20.18 | |
% 136.14/20.18 | | Case 1:
% 136.14/20.18 | | |
% 136.14/20.18 | | | (22) all_57_2 = e0 & op(e2, e3) = e0
% 136.14/20.18 | | |
% 136.14/20.18 | | | ALPHA: (22) implies:
% 136.14/20.18 | | | (23) all_57_2 = e0
% 136.14/20.18 | | |
% 136.14/20.18 | | | BETA: splitting (10) gives:
% 136.14/20.18 | | |
% 136.14/20.18 | | | Case 1:
% 136.14/20.18 | | | |
% 136.14/20.18 | | | | (24) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0)
% 136.14/20.18 | | | | = e3)
% 136.14/20.18 | | | |
% 136.14/20.18 | | | | BETA: splitting (24) gives:
% 136.14/20.18 | | | |
% 136.14/20.18 | | | | Case 1:
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | (25) all_57_9 = e3 & op(e3, e0) = e3
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | REF_CLOSE: (6), (19), (25) are inconsistent by sub-proof #614.
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | Case 2:
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | (26) all_57_10 = e3 & op(e2, e0) = e3
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | REF_CLOSE: (2), (4), (11), (26) are inconsistent by sub-proof #749.
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | End of split
% 136.14/20.18 | | | |
% 136.14/20.18 | | | Case 2:
% 136.14/20.18 | | | |
% 136.14/20.18 | | | | (27) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0,
% 136.14/20.18 | | | | e0) = e3)
% 136.14/20.18 | | | |
% 136.14/20.18 | | | | BETA: splitting (27) gives:
% 136.14/20.18 | | | |
% 136.14/20.18 | | | | Case 1:
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | (28) all_57_11 = e3 & op(e1, e0) = e3
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | ALPHA: (28) implies:
% 136.14/20.18 | | | | | (29) all_57_11 = e3
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | BETA: splitting (20) gives:
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | Case 1:
% 136.14/20.18 | | | | | |
% 136.14/20.18 | | | | | | (30) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2,
% 136.14/20.18 | | | | | | e0) = e1)
% 136.14/20.18 | | | | | |
% 136.14/20.18 | | | | | | BETA: splitting (30) gives:
% 136.14/20.18 | | | | | |
% 136.14/20.18 | | | | | | Case 1:
% 136.14/20.18 | | | | | | |
% 136.14/20.18 | | | | | | | (31) all_57_9 = e1 & op(e3, e0) = e1
% 136.14/20.18 | | | | | | |
% 136.14/20.18 | | | | | | | REF_CLOSE: (16), (19), (31) are inconsistent by sub-proof #298.
% 136.14/20.18 | | | | | | |
% 136.14/20.18 | | | | | | Case 2:
% 136.14/20.18 | | | | | | |
% 136.14/20.18 | | | | | | | (32) all_57_10 = e1 & op(e2, e0) = e1
% 136.14/20.18 | | | | | | |
% 136.14/20.18 | | | | | | | ALPHA: (32) implies:
% 136.14/20.18 | | | | | | | (33) all_57_10 = e1
% 136.14/20.18 | | | | | | |
% 136.14/20.18 | | | | | | | BETA: splitting (1) gives:
% 136.14/20.18 | | | | | | |
% 136.14/20.18 | | | | | | | Case 1:
% 136.14/20.18 | | | | | | | |
% 136.14/20.18 | | | | | | | | (34) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 &
% 136.14/20.18 | | | | | | | | op(e2, e2) = e2)
% 136.14/20.18 | | | | | | | |
% 136.14/20.18 | | | | | | | | BETA: splitting (34) gives:
% 136.14/20.18 | | | | | | | |
% 136.14/20.18 | | | | | | | | Case 1:
% 136.14/20.18 | | | | | | | | |
% 136.14/20.18 | | | | | | | | | (35) all_57_2 = e2 & op(e2, e3) = e2
% 136.14/20.18 | | | | | | | | |
% 136.14/20.18 | | | | | | | | | REF_CLOSE: (3), (23), (35) are inconsistent by sub-proof #680.
% 136.14/20.18 | | | | | | | | |
% 136.14/20.18 | | | | | | | | Case 2:
% 136.14/20.18 | | | | | | | | |
% 136.14/20.18 | | | | | | | | | (36) all_57_3 = e2 & op(e2, e2) = e2
% 136.14/20.18 | | | | | | | | |
% 136.14/20.18 | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (10), (11), (12),
% 136.14/20.18 | | | | | | | | | (13), (14), (15), (16), (20), (29), (36) are
% 136.14/20.18 | | | | | | | | | inconsistent by sub-proof #297.
% 136.14/20.18 | | | | | | | | |
% 136.14/20.18 | | | | | | | | End of split
% 136.14/20.18 | | | | | | | |
% 136.14/20.18 | | | | | | | Case 2:
% 136.14/20.18 | | | | | | | |
% 136.14/20.18 | | | | | | | | (37) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 &
% 136.14/20.18 | | | | | | | | op(e2, e0) = e2)
% 136.14/20.18 | | | | | | | |
% 136.14/20.18 | | | | | | | | BETA: splitting (37) gives:
% 136.14/20.18 | | | | | | | |
% 136.14/20.18 | | | | | | | | Case 1:
% 136.14/20.18 | | | | | | | | |
% 136.14/20.18 | | | | | | | | | (38) all_57_5 = e2 & op(e2, e1) = e2
% 136.14/20.18 | | | | | | | | |
% 136.14/20.18 | | | | | | | | | ALPHA: (38) implies:
% 136.14/20.18 | | | | | | | | | (39) all_57_5 = e2
% 136.14/20.18 | | | | | | | | |
% 136.14/20.18 | | | | | | | | | BETA: splitting (17) gives:
% 136.14/20.18 | | | | | | | | |
% 136.14/20.18 | | | | | | | | | Case 1:
% 136.14/20.18 | | | | | | | | | |
% 136.14/20.18 | | | | | | | | | | (40) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 &
% 136.14/20.18 | | | | | | | | | | op(e2, e2) = e1)
% 136.14/20.18 | | | | | | | | | |
% 136.14/20.18 | | | | | | | | | | BETA: splitting (40) gives:
% 136.14/20.18 | | | | | | | | | |
% 136.14/20.18 | | | | | | | | | | Case 1:
% 136.14/20.18 | | | | | | | | | | |
% 136.14/20.18 | | | | | | | | | | | (41) all_57_2 = e1 & op(e2, e3) = e1
% 136.14/20.18 | | | | | | | | | | |
% 136.14/20.18 | | | | | | | | | | | ALPHA: (41) implies:
% 136.14/20.18 | | | | | | | | | | | (42) all_57_2 = e1
% 136.14/20.18 | | | | | | | | | | |
% 136.14/20.18 | | | | | | | | | | | COMBINE_EQS: (23), (42) imply:
% 136.14/20.18 | | | | | | | | | | | (43) e1 = e0
% 136.14/20.18 | | | | | | | | | | |
% 136.14/20.18 | | | | | | | | | | | SIMP: (43) implies:
% 136.14/20.18 | | | | | | | | | | | (44) e1 = e0
% 136.14/20.18 | | | | | | | | | | |
% 136.14/20.18 | | | | | | | | | | | COMBINE_EQS: (33), (44) imply:
% 136.14/20.18 | | | | | | | | | | | (45) all_57_10 = e0
% 136.14/20.18 | | | | | | | | | | |
% 136.14/20.18 | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (7), (10), (11), (12), (15),
% 136.14/20.18 | | | | | | | | | | | (16), (19), (20), (45) are inconsistent by
% 136.14/20.18 | | | | | | | | | | | sub-proof #294.
% 136.14/20.18 | | | | | | | | | | |
% 136.14/20.18 | | | | | | | | | | Case 2:
% 136.14/20.18 | | | | | | | | | | |
% 136.14/20.18 | | | | | | | | | | | (46) all_57_3 = e1 & op(e2, e2) = e1
% 136.14/20.18 | | | | | | | | | | |
% 136.14/20.18 | | | | | | | | | | | ALPHA: (46) implies:
% 136.14/20.18 | | | | | | | | | | | (47) op(e2, e2) = e1
% 136.14/20.18 | | | | | | | | | | |
% 136.14/20.18 | | | | | | | | | | | REF_CLOSE: (4), (8), (15), (47) are inconsistent by sub-proof
% 136.14/20.18 | | | | | | | | | | | #325.
% 136.14/20.18 | | | | | | | | | | |
% 136.14/20.18 | | | | | | | | | | End of split
% 136.14/20.18 | | | | | | | | | |
% 136.14/20.18 | | | | | | | | | Case 2:
% 136.14/20.18 | | | | | | | | | |
% 136.14/20.18 | | | | | | | | | | (48) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1
% 136.14/20.18 | | | | | | | | | | & op(e2, e0) = e1)
% 136.14/20.18 | | | | | | | | | |
% 136.14/20.18 | | | | | | | | | | BETA: splitting (48) gives:
% 136.14/20.18 | | | | | | | | | |
% 136.14/20.18 | | | | | | | | | | Case 1:
% 136.14/20.18 | | | | | | | | | | |
% 136.14/20.18 | | | | | | | | | | | (49) all_57_5 = e1 & op(e2, e1) = e1
% 136.14/20.18 | | | | | | | | | | |
% 136.14/20.18 | | | | | | | | | | | ALPHA: (49) implies:
% 136.14/20.18 | | | | | | | | | | | (50) all_57_5 = e1
% 136.14/20.18 | | | | | | | | | | |
% 136.14/20.18 | | | | | | | | | | | REF_CLOSE: (5), (39), (50) are inconsistent by sub-proof
% 136.14/20.18 | | | | | | | | | | | #418.
% 136.14/20.18 | | | | | | | | | | |
% 136.14/20.18 | | | | | | | | | | Case 2:
% 136.14/20.18 | | | | | | | | | | |
% 136.14/20.18 | | | | | | | | | | |
% 136.14/20.18 | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (7), (9), (10), (11), (12),
% 136.14/20.18 | | | | | | | | | | | (15), (16), (19), (20), (32) are inconsistent by
% 136.14/20.18 | | | | | | | | | | | sub-proof #293.
% 136.14/20.18 | | | | | | | | | | |
% 136.14/20.18 | | | | | | | | | | End of split
% 136.14/20.18 | | | | | | | | | |
% 136.14/20.18 | | | | | | | | | End of split
% 136.14/20.18 | | | | | | | | |
% 136.14/20.18 | | | | | | | | Case 2:
% 136.14/20.18 | | | | | | | | |
% 136.14/20.18 | | | | | | | | | (51) all_57_10 = e2 & op(e2, e0) = e2
% 136.14/20.18 | | | | | | | | |
% 136.14/20.18 | | | | | | | | | ALPHA: (51) implies:
% 136.14/20.18 | | | | | | | | | (52) op(e2, e0) = e2
% 136.14/20.18 | | | | | | | | |
% 136.14/20.18 | | | | | | | | | REF_CLOSE: (3), (4), (9), (52) are inconsistent by sub-proof
% 136.14/20.18 | | | | | | | | | #451.
% 136.14/20.18 | | | | | | | | |
% 136.14/20.18 | | | | | | | | End of split
% 136.14/20.18 | | | | | | | |
% 136.14/20.18 | | | | | | | End of split
% 136.14/20.18 | | | | | | |
% 136.14/20.18 | | | | | | End of split
% 136.14/20.18 | | | | | |
% 136.14/20.18 | | | | | Case 2:
% 136.14/20.18 | | | | | |
% 136.14/20.18 | | | | | | (53) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 &
% 136.14/20.18 | | | | | | op(e0, e0) = e1)
% 136.14/20.18 | | | | | |
% 136.14/20.18 | | | | | | REF_CLOSE: (4), (5), (12), (15), (29), (53) are inconsistent by
% 136.14/20.18 | | | | | | sub-proof #295.
% 136.14/20.18 | | | | | |
% 136.14/20.18 | | | | | End of split
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | Case 2:
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | (54) all_57_15 = e3 & op(e0, e0) = e3
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | ALPHA: (54) implies:
% 136.14/20.18 | | | | | (55) op(e0, e0) = e3
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | REF_CLOSE: (4), (7), (12), (55) are inconsistent by sub-proof #634.
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | End of split
% 136.14/20.18 | | | |
% 136.14/20.18 | | | End of split
% 136.14/20.18 | | |
% 136.14/20.18 | | Case 2:
% 136.14/20.18 | | |
% 136.14/20.18 | | | (56) all_57_3 = e0 & op(e2, e2) = e0
% 136.14/20.18 | | |
% 136.14/20.18 | | | ALPHA: (56) implies:
% 136.14/20.18 | | | (57) op(e2, e2) = e0
% 136.14/20.18 | | |
% 136.14/20.18 | | | REF_CLOSE: (4), (6), (8), (57) are inconsistent by sub-proof #641.
% 136.14/20.18 | | |
% 136.14/20.18 | | End of split
% 136.14/20.18 | |
% 136.14/20.18 | Case 2:
% 136.14/20.18 | |
% 136.14/20.18 | | (58) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 136.14/20.18 | | e0)
% 136.14/20.18 | |
% 136.14/20.18 | | BETA: splitting (58) gives:
% 136.14/20.18 | |
% 136.14/20.18 | | Case 1:
% 136.14/20.18 | | |
% 136.14/20.18 | | | (59) all_57_5 = e0 & op(e2, e1) = e0
% 136.14/20.18 | | |
% 136.14/20.18 | | | ALPHA: (59) implies:
% 136.14/20.18 | | | (60) all_57_5 = e0
% 136.14/20.18 | | |
% 136.14/20.18 | | | BETA: splitting (10) gives:
% 136.14/20.18 | | |
% 136.14/20.18 | | | Case 1:
% 136.14/20.18 | | | |
% 136.14/20.18 | | | | (61) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0)
% 136.14/20.18 | | | | = e3)
% 136.14/20.18 | | | |
% 136.14/20.18 | | | | BETA: splitting (61) gives:
% 136.14/20.18 | | | |
% 136.14/20.18 | | | | Case 1:
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | (62) all_57_9 = e3 & op(e3, e0) = e3
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | REF_CLOSE: (6), (19), (62) are inconsistent by sub-proof #614.
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | Case 2:
% 136.14/20.18 | | | | |
% 136.14/20.18 | | | | | (63) all_57_10 = e3 & op(e2, e0) = e3
% 136.14/20.18 | | | | |
% 136.14/20.19 | | | | | REF_CLOSE: (2), (4), (11), (63) are inconsistent by sub-proof #749.
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | End of split
% 136.14/20.19 | | | |
% 136.14/20.19 | | | Case 2:
% 136.14/20.19 | | | |
% 136.14/20.19 | | | | (64) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0,
% 136.14/20.19 | | | | e0) = e3)
% 136.14/20.19 | | | |
% 136.14/20.19 | | | | BETA: splitting (64) gives:
% 136.14/20.19 | | | |
% 136.14/20.19 | | | | Case 1:
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | | (65) all_57_11 = e3 & op(e1, e0) = e3
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | | ALPHA: (65) implies:
% 136.14/20.19 | | | | | (66) all_57_11 = e3
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | | BETA: splitting (20) gives:
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | | Case 1:
% 136.14/20.19 | | | | | |
% 136.14/20.19 | | | | | | (67) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2,
% 136.14/20.19 | | | | | | e0) = e1)
% 136.14/20.19 | | | | | |
% 136.14/20.19 | | | | | | BETA: splitting (67) gives:
% 136.14/20.19 | | | | | |
% 136.14/20.19 | | | | | | Case 1:
% 136.14/20.19 | | | | | | |
% 136.14/20.19 | | | | | | | (68) all_57_9 = e1 & op(e3, e0) = e1
% 136.14/20.19 | | | | | | |
% 136.14/20.19 | | | | | | | REF_CLOSE: (16), (19), (68) are inconsistent by sub-proof #298.
% 136.14/20.19 | | | | | | |
% 136.14/20.19 | | | | | | Case 2:
% 136.14/20.19 | | | | | | |
% 136.14/20.19 | | | | | | | (69) all_57_10 = e1 & op(e2, e0) = e1
% 136.14/20.19 | | | | | | |
% 136.14/20.19 | | | | | | | ALPHA: (69) implies:
% 136.14/20.19 | | | | | | | (70) all_57_10 = e1
% 136.14/20.19 | | | | | | |
% 136.14/20.19 | | | | | | | BETA: splitting (1) gives:
% 136.14/20.19 | | | | | | |
% 136.14/20.19 | | | | | | | Case 1:
% 136.14/20.19 | | | | | | | |
% 136.14/20.19 | | | | | | | | (71) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 &
% 136.14/20.19 | | | | | | | | op(e2, e2) = e2)
% 136.14/20.19 | | | | | | | |
% 136.14/20.19 | | | | | | | | BETA: splitting (71) gives:
% 136.14/20.19 | | | | | | | |
% 136.14/20.19 | | | | | | | | Case 1:
% 136.14/20.19 | | | | | | | | |
% 136.14/20.19 | | | | | | | | | (72) all_57_2 = e2 & op(e2, e3) = e2
% 136.14/20.19 | | | | | | | | |
% 136.14/20.19 | | | | | | | | | ALPHA: (72) implies:
% 136.14/20.19 | | | | | | | | | (73) op(e2, e3) = e2
% 136.14/20.19 | | | | | | | | |
% 136.14/20.19 | | | | | | | | | BETA: splitting (17) gives:
% 136.14/20.19 | | | | | | | | |
% 136.14/20.19 | | | | | | | | | Case 1:
% 136.14/20.19 | | | | | | | | | |
% 136.14/20.19 | | | | | | | | | | (74) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 &
% 136.14/20.19 | | | | | | | | | | op(e2, e2) = e1)
% 136.14/20.19 | | | | | | | | | |
% 136.14/20.19 | | | | | | | | | | REF_CLOSE: (4), (5), (8), (15), (73), (74) are inconsistent
% 136.14/20.19 | | | | | | | | | | by sub-proof #292.
% 136.14/20.19 | | | | | | | | | |
% 136.14/20.19 | | | | | | | | | Case 2:
% 136.14/20.19 | | | | | | | | | |
% 136.14/20.19 | | | | | | | | | | (75) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1
% 136.14/20.19 | | | | | | | | | | & op(e2, e0) = e1)
% 136.14/20.19 | | | | | | | | | |
% 136.14/20.19 | | | | | | | | | | BETA: splitting (75) gives:
% 136.14/20.19 | | | | | | | | | |
% 136.14/20.19 | | | | | | | | | | Case 1:
% 136.14/20.19 | | | | | | | | | | |
% 136.14/20.19 | | | | | | | | | | | (76) all_57_5 = e1 & op(e2, e1) = e1
% 136.14/20.19 | | | | | | | | | | |
% 136.14/20.19 | | | | | | | | | | | ALPHA: (76) implies:
% 136.14/20.19 | | | | | | | | | | | (77) all_57_5 = e1
% 136.14/20.19 | | | | | | | | | | |
% 136.14/20.19 | | | | | | | | | | | COMBINE_EQS: (60), (77) imply:
% 136.14/20.19 | | | | | | | | | | | (78) e1 = e0
% 136.14/20.19 | | | | | | | | | | |
% 136.14/20.19 | | | | | | | | | | | COMBINE_EQS: (70), (78) imply:
% 136.14/20.19 | | | | | | | | | | | (79) all_57_10 = e0
% 136.14/20.19 | | | | | | | | | | |
% 136.14/20.19 | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (7), (10), (11), (12), (15),
% 136.14/20.19 | | | | | | | | | | | (16), (19), (20), (79) are inconsistent by
% 136.14/20.19 | | | | | | | | | | | sub-proof #294.
% 136.14/20.19 | | | | | | | | | | |
% 136.14/20.19 | | | | | | | | | | Case 2:
% 136.14/20.19 | | | | | | | | | | |
% 136.14/20.19 | | | | | | | | | | |
% 136.14/20.19 | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (7), (9), (10), (11), (12),
% 136.14/20.19 | | | | | | | | | | | (15), (16), (19), (20), (69) are inconsistent by
% 136.14/20.19 | | | | | | | | | | | sub-proof #293.
% 136.14/20.19 | | | | | | | | | | |
% 136.14/20.19 | | | | | | | | | | End of split
% 136.14/20.19 | | | | | | | | | |
% 136.14/20.19 | | | | | | | | | End of split
% 136.14/20.19 | | | | | | | | |
% 136.14/20.19 | | | | | | | | Case 2:
% 136.14/20.19 | | | | | | | | |
% 136.14/20.19 | | | | | | | | | (80) all_57_3 = e2 & op(e2, e2) = e2
% 136.14/20.19 | | | | | | | | |
% 136.14/20.19 | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (10), (11), (12),
% 136.14/20.19 | | | | | | | | | (13), (14), (15), (16), (20), (66), (80) are
% 136.14/20.19 | | | | | | | | | inconsistent by sub-proof #297.
% 136.14/20.19 | | | | | | | | |
% 136.14/20.19 | | | | | | | | End of split
% 136.14/20.19 | | | | | | | |
% 136.14/20.19 | | | | | | | Case 2:
% 136.14/20.19 | | | | | | | |
% 136.14/20.19 | | | | | | | | (81) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 &
% 136.14/20.19 | | | | | | | | op(e2, e0) = e2)
% 136.14/20.19 | | | | | | | |
% 136.14/20.19 | | | | | | | | BETA: splitting (81) gives:
% 136.14/20.19 | | | | | | | |
% 136.14/20.19 | | | | | | | | Case 1:
% 136.14/20.19 | | | | | | | | |
% 136.14/20.19 | | | | | | | | | (82) all_57_5 = e2 & op(e2, e1) = e2
% 136.14/20.19 | | | | | | | | |
% 136.14/20.19 | | | | | | | | | ALPHA: (82) implies:
% 136.14/20.19 | | | | | | | | | (83) all_57_5 = e2
% 136.14/20.19 | | | | | | | | |
% 136.14/20.19 | | | | | | | | | REF_CLOSE: (3), (60), (83) are inconsistent by sub-proof #372.
% 136.14/20.19 | | | | | | | | |
% 136.14/20.19 | | | | | | | | Case 2:
% 136.14/20.19 | | | | | | | | |
% 136.14/20.19 | | | | | | | | | (84) all_57_10 = e2 & op(e2, e0) = e2
% 136.14/20.19 | | | | | | | | |
% 136.14/20.19 | | | | | | | | | ALPHA: (84) implies:
% 136.14/20.19 | | | | | | | | | (85) op(e2, e0) = e2
% 136.14/20.19 | | | | | | | | |
% 136.14/20.19 | | | | | | | | | REF_CLOSE: (3), (4), (9), (85) are inconsistent by sub-proof
% 136.14/20.19 | | | | | | | | | #451.
% 136.14/20.19 | | | | | | | | |
% 136.14/20.19 | | | | | | | | End of split
% 136.14/20.19 | | | | | | | |
% 136.14/20.19 | | | | | | | End of split
% 136.14/20.19 | | | | | | |
% 136.14/20.19 | | | | | | End of split
% 136.14/20.19 | | | | | |
% 136.14/20.19 | | | | | Case 2:
% 136.14/20.19 | | | | | |
% 136.14/20.19 | | | | | | (86) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 &
% 136.14/20.19 | | | | | | op(e0, e0) = e1)
% 136.14/20.19 | | | | | |
% 136.14/20.19 | | | | | | REF_CLOSE: (4), (5), (12), (15), (66), (86) are inconsistent by
% 136.14/20.19 | | | | | | sub-proof #295.
% 136.14/20.19 | | | | | |
% 136.14/20.19 | | | | | End of split
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | Case 2:
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | | (87) all_57_15 = e3 & op(e0, e0) = e3
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | | ALPHA: (87) implies:
% 136.14/20.19 | | | | | (88) op(e0, e0) = e3
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | | REF_CLOSE: (4), (7), (12), (88) are inconsistent by sub-proof #634.
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | End of split
% 136.14/20.19 | | | |
% 136.14/20.19 | | | End of split
% 136.14/20.19 | | |
% 136.14/20.19 | | Case 2:
% 136.14/20.19 | | |
% 136.14/20.19 | | | (89) all_57_10 = e0 & op(e2, e0) = e0
% 136.14/20.19 | | |
% 136.14/20.19 | | | ALPHA: (89) implies:
% 136.14/20.19 | | | (90) all_57_10 = e0
% 136.14/20.19 | | |
% 136.14/20.19 | | | REF_CLOSE: (2), (4), (5), (6), (7), (10), (11), (12), (15), (16), (19),
% 136.14/20.19 | | | (20), (90) are inconsistent by sub-proof #294.
% 136.14/20.19 | | |
% 136.14/20.19 | | End of split
% 136.14/20.19 | |
% 136.14/20.19 | End of split
% 136.14/20.19 |
% 136.14/20.19 End of proof
% 136.14/20.19
% 136.14/20.19 Sub-proof #292 shows that the following formulas are inconsistent:
% 136.14/20.19 ----------------------------------------------------------------
% 136.14/20.19 (1) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 136.14/20.19 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.19 (3) ~ (e2 = e1)
% 136.14/20.19 (4) op(e2, e2) = e3
% 136.14/20.19 (5) ~ (e3 = e1)
% 136.14/20.19 (6) op(e2, e3) = e2
% 136.14/20.19
% 136.14/20.19 Begin of proof
% 136.14/20.19 |
% 136.14/20.19 | BETA: splitting (1) gives:
% 136.14/20.19 |
% 136.14/20.19 | Case 1:
% 136.14/20.19 | |
% 136.14/20.19 | | (7) all_57_2 = e1 & op(e2, e3) = e1
% 136.14/20.19 | |
% 136.14/20.19 | | ALPHA: (7) implies:
% 136.14/20.19 | | (8) op(e2, e3) = e1
% 136.14/20.19 | |
% 136.14/20.19 | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #450.
% 136.14/20.19 | |
% 136.14/20.19 | Case 2:
% 136.14/20.19 | |
% 136.14/20.19 | | (9) all_57_3 = e1 & op(e2, e2) = e1
% 136.14/20.19 | |
% 136.14/20.19 | | ALPHA: (9) implies:
% 136.14/20.19 | | (10) op(e2, e2) = e1
% 136.14/20.19 | |
% 136.14/20.19 | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #325.
% 136.14/20.19 | |
% 136.14/20.19 | End of split
% 136.14/20.19 |
% 136.14/20.19 End of proof
% 136.14/20.19
% 136.14/20.19 Sub-proof #293 shows that the following formulas are inconsistent:
% 136.14/20.19 ----------------------------------------------------------------
% 136.14/20.19 (1) op(e2, e0) = all_52_13
% 136.14/20.19 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.19 (3) ~ (e2 = e1)
% 136.14/20.19 (4) ~ (e3 = e0)
% 136.14/20.19 (5) ~ (e3 = e2)
% 136.14/20.19 (6) op(e2, e0) = e0
% 136.14/20.19 (7) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 136.14/20.19 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 136.14/20.19 (8) all_57_10 = e1 & op(e2, e0) = e1
% 136.14/20.19 (9) ~ (all_52_13 = e3)
% 136.14/20.19 (10) op(e0, e0) = e2
% 136.14/20.19 (11) ~ (e3 = e1)
% 136.14/20.19 (12) ~ (e1 = e0)
% 136.14/20.19 (13) all_57_9 = e0
% 136.14/20.19 (14) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 136.14/20.19 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 136.14/20.19
% 136.14/20.19 Begin of proof
% 136.14/20.19 |
% 136.14/20.19 | ALPHA: (8) implies:
% 136.14/20.19 | (15) all_57_10 = e1
% 136.14/20.19 | (16) op(e2, e0) = e1
% 136.14/20.19 |
% 136.14/20.19 | GROUND_INST: instantiating (2) with e0, e1, e0, e2, simplifying with (6), (16)
% 136.14/20.19 | gives:
% 136.14/20.19 | (17) e1 = e0
% 136.14/20.19 |
% 136.14/20.19 | COMBINE_EQS: (15), (17) imply:
% 136.14/20.19 | (18) all_57_10 = e0
% 136.14/20.19 |
% 136.14/20.19 | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (10), (11), (12), (13), (14),
% 136.14/20.19 | (18) are inconsistent by sub-proof #294.
% 136.14/20.19 |
% 136.14/20.19 End of proof
% 136.14/20.19
% 136.14/20.19 Sub-proof #294 shows that the following formulas are inconsistent:
% 136.14/20.19 ----------------------------------------------------------------
% 136.14/20.19 (1) op(e2, e0) = all_52_13
% 136.14/20.19 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.19 (3) ~ (e2 = e1)
% 136.14/20.19 (4) ~ (e3 = e0)
% 136.14/20.19 (5) ~ (e3 = e2)
% 136.14/20.19 (6) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 136.14/20.19 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 136.14/20.19 (7) ~ (all_52_13 = e3)
% 136.14/20.19 (8) all_57_10 = e0
% 136.14/20.19 (9) op(e0, e0) = e2
% 136.14/20.19 (10) ~ (e3 = e1)
% 136.14/20.19 (11) ~ (e1 = e0)
% 136.14/20.19 (12) all_57_9 = e0
% 136.14/20.19 (13) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 136.14/20.19 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 136.14/20.19
% 136.14/20.19 Begin of proof
% 136.14/20.19 |
% 136.14/20.19 | BETA: splitting (6) gives:
% 136.14/20.19 |
% 136.14/20.19 | Case 1:
% 136.14/20.19 | |
% 136.14/20.19 | | (14) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 136.14/20.19 | | e3)
% 136.14/20.19 | |
% 136.14/20.19 | | BETA: splitting (14) gives:
% 136.14/20.19 | |
% 136.14/20.19 | | Case 1:
% 136.14/20.19 | | |
% 136.14/20.19 | | | (15) all_57_9 = e3 & op(e3, e0) = e3
% 136.14/20.19 | | |
% 136.14/20.19 | | | REF_CLOSE: (4), (12), (15) are inconsistent by sub-proof #614.
% 136.14/20.19 | | |
% 136.14/20.19 | | Case 2:
% 136.14/20.19 | | |
% 136.14/20.19 | | | (16) all_57_10 = e3 & op(e2, e0) = e3
% 136.14/20.19 | | |
% 136.14/20.19 | | | REF_CLOSE: (1), (2), (7), (16) are inconsistent by sub-proof #749.
% 136.14/20.19 | | |
% 136.14/20.19 | | End of split
% 136.14/20.19 | |
% 136.14/20.19 | Case 2:
% 136.14/20.19 | |
% 136.14/20.19 | | (17) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 136.14/20.19 | | e3)
% 136.14/20.19 | |
% 136.14/20.19 | | BETA: splitting (17) gives:
% 136.14/20.19 | |
% 136.14/20.19 | | Case 1:
% 136.14/20.19 | | |
% 136.14/20.19 | | | (18) all_57_11 = e3 & op(e1, e0) = e3
% 136.14/20.19 | | |
% 136.14/20.19 | | | ALPHA: (18) implies:
% 136.14/20.19 | | | (19) all_57_11 = e3
% 136.14/20.19 | | |
% 136.14/20.19 | | | BETA: splitting (13) gives:
% 136.14/20.19 | | |
% 136.14/20.19 | | | Case 1:
% 136.14/20.19 | | | |
% 136.14/20.19 | | | | (20) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0)
% 136.14/20.19 | | | | = e1)
% 136.14/20.19 | | | |
% 136.14/20.19 | | | | BETA: splitting (20) gives:
% 136.14/20.19 | | | |
% 136.14/20.19 | | | | Case 1:
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | | (21) all_57_9 = e1 & op(e3, e0) = e1
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | | REF_CLOSE: (11), (12), (21) are inconsistent by sub-proof #298.
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | Case 2:
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | | (22) all_57_10 = e1 & op(e2, e0) = e1
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | | ALPHA: (22) implies:
% 136.14/20.19 | | | | | (23) all_57_10 = e1
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | | REF_CLOSE: (8), (11), (23) are inconsistent by sub-proof #639.
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | End of split
% 136.14/20.19 | | | |
% 136.14/20.19 | | | Case 2:
% 136.14/20.19 | | | |
% 136.14/20.19 | | | | (24) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0,
% 136.14/20.19 | | | | e0) = e1)
% 136.14/20.19 | | | |
% 136.14/20.19 | | | | REF_CLOSE: (2), (3), (9), (10), (19), (24) are inconsistent by sub-proof
% 136.14/20.19 | | | | #295.
% 136.14/20.19 | | | |
% 136.14/20.19 | | | End of split
% 136.14/20.19 | | |
% 136.14/20.19 | | Case 2:
% 136.14/20.19 | | |
% 136.14/20.19 | | | (25) all_57_15 = e3 & op(e0, e0) = e3
% 136.14/20.19 | | |
% 136.14/20.19 | | | ALPHA: (25) implies:
% 136.14/20.19 | | | (26) op(e0, e0) = e3
% 136.14/20.19 | | |
% 136.14/20.19 | | | REF_CLOSE: (2), (5), (9), (26) are inconsistent by sub-proof #634.
% 136.14/20.19 | | |
% 136.14/20.19 | | End of split
% 136.14/20.19 | |
% 136.14/20.19 | End of split
% 136.14/20.19 |
% 136.14/20.19 End of proof
% 136.14/20.19
% 136.14/20.19 Sub-proof #295 shows that the following formulas are inconsistent:
% 136.14/20.19 ----------------------------------------------------------------
% 136.14/20.19 (1) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 136.14/20.19 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.19 (3) ~ (e2 = e1)
% 136.14/20.19 (4) all_57_11 = e3
% 136.14/20.19 (5) op(e0, e0) = e2
% 136.14/20.19 (6) ~ (e3 = e1)
% 136.14/20.19
% 136.14/20.19 Begin of proof
% 136.14/20.19 |
% 136.14/20.19 | BETA: splitting (1) gives:
% 136.14/20.19 |
% 136.14/20.19 | Case 1:
% 136.14/20.19 | |
% 136.14/20.19 | | (7) all_57_11 = e1 & op(e1, e0) = e1
% 136.14/20.19 | |
% 136.14/20.19 | | REF_CLOSE: (4), (6), (7) are inconsistent by sub-proof #296.
% 136.14/20.19 | |
% 136.14/20.19 | Case 2:
% 136.14/20.19 | |
% 136.14/20.19 | | (8) all_57_15 = e1 & op(e0, e0) = e1
% 136.14/20.19 | |
% 136.14/20.19 | | ALPHA: (8) implies:
% 136.14/20.19 | | (9) op(e0, e0) = e1
% 136.14/20.19 | |
% 136.14/20.19 | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #636.
% 136.14/20.19 | |
% 136.14/20.19 | End of split
% 136.14/20.19 |
% 136.14/20.19 End of proof
% 136.14/20.19
% 136.14/20.19 Sub-proof #296 shows that the following formulas are inconsistent:
% 136.14/20.19 ----------------------------------------------------------------
% 136.14/20.19 (1) all_57_11 = e1 & op(e1, e0) = e1
% 136.14/20.19 (2) all_57_11 = e3
% 136.14/20.19 (3) ~ (e3 = e1)
% 136.14/20.19
% 136.14/20.19 Begin of proof
% 136.14/20.19 |
% 136.14/20.19 | ALPHA: (1) implies:
% 136.14/20.19 | (4) all_57_11 = e1
% 136.14/20.19 |
% 136.14/20.19 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.19 | (5) e3 = e1
% 136.14/20.19 |
% 136.14/20.19 | REDUCE: (3), (5) imply:
% 136.14/20.19 | (6) $false
% 136.14/20.19 |
% 136.14/20.19 | CLOSE: (6) is inconsistent.
% 136.14/20.19 |
% 136.14/20.19 End of proof
% 136.14/20.19
% 136.14/20.19 Sub-proof #297 shows that the following formulas are inconsistent:
% 136.14/20.19 ----------------------------------------------------------------
% 136.14/20.19 (1) op(e2, e0) = all_52_13
% 136.14/20.19 (2) ~ (e2 = e0)
% 136.14/20.19 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.19 (4) ~ (e2 = e1)
% 136.14/20.19 (5) ~ (e3 = e0)
% 136.14/20.19 (6) ~ (e3 = e2)
% 136.14/20.19 (7) all_57_3 = e2 & op(e2, e2) = e2
% 136.14/20.19 (8) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 136.14/20.19 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 136.14/20.19 (9) all_57_11 = e3
% 136.14/20.19 (10) ~ (all_52_13 = e3)
% 136.14/20.19 (11) op(e0, e0) = e2
% 136.14/20.19 (12) all_57_3 = e3
% 136.14/20.19 (13) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 136.14/20.19 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 136.14/20.19 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 136.14/20.19 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 136.14/20.19 (14) ~ (e3 = e1)
% 136.14/20.19 (15) ~ (e1 = e0)
% 136.14/20.19 (16) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 136.14/20.19 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 136.14/20.19
% 136.14/20.19 Begin of proof
% 136.14/20.19 |
% 136.14/20.19 | ALPHA: (7) implies:
% 136.14/20.19 | (17) all_57_3 = e2
% 136.14/20.19 |
% 136.14/20.19 | COMBINE_EQS: (12), (17) imply:
% 136.14/20.19 | (18) e3 = e2
% 136.14/20.19 |
% 136.14/20.19 | COMBINE_EQS: (9), (18) imply:
% 136.14/20.19 | (19) all_57_11 = e2
% 136.14/20.19 |
% 136.14/20.19 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (10), (11), (13), (14), (15),
% 136.14/20.19 | (16), (19) are inconsistent by sub-proof #633.
% 136.14/20.19 |
% 136.14/20.19 End of proof
% 136.14/20.19
% 136.14/20.19 Sub-proof #298 shows that the following formulas are inconsistent:
% 136.14/20.19 ----------------------------------------------------------------
% 136.14/20.19 (1) all_57_9 = e1 & op(e3, e0) = e1
% 136.14/20.19 (2) all_57_9 = e0
% 136.14/20.19 (3) ~ (e1 = e0)
% 136.14/20.19
% 136.14/20.19 Begin of proof
% 136.14/20.19 |
% 136.14/20.19 | ALPHA: (1) implies:
% 136.14/20.19 | (4) all_57_9 = e1
% 136.14/20.19 |
% 136.14/20.19 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.19 | (5) e1 = e0
% 136.14/20.19 |
% 136.14/20.19 | REDUCE: (3), (5) imply:
% 136.14/20.19 | (6) $false
% 136.14/20.19 |
% 136.14/20.19 | CLOSE: (6) is inconsistent.
% 136.14/20.19 |
% 136.14/20.19 End of proof
% 136.14/20.19
% 136.14/20.19 Sub-proof #299 shows that the following formulas are inconsistent:
% 136.14/20.19 ----------------------------------------------------------------
% 136.14/20.19 (1) all_57_9 = e0 & op(e3, e0) = e0
% 136.14/20.19 (2) all_57_9 = e3
% 136.14/20.19 (3) ~ (e3 = e0)
% 136.14/20.19
% 136.14/20.19 Begin of proof
% 136.14/20.19 |
% 136.14/20.19 | ALPHA: (1) implies:
% 136.14/20.19 | (4) all_57_9 = e0
% 136.14/20.19 |
% 136.14/20.19 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.19 | (5) e3 = e0
% 136.14/20.19 |
% 136.14/20.19 | REDUCE: (3), (5) imply:
% 136.14/20.19 | (6) $false
% 136.14/20.19 |
% 136.14/20.19 | CLOSE: (6) is inconsistent.
% 136.14/20.19 |
% 136.14/20.19 End of proof
% 136.14/20.19
% 136.14/20.19 Sub-proof #300 shows that the following formulas are inconsistent:
% 136.14/20.19 ----------------------------------------------------------------
% 136.14/20.19 (1) op(e0, e0) = e0
% 136.14/20.19 (2) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 136.14/20.19 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 136.14/20.19 (3) ~ (e2 = e0)
% 136.14/20.19 (4) all_57_1 = e2
% 136.14/20.19 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.19 (6) ~ (e2 = e1)
% 136.14/20.19 (7) ~ (e3 = e0)
% 136.14/20.19 (8) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 136.14/20.19 (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 136.14/20.19 (9) ~ (e3 = e2)
% 136.14/20.19 (10) op(e1, e1) = e3
% 136.14/20.19 (11) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 136.14/20.19 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 136.14/20.19 (12) all_57_12 = e3
% 136.14/20.19 (13) all_57_3 = e3
% 136.14/20.19 (14) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.14/20.19 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.14/20.19 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0)
% 136.14/20.19 = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 136.14/20.19 $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~
% 136.14/20.19 (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 136.14/20.19 (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 136.14/20.19 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.14/20.19 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.14/20.19 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.14/20.19 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 136.14/20.19 op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.14/20.19 op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 136.14/20.19 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13
% 136.14/20.19 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 136.14/20.19 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1,
% 136.14/20.19 e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 136.14/20.19 $i(all_56_21) & $i(all_56_29))
% 136.14/20.19 (15) ~ (e3 = e1)
% 136.14/20.19 (16) ~ (e1 = e0)
% 136.14/20.19 (17) op(e0, e0) = all_56_31
% 136.14/20.19
% 136.14/20.19 Begin of proof
% 136.14/20.19 |
% 136.14/20.19 | BETA: splitting (14) gives:
% 136.14/20.19 |
% 136.14/20.19 | Case 1:
% 136.14/20.19 | |
% 136.14/20.19 | | (18) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 136.14/20.19 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.14/20.19 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.14/20.19 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9)
% 136.14/20.19 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 136.14/20.19 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 136.14/20.19 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 136.14/20.19 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 136.14/20.19 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 136.14/20.19 | | $i(all_56_27))
% 136.14/20.19 | |
% 136.14/20.19 | | REF_CLOSE: (1), (3), (5), (7), (17), (18) are inconsistent by sub-proof
% 136.14/20.19 | | #713.
% 136.14/20.19 | |
% 136.14/20.19 | Case 2:
% 136.14/20.19 | |
% 136.14/20.19 | | (19) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.14/20.19 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.14/20.19 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 136.14/20.19 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 136.14/20.19 | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 136.14/20.19 | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 136.14/20.19 | | ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 136.14/20.19 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 136.14/20.19 | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.14/20.19 | | $i(all_56_29))
% 136.14/20.19 | |
% 136.14/20.19 | | BETA: splitting (19) gives:
% 136.14/20.19 | |
% 136.14/20.19 | | Case 1:
% 136.14/20.19 | | |
% 136.14/20.19 | | | (20) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.14/20.19 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.14/20.19 | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 136.14/20.19 | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 136.14/20.19 | | | $i(all_56_15) & $i(all_56_23)
% 136.14/20.19 | | |
% 136.14/20.19 | | | ALPHA: (20) implies:
% 136.14/20.19 | | | (21) op(e1, e1) = e0
% 136.14/20.19 | | |
% 136.14/20.19 | | | REF_CLOSE: (5), (7), (10), (21) are inconsistent by sub-proof #753.
% 136.14/20.19 | | |
% 136.14/20.19 | | Case 2:
% 136.14/20.19 | | |
% 136.14/20.19 | | | (22) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 136.14/20.19 | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 136.14/20.19 | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.14/20.19 | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 136.14/20.19 | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 136.14/20.19 | | |
% 136.14/20.19 | | | ALPHA: (22) implies:
% 136.14/20.19 | | | (23) all_56_31 = e1
% 136.14/20.19 | | | (24) op(e0, e1) = e0
% 136.14/20.19 | | |
% 136.14/20.19 | | | REDUCE: (17), (23) imply:
% 136.14/20.19 | | | (25) op(e0, e0) = e1
% 136.14/20.19 | | |
% 136.14/20.19 | | | BETA: splitting (8) gives:
% 136.14/20.19 | | |
% 136.14/20.19 | | | Case 1:
% 136.14/20.19 | | | |
% 136.14/20.19 | | | | (26) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0,
% 136.14/20.19 | | | | e2) = e2)
% 136.14/20.19 | | | |
% 136.14/20.19 | | | | BETA: splitting (26) gives:
% 136.14/20.19 | | | |
% 136.14/20.19 | | | | Case 1:
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | | (27) all_57_12 = e2 & op(e0, e3) = e2
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | | ALPHA: (27) implies:
% 136.14/20.19 | | | | | (28) all_57_12 = e2
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | | REF_CLOSE: (9), (12), (28) are inconsistent by sub-proof #518.
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | Case 2:
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | | (29) all_57_13 = e2 & op(e0, e2) = e2
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | | ALPHA: (29) implies:
% 136.14/20.19 | | | | | (30) all_57_13 = e2
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (11), (13), (15), (16), (30) are
% 136.14/20.19 | | | | | inconsistent by sub-proof #301.
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | End of split
% 136.14/20.19 | | | |
% 136.14/20.19 | | | Case 2:
% 136.14/20.19 | | | |
% 136.14/20.19 | | | | (31) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0,
% 136.14/20.19 | | | | e0) = e2)
% 136.14/20.19 | | | |
% 136.14/20.19 | | | | BETA: splitting (31) gives:
% 136.14/20.19 | | | |
% 136.14/20.19 | | | | Case 1:
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | | (32) all_57_14 = e2 & op(e0, e1) = e2
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | | ALPHA: (32) implies:
% 136.14/20.19 | | | | | (33) op(e0, e1) = e2
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | | REF_CLOSE: (3), (5), (24), (33) are inconsistent by sub-proof #660.
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | Case 2:
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | | (34) all_57_15 = e2 & op(e0, e0) = e2
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | | ALPHA: (34) implies:
% 136.14/20.19 | | | | | (35) op(e0, e0) = e2
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | | REF_CLOSE: (5), (6), (25), (35) are inconsistent by sub-proof #636.
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | End of split
% 136.14/20.19 | | | |
% 136.14/20.19 | | | End of split
% 136.14/20.19 | | |
% 136.14/20.19 | | End of split
% 136.14/20.19 | |
% 136.14/20.19 | End of split
% 136.14/20.19 |
% 136.14/20.19 End of proof
% 136.14/20.19
% 136.14/20.19 Sub-proof #301 shows that the following formulas are inconsistent:
% 136.14/20.19 ----------------------------------------------------------------
% 136.14/20.19 (1) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 136.14/20.19 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 136.14/20.19 (2) ~ (e2 = e0)
% 136.14/20.19 (3) all_57_1 = e2
% 136.14/20.19 (4) ~ (e2 = e1)
% 136.14/20.19 (5) ~ (e3 = e0)
% 136.14/20.19 (6) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 136.14/20.19 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 136.14/20.19 (7) all_57_13 = e2
% 136.14/20.19 (8) all_57_3 = e3
% 136.14/20.19 (9) ~ (e3 = e1)
% 136.14/20.19 (10) ~ (e1 = e0)
% 136.14/20.19
% 136.14/20.19 Begin of proof
% 136.14/20.19 |
% 136.14/20.19 | BETA: splitting (6) gives:
% 136.14/20.19 |
% 136.14/20.19 | Case 1:
% 136.14/20.19 | |
% 136.14/20.19 | | (11) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 136.14/20.19 | | e1)
% 136.14/20.19 | |
% 136.14/20.19 | | BETA: splitting (11) gives:
% 136.14/20.19 | |
% 136.14/20.19 | | Case 1:
% 136.14/20.19 | | |
% 136.14/20.19 | | | (12) all_57_1 = e1 & op(e3, e2) = e1
% 136.14/20.19 | | |
% 136.14/20.19 | | | REF_CLOSE: (3), (4), (12) are inconsistent by sub-proof #465.
% 136.14/20.19 | | |
% 136.14/20.19 | | Case 2:
% 136.14/20.19 | | |
% 136.14/20.19 | | | (13) all_57_3 = e1 & op(e2, e2) = e1
% 136.14/20.19 | | |
% 136.14/20.19 | | | REF_CLOSE: (8), (9), (13) are inconsistent by sub-proof #303.
% 136.14/20.19 | | |
% 136.14/20.19 | | End of split
% 136.14/20.19 | |
% 136.14/20.19 | Case 2:
% 136.14/20.19 | |
% 136.14/20.19 | | (14) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 136.14/20.19 | | e1)
% 136.14/20.19 | |
% 136.14/20.19 | | BETA: splitting (14) gives:
% 136.14/20.19 | |
% 136.14/20.19 | | Case 1:
% 136.14/20.19 | | |
% 136.14/20.19 | | | (15) all_57_7 = e1 & op(e1, e2) = e1
% 136.14/20.19 | | |
% 136.14/20.19 | | | ALPHA: (15) implies:
% 136.14/20.19 | | | (16) all_57_7 = e1
% 136.14/20.19 | | |
% 136.14/20.19 | | | BETA: splitting (1) gives:
% 136.14/20.19 | | |
% 136.14/20.19 | | | Case 1:
% 136.14/20.19 | | | |
% 136.14/20.19 | | | | (17) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2)
% 136.14/20.19 | | | | = e0)
% 136.14/20.19 | | | |
% 136.14/20.19 | | | | BETA: splitting (17) gives:
% 136.14/20.19 | | | |
% 136.14/20.19 | | | | Case 1:
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | | (18) all_57_1 = e0 & op(e3, e2) = e0
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | | REF_CLOSE: (2), (3), (18) are inconsistent by sub-proof #466.
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | Case 2:
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | | (19) all_57_3 = e0 & op(e2, e2) = e0
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | | REF_CLOSE: (5), (8), (19) are inconsistent by sub-proof #302.
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | End of split
% 136.14/20.19 | | | |
% 136.14/20.19 | | | Case 2:
% 136.14/20.19 | | | |
% 136.14/20.19 | | | | (20) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2)
% 136.14/20.19 | | | | = e0)
% 136.14/20.19 | | | |
% 136.14/20.19 | | | | BETA: splitting (20) gives:
% 136.14/20.19 | | | |
% 136.14/20.19 | | | | Case 1:
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | | (21) all_57_7 = e0 & op(e1, e2) = e0
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | | ALPHA: (21) implies:
% 136.14/20.19 | | | | | (22) all_57_7 = e0
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | | REF_CLOSE: (10), (16), (22) are inconsistent by sub-proof #464.
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | Case 2:
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | | (23) all_57_13 = e0 & op(e0, e2) = e0
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | | ALPHA: (23) implies:
% 136.14/20.19 | | | | | (24) all_57_13 = e0
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | | REF_CLOSE: (2), (7), (24) are inconsistent by sub-proof #404.
% 136.14/20.19 | | | | |
% 136.14/20.19 | | | | End of split
% 136.14/20.19 | | | |
% 136.14/20.19 | | | End of split
% 136.14/20.19 | | |
% 136.14/20.19 | | Case 2:
% 136.14/20.19 | | |
% 136.14/20.19 | | | (25) all_57_13 = e1 & op(e0, e2) = e1
% 136.14/20.19 | | |
% 136.14/20.19 | | | ALPHA: (25) implies:
% 136.14/20.19 | | | (26) all_57_13 = e1
% 136.14/20.19 | | |
% 136.14/20.19 | | | REF_CLOSE: (4), (7), (26) are inconsistent by sub-proof #567.
% 136.14/20.19 | | |
% 136.14/20.19 | | End of split
% 136.14/20.19 | |
% 136.14/20.19 | End of split
% 136.14/20.19 |
% 136.14/20.19 End of proof
% 136.14/20.19
% 136.14/20.19 Sub-proof #302 shows that the following formulas are inconsistent:
% 136.14/20.19 ----------------------------------------------------------------
% 136.14/20.19 (1) all_57_3 = e0 & op(e2, e2) = e0
% 136.14/20.19 (2) all_57_3 = e3
% 136.14/20.19 (3) ~ (e3 = e0)
% 136.14/20.19
% 136.14/20.19 Begin of proof
% 136.14/20.19 |
% 136.14/20.19 | ALPHA: (1) implies:
% 136.14/20.20 | (4) all_57_3 = e0
% 136.14/20.20 |
% 136.14/20.20 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.20 | (5) e3 = e0
% 136.14/20.20 |
% 136.14/20.20 | SIMP: (5) implies:
% 136.14/20.20 | (6) e3 = e0
% 136.14/20.20 |
% 136.14/20.20 | REDUCE: (3), (6) imply:
% 136.14/20.20 | (7) $false
% 136.14/20.20 |
% 136.14/20.20 | CLOSE: (7) is inconsistent.
% 136.14/20.20 |
% 136.14/20.20 End of proof
% 136.14/20.20
% 136.14/20.20 Sub-proof #303 shows that the following formulas are inconsistent:
% 136.14/20.20 ----------------------------------------------------------------
% 136.14/20.20 (1) all_57_3 = e1 & op(e2, e2) = e1
% 136.14/20.20 (2) all_57_3 = e3
% 136.14/20.20 (3) ~ (e3 = e1)
% 136.14/20.20
% 136.14/20.20 Begin of proof
% 136.14/20.20 |
% 136.14/20.20 | ALPHA: (1) implies:
% 136.14/20.20 | (4) all_57_3 = e1
% 136.14/20.20 |
% 136.14/20.20 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.20 | (5) e3 = e1
% 136.14/20.20 |
% 136.14/20.20 | SIMP: (5) implies:
% 136.14/20.20 | (6) e3 = e1
% 136.14/20.20 |
% 136.14/20.20 | REDUCE: (3), (6) imply:
% 136.14/20.20 | (7) $false
% 136.14/20.20 |
% 136.14/20.20 | CLOSE: (7) is inconsistent.
% 136.14/20.20 |
% 136.14/20.20 End of proof
% 136.14/20.20
% 136.14/20.20 Sub-proof #304 shows that the following formulas are inconsistent:
% 136.14/20.20 ----------------------------------------------------------------
% 136.14/20.20 (1) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2)
% 136.14/20.20 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 136.14/20.20 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25
% 136.14/20.20 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 136.14/20.20 $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~
% 136.14/20.20 (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 136.14/20.20 (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 136.14/20.20 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 136.14/20.20 = all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.14/20.20 $i(all_56_29))
% 136.14/20.20 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.20 (3) ~ (all_52_2 = e1)
% 136.14/20.20 (4) op(e2, e2) = e3
% 136.14/20.20 (5) op(e1, e3) = all_52_2
% 136.14/20.20 (6) ~ (e3 = e1)
% 136.14/20.20
% 136.14/20.20 Begin of proof
% 136.14/20.20 |
% 136.14/20.20 | BETA: splitting (1) gives:
% 136.14/20.20 |
% 136.14/20.20 | Case 1:
% 136.14/20.20 | |
% 136.14/20.20 | | (7) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.14/20.20 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.14/20.20 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.14/20.20 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1)
% 136.14/20.20 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)
% 136.14/20.20 | |
% 136.14/20.20 | | ALPHA: (7) implies:
% 136.14/20.20 | | (8) op(e1, e3) = e1
% 136.14/20.20 | |
% 136.14/20.20 | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #725.
% 136.14/20.20 | |
% 136.14/20.20 | Case 2:
% 136.14/20.20 | |
% 136.14/20.20 | | (9) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13
% 136.14/20.20 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1
% 136.14/20.20 | | & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 136.14/20.20 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 136.14/20.20 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 136.14/20.20 | |
% 136.14/20.20 | | ALPHA: (9) implies:
% 136.14/20.20 | | (10) op(e2, e2) = e1
% 136.14/20.20 | |
% 136.14/20.20 | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #325.
% 136.14/20.20 | |
% 136.14/20.20 | End of split
% 136.14/20.20 |
% 136.14/20.20 End of proof
% 136.14/20.20
% 136.14/20.20 Sub-proof #305 shows that the following formulas are inconsistent:
% 136.14/20.20 ----------------------------------------------------------------
% 136.14/20.20 (1) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 & $i(all_22_1)
% 136.14/20.20 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.20 (3) op(e3, e3) = e1
% 136.14/20.20
% 136.14/20.20 Begin of proof
% 136.14/20.20 |
% 136.14/20.20 | ALPHA: (1) implies:
% 136.14/20.20 | (4) ~ (all_22_1 = e1)
% 136.14/20.20 | (5) op(e3, e3) = all_22_1
% 136.14/20.20 |
% 136.14/20.20 | GROUND_INST: instantiating (2) with e1, all_22_1, e3, e3, simplifying with
% 136.14/20.20 | (3), (5) gives:
% 136.14/20.20 | (6) all_22_1 = e1
% 136.14/20.20 |
% 136.14/20.20 | REDUCE: (4), (6) imply:
% 136.14/20.20 | (7) $false
% 136.14/20.20 |
% 136.14/20.20 | CLOSE: (7) is inconsistent.
% 136.14/20.20 |
% 136.14/20.20 End of proof
% 136.14/20.20
% 136.14/20.20 Sub-proof #306 shows that the following formulas are inconsistent:
% 136.14/20.20 ----------------------------------------------------------------
% 136.14/20.20 (1) all_54_1 = e1 | all_54_1 = e0
% 136.14/20.20 (2) all_54_1 = all_22_0
% 136.14/20.20 (3) ~ (all_22_0 = e1)
% 136.14/20.20 (4) ~ (all_22_0 = e0)
% 136.14/20.20
% 136.14/20.20 Begin of proof
% 136.14/20.20 |
% 136.14/20.20 | BETA: splitting (1) gives:
% 136.14/20.20 |
% 136.14/20.20 | Case 1:
% 136.14/20.20 | |
% 136.14/20.20 | | (5) all_54_1 = e1
% 136.14/20.20 | |
% 136.14/20.20 | | COMBINE_EQS: (2), (5) imply:
% 136.14/20.20 | | (6) all_22_0 = e1
% 136.14/20.20 | |
% 136.14/20.20 | | SIMP: (6) implies:
% 136.14/20.20 | | (7) all_22_0 = e1
% 136.14/20.20 | |
% 136.14/20.20 | | REDUCE: (3), (7) imply:
% 136.14/20.20 | | (8) $false
% 136.14/20.20 | |
% 136.14/20.20 | | CLOSE: (8) is inconsistent.
% 136.14/20.20 | |
% 136.14/20.20 | Case 2:
% 136.14/20.20 | |
% 136.14/20.20 | | (9) all_54_1 = e0
% 136.14/20.20 | |
% 136.14/20.20 | | COMBINE_EQS: (2), (9) imply:
% 136.14/20.20 | | (10) all_22_0 = e0
% 136.14/20.20 | |
% 136.14/20.20 | | SIMP: (10) implies:
% 136.14/20.20 | | (11) all_22_0 = e0
% 136.14/20.20 | |
% 136.14/20.20 | | REDUCE: (4), (11) imply:
% 136.14/20.20 | | (12) $false
% 136.14/20.20 | |
% 136.14/20.20 | | CLOSE: (12) is inconsistent.
% 136.14/20.20 | |
% 136.14/20.20 | End of split
% 136.14/20.20 |
% 136.14/20.20 End of proof
% 136.14/20.20
% 136.14/20.20 Sub-proof #307 shows that the following formulas are inconsistent:
% 136.14/20.20 ----------------------------------------------------------------
% 136.14/20.20 (1) ~ (all_22_0 = e0)
% 136.14/20.20 (2) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0)
% 136.14/20.20 (3) op(e3, e3) = e1
% 136.14/20.20 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.20 (5) ~ (e1 = e0)
% 136.14/20.20 (6) op(e3, e2) = all_22_0
% 136.14/20.20
% 136.14/20.20 Begin of proof
% 136.14/20.20 |
% 136.14/20.20 | BETA: splitting (2) gives:
% 136.14/20.20 |
% 136.14/20.20 | Case 1:
% 136.14/20.20 | |
% 136.14/20.20 | | (7) all_57_0 = e0 & op(e3, e3) = e0
% 136.14/20.20 | |
% 136.14/20.20 | | ALPHA: (7) implies:
% 136.14/20.20 | | (8) op(e3, e3) = e0
% 136.14/20.20 | |
% 136.14/20.20 | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #717.
% 136.14/20.20 | |
% 136.14/20.20 | Case 2:
% 136.14/20.20 | |
% 136.14/20.20 | | (9) all_57_1 = e0 & op(e3, e2) = e0
% 136.14/20.20 | |
% 136.14/20.20 | | REF_CLOSE: (1), (4), (6), (9) are inconsistent by sub-proof #309.
% 136.14/20.20 | |
% 136.14/20.20 | End of split
% 136.14/20.20 |
% 136.14/20.20 End of proof
% 136.14/20.20
% 136.14/20.20 Sub-proof #308 shows that the following formulas are inconsistent:
% 136.14/20.20 ----------------------------------------------------------------
% 136.14/20.20 (1) ~ (all_22_0 = e0)
% 136.14/20.20 (2) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 136.14/20.20 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 136.14/20.20 (3) ~ (e2 = e0)
% 136.14/20.20 (4) op(e3, e3) = e1
% 136.14/20.20 (5) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 136.14/20.20 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 136.14/20.20 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.20 (7) ~ (e2 = e1)
% 136.14/20.20 (8) ~ (e3 = e0)
% 136.14/20.20 (9) ~ (e3 = e2)
% 136.14/20.20 (10) op(e2, e2) = e3
% 136.14/20.20 (11) ~ (all_52_4 = e3)
% 136.14/20.20 (12) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 136.14/20.20 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 136.14/20.20 (13) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 136.14/20.20 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 136.14/20.20 (14) op(e3, e2) = all_52_4
% 136.14/20.20 (15) ~ (e3 = e1)
% 136.14/20.20 (16) ~ (e1 = e0)
% 136.14/20.20 (17) all_57_7 = e2
% 136.14/20.20 (18) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 136.14/20.20 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 136.14/20.20 (19) op(e3, e2) = all_22_0
% 136.14/20.20
% 136.14/20.20 Begin of proof
% 136.14/20.20 |
% 136.14/20.20 | BETA: splitting (2) gives:
% 136.14/20.20 |
% 136.14/20.20 | Case 1:
% 136.14/20.20 | |
% 136.14/20.20 | | (20) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 136.14/20.20 | | e0)
% 136.14/20.20 | |
% 136.14/20.20 | | BETA: splitting (20) gives:
% 136.14/20.20 | |
% 136.14/20.20 | | Case 1:
% 136.14/20.20 | | |
% 136.14/20.20 | | | (21) all_57_1 = e0 & op(e3, e2) = e0
% 136.14/20.20 | | |
% 136.14/20.20 | | | REF_CLOSE: (1), (6), (19), (21) are inconsistent by sub-proof #309.
% 136.14/20.20 | | |
% 136.14/20.20 | | Case 2:
% 136.14/20.20 | | |
% 136.14/20.20 | | | (22) all_57_3 = e0 & op(e2, e2) = e0
% 136.14/20.20 | | |
% 136.14/20.20 | | | ALPHA: (22) implies:
% 136.14/20.20 | | | (23) op(e2, e2) = e0
% 136.14/20.20 | | |
% 136.14/20.20 | | | REF_CLOSE: (6), (8), (10), (23) are inconsistent by sub-proof #641.
% 136.14/20.20 | | |
% 136.14/20.20 | | End of split
% 136.14/20.20 | |
% 136.14/20.20 | Case 2:
% 136.14/20.20 | |
% 136.14/20.20 | | (24) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 136.14/20.20 | | e0)
% 136.14/20.20 | |
% 136.14/20.20 | | BETA: splitting (24) gives:
% 136.14/20.20 | |
% 136.14/20.20 | | Case 1:
% 136.14/20.20 | | |
% 136.14/20.20 | | | (25) all_57_7 = e0 & op(e1, e2) = e0
% 136.14/20.20 | | |
% 136.14/20.20 | | | REF_CLOSE: (3), (17), (25) are inconsistent by sub-proof #664.
% 136.14/20.20 | | |
% 136.14/20.20 | | Case 2:
% 136.14/20.20 | | |
% 136.14/20.20 | | | (26) all_57_13 = e0 & op(e0, e2) = e0
% 136.14/20.20 | | |
% 136.14/20.20 | | | ALPHA: (26) implies:
% 136.14/20.20 | | | (27) all_57_13 = e0
% 136.14/20.20 | | |
% 136.14/20.20 | | | BETA: splitting (13) gives:
% 136.14/20.20 | | |
% 136.14/20.20 | | | Case 1:
% 136.14/20.20 | | | |
% 136.14/20.20 | | | | (28) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2)
% 136.14/20.20 | | | | = e1)
% 136.14/20.20 | | | |
% 136.14/20.20 | | | | BETA: splitting (28) gives:
% 136.14/20.20 | | | |
% 136.14/20.20 | | | | Case 1:
% 136.14/20.20 | | | | |
% 136.14/20.20 | | | | | (29) all_57_1 = e1 & op(e3, e2) = e1
% 136.14/20.20 | | | | |
% 136.14/20.20 | | | | | ALPHA: (29) implies:
% 136.14/20.20 | | | | | (30) all_57_1 = e1
% 136.14/20.20 | | | | | (31) op(e3, e2) = e1
% 136.14/20.20 | | | | |
% 136.14/20.20 | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (11), (12), (14), (15),
% 136.14/20.20 | | | | | (16), (18), (30), (31) are inconsistent by sub-proof #610.
% 136.14/20.20 | | | | |
% 136.14/20.20 | | | | Case 2:
% 136.14/20.20 | | | | |
% 136.14/20.20 | | | | | (32) all_57_3 = e1 & op(e2, e2) = e1
% 136.14/20.20 | | | | |
% 136.14/20.20 | | | | | ALPHA: (32) implies:
% 136.14/20.20 | | | | | (33) op(e2, e2) = e1
% 136.14/20.20 | | | | |
% 136.14/20.20 | | | | | REF_CLOSE: (6), (10), (15), (33) are inconsistent by sub-proof #325.
% 136.14/20.20 | | | | |
% 136.14/20.20 | | | | End of split
% 136.14/20.20 | | | |
% 136.14/20.20 | | | Case 2:
% 136.14/20.20 | | | |
% 136.14/20.20 | | | | (34) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2)
% 136.14/20.20 | | | | = e1)
% 136.14/20.20 | | | |
% 136.14/20.20 | | | | BETA: splitting (34) gives:
% 136.14/20.20 | | | |
% 136.14/20.20 | | | | Case 1:
% 136.14/20.20 | | | | |
% 136.14/20.20 | | | | | (35) all_57_7 = e1 & op(e1, e2) = e1
% 136.14/20.20 | | | | |
% 136.14/20.20 | | | | | REF_CLOSE: (7), (17), (35) are inconsistent by sub-proof #727.
% 136.14/20.20 | | | | |
% 136.14/20.20 | | | | Case 2:
% 136.14/20.20 | | | | |
% 136.14/20.20 | | | | | (36) all_57_13 = e1 & op(e0, e2) = e1
% 136.14/20.20 | | | | |
% 136.14/20.20 | | | | | ALPHA: (36) implies:
% 136.14/20.20 | | | | | (37) all_57_13 = e1
% 136.14/20.20 | | | | |
% 136.14/20.20 | | | | | REF_CLOSE: (16), (27), (37) are inconsistent by sub-proof #681.
% 136.14/20.20 | | | | |
% 136.14/20.20 | | | | End of split
% 136.14/20.20 | | | |
% 136.14/20.20 | | | End of split
% 136.14/20.20 | | |
% 136.14/20.20 | | End of split
% 136.14/20.20 | |
% 136.14/20.20 | End of split
% 136.14/20.20 |
% 136.14/20.20 End of proof
% 136.14/20.20
% 136.14/20.20 Sub-proof #309 shows that the following formulas are inconsistent:
% 136.14/20.20 ----------------------------------------------------------------
% 136.14/20.20 (1) all_57_1 = e0 & op(e3, e2) = e0
% 136.14/20.20 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.20 (3) op(e3, e2) = all_22_0
% 136.14/20.20 (4) ~ (all_22_0 = e0)
% 136.14/20.20
% 136.14/20.20 Begin of proof
% 136.14/20.20 |
% 136.14/20.20 | ALPHA: (1) implies:
% 136.14/20.20 | (5) op(e3, e2) = e0
% 136.14/20.20 |
% 136.14/20.20 | GROUND_INST: instantiating (2) with e0, all_22_0, e2, e3, simplifying with
% 136.14/20.20 | (3), (5) gives:
% 136.14/20.20 | (6) all_22_0 = e0
% 136.14/20.20 |
% 136.14/20.20 | REDUCE: (4), (6) imply:
% 136.14/20.20 | (7) $false
% 136.14/20.20 |
% 136.14/20.20 | CLOSE: (7) is inconsistent.
% 136.14/20.20 |
% 136.14/20.20 End of proof
% 136.14/20.20
% 136.14/20.20 Sub-proof #310 shows that the following formulas are inconsistent:
% 136.14/20.20 ----------------------------------------------------------------
% 136.14/20.20 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.20 (2) ~ (all_52_9 = e3)
% 136.14/20.20 (3) op(e2, e1) = all_52_9
% 136.14/20.20 (4) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3)
% 136.14/20.20 (5) op(e3, e1) = all_52_8
% 136.14/20.20 (6) ~ (all_52_8 = e3)
% 136.14/20.20
% 136.14/20.20 Begin of proof
% 136.14/20.20 |
% 136.14/20.20 | BETA: splitting (4) gives:
% 136.14/20.20 |
% 136.14/20.20 | Case 1:
% 136.14/20.20 | |
% 136.14/20.20 | | (7) all_57_4 = e3 & op(e3, e1) = e3
% 136.14/20.20 | |
% 136.14/20.20 | | ALPHA: (7) implies:
% 136.14/20.20 | | (8) op(e3, e1) = e3
% 136.14/20.20 | |
% 136.14/20.20 | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #705.
% 136.14/20.20 | |
% 136.14/20.20 | Case 2:
% 136.14/20.20 | |
% 136.14/20.20 | | (9) all_57_5 = e3 & op(e2, e1) = e3
% 136.14/20.20 | |
% 136.14/20.20 | | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #547.
% 136.14/20.20 | |
% 136.14/20.20 | End of split
% 136.14/20.20 |
% 136.14/20.20 End of proof
% 136.14/20.20
% 136.14/20.20 Sub-proof #311 shows that the following formulas are inconsistent:
% 136.14/20.20 ----------------------------------------------------------------
% 136.14/20.20 (1) ~ (all_52_13 = e0)
% 136.14/20.20 (2) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 136.14/20.20 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.20 (4) ~ (all_52_1 = all_52_13)
% 136.14/20.20 (5) ~ (all_52_13 = e3)
% 136.14/20.20 (6) all_54_6 = all_52_9
% 136.14/20.20 (7) op(e2, e3) = all_52_1
% 136.14/20.20 (8) all_54_7 = all_52_13
% 136.14/20.20 (9) ~ (all_52_9 = e0)
% 136.14/20.20 (10) op(e2, e3) = e2
% 136.14/20.20 (11) all_54_6 = e1 | all_54_6 = e0
% 136.14/20.20 (12) ~ (all_52_9 = all_52_13)
% 136.14/20.20
% 136.14/20.20 Begin of proof
% 136.14/20.20 |
% 136.14/20.20 | BETA: splitting (11) gives:
% 136.14/20.20 |
% 136.14/20.20 | Case 1:
% 136.14/20.20 | |
% 136.14/20.20 | | (13) all_54_6 = e1
% 136.14/20.20 | |
% 136.14/20.20 | | COMBINE_EQS: (6), (13) imply:
% 136.14/20.20 | | (14) all_52_9 = e1
% 136.14/20.20 | |
% 136.14/20.20 | | SIMP: (14) implies:
% 136.14/20.20 | | (15) all_52_9 = e1
% 136.14/20.20 | |
% 136.14/20.20 | | REDUCE: (12), (15) imply:
% 136.14/20.20 | | (16) ~ (all_52_13 = e1)
% 136.14/20.20 | |
% 136.14/20.20 | | SIMP: (16) implies:
% 136.14/20.20 | | (17) ~ (all_52_13 = e1)
% 136.14/20.20 | |
% 136.14/20.20 | | BETA: splitting (2) gives:
% 136.14/20.20 | |
% 136.14/20.20 | | Case 1:
% 136.14/20.20 | | |
% 136.14/20.20 | | | (18) all_54_7 = e3
% 136.14/20.20 | | |
% 136.14/20.20 | | | REF_CLOSE: (5), (8), (18) are inconsistent by sub-proof #338.
% 136.14/20.20 | | |
% 136.14/20.20 | | Case 2:
% 136.14/20.20 | | |
% 136.14/20.20 | | | (19) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 136.14/20.20 | | |
% 136.14/20.20 | | | REF_CLOSE: (1), (3), (4), (7), (8), (10), (17), (19) are inconsistent by
% 136.14/20.20 | | | sub-proof #312.
% 136.14/20.20 | | |
% 136.14/20.20 | | End of split
% 136.14/20.20 | |
% 136.14/20.20 | Case 2:
% 136.14/20.20 | |
% 136.14/20.20 | | (20) all_54_6 = e0
% 136.14/20.20 | |
% 136.14/20.20 | | REF_CLOSE: (6), (9), (20) are inconsistent by sub-proof #480.
% 136.14/20.20 | |
% 136.14/20.20 | End of split
% 136.14/20.20 |
% 136.14/20.20 End of proof
% 136.14/20.20
% 136.14/20.20 Sub-proof #312 shows that the following formulas are inconsistent:
% 136.14/20.20 ----------------------------------------------------------------
% 136.14/20.20 (1) ~ (all_52_13 = e0)
% 136.14/20.20 (2) ~ (all_52_13 = e1)
% 136.14/20.20 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.20 (4) ~ (all_52_1 = all_52_13)
% 136.14/20.20 (5) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 136.14/20.20 (6) op(e2, e3) = all_52_1
% 136.14/20.20 (7) all_54_7 = all_52_13
% 136.14/20.20 (8) op(e2, e3) = e2
% 136.14/20.20
% 136.14/20.20 Begin of proof
% 136.14/20.20 |
% 136.14/20.20 | BETA: splitting (5) gives:
% 136.14/20.20 |
% 136.14/20.20 | Case 1:
% 136.14/20.20 | |
% 136.14/20.20 | | (9) all_54_7 = e2
% 136.14/20.20 | |
% 136.14/20.20 | | COMBINE_EQS: (7), (9) imply:
% 136.14/20.20 | | (10) all_52_13 = e2
% 136.14/20.20 | |
% 136.14/20.20 | | SIMP: (10) implies:
% 136.14/20.20 | | (11) all_52_13 = e2
% 136.14/20.20 | |
% 136.14/20.20 | | REDUCE: (4), (11) imply:
% 136.14/20.20 | | (12) ~ (all_52_1 = e2)
% 136.14/20.20 | |
% 136.14/20.20 | | REF_CLOSE: (3), (6), (8), (12) are inconsistent by sub-proof #779.
% 136.14/20.20 | |
% 136.14/20.20 | Case 2:
% 136.14/20.20 | |
% 136.14/20.20 | | (13) all_54_7 = e1 | all_54_7 = e0
% 136.14/20.20 | |
% 136.14/20.20 | | REF_CLOSE: (1), (2), (7), (13) are inconsistent by sub-proof #313.
% 136.14/20.20 | |
% 136.14/20.20 | End of split
% 136.14/20.20 |
% 136.14/20.20 End of proof
% 136.14/20.20
% 136.14/20.20 Sub-proof #313 shows that the following formulas are inconsistent:
% 136.14/20.20 ----------------------------------------------------------------
% 136.14/20.20 (1) all_54_7 = e1 | all_54_7 = e0
% 136.14/20.20 (2) all_54_7 = all_52_13
% 136.14/20.20 (3) ~ (all_52_13 = e1)
% 136.14/20.20 (4) ~ (all_52_13 = e0)
% 136.14/20.20
% 136.14/20.20 Begin of proof
% 136.14/20.20 |
% 136.14/20.20 | BETA: splitting (1) gives:
% 136.14/20.20 |
% 136.14/20.20 | Case 1:
% 136.14/20.20 | |
% 136.14/20.20 | | (5) all_54_7 = e1
% 136.14/20.20 | |
% 136.14/20.20 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #314.
% 136.14/20.20 | |
% 136.14/20.20 | Case 2:
% 136.14/20.20 | |
% 136.14/20.20 | | (6) all_54_7 = e0
% 136.14/20.20 | |
% 136.14/20.20 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #326.
% 136.14/20.20 | |
% 136.14/20.20 | End of split
% 136.14/20.20 |
% 136.14/20.20 End of proof
% 136.14/20.20
% 136.14/20.20 Sub-proof #314 shows that the following formulas are inconsistent:
% 136.14/20.20 ----------------------------------------------------------------
% 136.14/20.20 (1) all_54_7 = all_52_13
% 136.14/20.20 (2) all_54_7 = e1
% 136.14/20.20 (3) ~ (all_52_13 = e1)
% 136.14/20.20
% 136.14/20.20 Begin of proof
% 136.14/20.20 |
% 136.14/20.20 | COMBINE_EQS: (1), (2) imply:
% 136.14/20.20 | (4) all_52_13 = e1
% 136.14/20.20 |
% 136.14/20.20 | SIMP: (4) implies:
% 136.14/20.20 | (5) all_52_13 = e1
% 136.14/20.20 |
% 136.14/20.20 | REDUCE: (3), (5) imply:
% 136.14/20.20 | (6) $false
% 136.14/20.20 |
% 136.14/20.20 | CLOSE: (6) is inconsistent.
% 136.14/20.20 |
% 136.14/20.20 End of proof
% 136.14/20.20
% 136.14/20.20 Sub-proof #315 shows that the following formulas are inconsistent:
% 136.14/20.20 ----------------------------------------------------------------
% 136.14/20.20 (1) all_54_6 = all_52_9
% 136.14/20.20 (2) all_54_6 = e3
% 136.14/20.20 (3) ~ (all_52_9 = e3)
% 136.14/20.20
% 136.14/20.20 Begin of proof
% 136.14/20.20 |
% 136.14/20.20 | COMBINE_EQS: (1), (2) imply:
% 136.14/20.20 | (4) all_52_9 = e3
% 136.14/20.20 |
% 136.14/20.20 | SIMP: (4) implies:
% 136.14/20.20 | (5) all_52_9 = e3
% 136.14/20.20 |
% 136.14/20.20 | REDUCE: (3), (5) imply:
% 136.14/20.20 | (6) $false
% 136.14/20.20 |
% 136.14/20.20 | CLOSE: (6) is inconsistent.
% 136.14/20.20 |
% 136.14/20.20 End of proof
% 136.14/20.20
% 136.14/20.20 Sub-proof #316 shows that the following formulas are inconsistent:
% 136.14/20.20 ----------------------------------------------------------------
% 136.14/20.20 (1) all_54_2 = all_52_8
% 136.14/20.20 (2) all_54_2 = e1
% 136.14/20.20 (3) ~ (all_52_8 = e1)
% 136.14/20.20
% 136.14/20.20 Begin of proof
% 136.14/20.20 |
% 136.14/20.20 | COMBINE_EQS: (1), (2) imply:
% 136.14/20.20 | (4) all_52_8 = e1
% 136.14/20.20 |
% 136.14/20.20 | SIMP: (4) implies:
% 136.14/20.20 | (5) all_52_8 = e1
% 136.14/20.20 |
% 136.14/20.20 | REDUCE: (3), (5) imply:
% 136.14/20.20 | (6) $false
% 136.14/20.20 |
% 136.14/20.20 | CLOSE: (6) is inconsistent.
% 136.14/20.20 |
% 136.14/20.20 End of proof
% 136.14/20.20
% 136.14/20.20 Sub-proof #317 shows that the following formulas are inconsistent:
% 136.14/20.20 ----------------------------------------------------------------
% 136.14/20.20 (1) all_54_2 = all_52_8
% 136.14/20.20 (2) all_54_2 = e2
% 136.14/20.20 (3) ~ (all_52_8 = e2)
% 136.14/20.20
% 136.14/20.20 Begin of proof
% 136.14/20.20 |
% 136.14/20.20 | COMBINE_EQS: (1), (2) imply:
% 136.14/20.20 | (4) all_52_8 = e2
% 136.14/20.20 |
% 136.14/20.20 | SIMP: (4) implies:
% 136.14/20.20 | (5) all_52_8 = e2
% 136.14/20.20 |
% 136.14/20.20 | REDUCE: (3), (5) imply:
% 136.14/20.20 | (6) $false
% 136.14/20.20 |
% 136.14/20.20 | CLOSE: (6) is inconsistent.
% 136.14/20.20 |
% 136.14/20.20 End of proof
% 136.14/20.20
% 136.14/20.20 Sub-proof #318 shows that the following formulas are inconsistent:
% 136.14/20.20 ----------------------------------------------------------------
% 136.14/20.20 (1) ~ (all_52_12 = e1)
% 136.14/20.20 (2) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2)
% 136.14/20.20 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3,
% 136.14/20.20 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 136.14/20.20 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 136.14/20.20 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 136.14/20.20 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.14/20.20 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) =
% 136.14/20.20 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.14/20.20 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 136.14/20.20 $i(all_56_21) & $i(all_56_29))
% 136.14/20.20 (3) op(e3, e3) = e1
% 136.14/20.20 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.20 (5) ~ (e2 = e1)
% 136.14/20.20 (6) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 136.14/20.20 (7) all_54_3 = all_52_12
% 136.14/20.20 (8) ~ (all_52_12 = e0)
% 136.14/20.20 (9) ~ (all_52_8 = all_52_12)
% 136.14/20.20 (10) ~ (all_52_12 = e2)
% 136.14/20.20 (11) op(e3, e1) = all_52_8
% 136.14/20.20
% 136.14/20.20 Begin of proof
% 136.14/20.20 |
% 136.14/20.20 | BETA: splitting (2) gives:
% 136.14/20.20 |
% 136.14/20.20 | Case 1:
% 136.14/20.20 | |
% 136.14/20.20 | | (12) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 136.14/20.20 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2
% 136.14/20.20 | | & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 136.14/20.20 | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 136.14/20.20 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)
% 136.14/20.20 | |
% 136.14/20.20 | | ALPHA: (12) implies:
% 136.14/20.20 | | (13) op(e3, e3) = e2
% 136.14/20.20 | |
% 136.14/20.20 | | REF_CLOSE: (3), (4), (5), (13) are inconsistent by sub-proof #743.
% 136.14/20.20 | |
% 136.14/20.20 | Case 2:
% 136.14/20.20 | |
% 136.14/20.20 | | (14) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13
% 136.14/20.20 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) =
% 136.14/20.20 | | e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 136.14/20.20 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 136.14/20.20 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 136.14/20.20 | |
% 136.14/20.20 | | ALPHA: (14) implies:
% 136.14/20.20 | | (15) op(e3, e1) = e3
% 136.14/20.20 | |
% 136.14/20.20 | | REF_CLOSE: (1), (4), (6), (7), (8), (9), (10), (11), (15) are inconsistent
% 136.14/20.20 | | by sub-proof #319.
% 136.14/20.20 | |
% 136.14/20.20 | End of split
% 136.14/20.20 |
% 136.14/20.20 End of proof
% 136.14/20.20
% 136.14/20.20 Sub-proof #319 shows that the following formulas are inconsistent:
% 136.14/20.20 ----------------------------------------------------------------
% 136.14/20.20 (1) ~ (all_52_12 = e1)
% 136.14/20.20 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.20 (3) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 136.14/20.20 (4) all_54_3 = all_52_12
% 136.14/20.20 (5) ~ (all_52_12 = e0)
% 136.14/20.20 (6) ~ (all_52_8 = all_52_12)
% 136.14/20.20 (7) ~ (all_52_12 = e2)
% 136.14/20.20 (8) op(e3, e1) = all_52_8
% 136.14/20.20 (9) op(e3, e1) = e3
% 136.14/20.20
% 136.14/20.20 Begin of proof
% 136.14/20.20 |
% 136.14/20.20 | BETA: splitting (3) gives:
% 136.14/20.20 |
% 136.14/20.20 | Case 1:
% 136.14/20.20 | |
% 136.14/20.20 | | (10) all_54_3 = e3
% 136.14/20.20 | |
% 136.14/20.20 | | COMBINE_EQS: (4), (10) imply:
% 136.14/20.20 | | (11) all_52_12 = e3
% 136.14/20.20 | |
% 136.14/20.20 | | REDUCE: (6), (11) imply:
% 136.14/20.20 | | (12) ~ (all_52_8 = e3)
% 136.14/20.20 | |
% 136.14/20.20 | | REF_CLOSE: (2), (8), (9), (12) are inconsistent by sub-proof #705.
% 136.14/20.20 | |
% 136.14/20.20 | Case 2:
% 136.14/20.20 | |
% 136.14/20.20 | | (13) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 136.14/20.20 | |
% 136.14/20.20 | | REF_CLOSE: (1), (4), (5), (7), (13) are inconsistent by sub-proof #320.
% 136.14/20.20 | |
% 136.14/20.20 | End of split
% 136.14/20.20 |
% 136.14/20.20 End of proof
% 136.14/20.20
% 136.14/20.20 Sub-proof #320 shows that the following formulas are inconsistent:
% 136.14/20.20 ----------------------------------------------------------------
% 136.14/20.20 (1) ~ (all_52_12 = e1)
% 136.14/20.20 (2) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 136.14/20.20 (3) all_54_3 = all_52_12
% 136.14/20.20 (4) ~ (all_52_12 = e0)
% 136.14/20.20 (5) ~ (all_52_12 = e2)
% 136.14/20.20
% 136.14/20.20 Begin of proof
% 136.14/20.20 |
% 136.14/20.20 | BETA: splitting (2) gives:
% 136.14/20.20 |
% 136.14/20.20 | Case 1:
% 136.14/20.20 | |
% 136.14/20.20 | | (6) all_54_3 = e2
% 136.14/20.20 | |
% 136.14/20.20 | | COMBINE_EQS: (3), (6) imply:
% 136.14/20.20 | | (7) all_52_12 = e2
% 136.14/20.20 | |
% 136.14/20.20 | | REDUCE: (5), (7) imply:
% 136.14/20.20 | | (8) $false
% 136.14/20.20 | |
% 136.14/20.20 | | CLOSE: (8) is inconsistent.
% 136.14/20.20 | |
% 136.14/20.20 | Case 2:
% 136.14/20.20 | |
% 136.14/20.20 | | (9) all_54_3 = e1 | all_54_3 = e0
% 136.14/20.20 | |
% 136.14/20.20 | | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #321.
% 136.14/20.20 | |
% 136.14/20.20 | End of split
% 136.14/20.20 |
% 136.14/20.20 End of proof
% 136.14/20.20
% 136.14/20.20 Sub-proof #321 shows that the following formulas are inconsistent:
% 136.14/20.20 ----------------------------------------------------------------
% 136.14/20.20 (1) all_54_3 = e1 | all_54_3 = e0
% 136.14/20.20 (2) all_54_3 = all_52_12
% 136.14/20.20 (3) ~ (all_52_12 = e1)
% 136.14/20.20 (4) ~ (all_52_12 = e0)
% 136.14/20.20
% 136.14/20.20 Begin of proof
% 136.14/20.20 |
% 136.14/20.20 | BETA: splitting (1) gives:
% 136.14/20.20 |
% 136.14/20.20 | Case 1:
% 136.14/20.20 | |
% 136.14/20.20 | | (5) all_54_3 = e1
% 136.14/20.20 | |
% 136.14/20.20 | | COMBINE_EQS: (2), (5) imply:
% 136.14/20.20 | | (6) all_52_12 = e1
% 136.14/20.20 | |
% 136.14/20.20 | | REDUCE: (3), (6) imply:
% 136.14/20.20 | | (7) $false
% 136.14/20.20 | |
% 136.14/20.20 | | CLOSE: (7) is inconsistent.
% 136.14/20.20 | |
% 136.14/20.20 | Case 2:
% 136.14/20.20 | |
% 136.14/20.20 | | (8) all_54_3 = e0
% 136.14/20.20 | |
% 136.14/20.20 | | COMBINE_EQS: (2), (8) imply:
% 136.14/20.20 | | (9) all_52_12 = e0
% 136.14/20.20 | |
% 136.14/20.20 | | REDUCE: (4), (9) imply:
% 136.14/20.20 | | (10) $false
% 136.14/20.20 | |
% 136.14/20.20 | | CLOSE: (10) is inconsistent.
% 136.14/20.20 | |
% 136.14/20.20 | End of split
% 136.14/20.20 |
% 136.14/20.20 End of proof
% 136.14/20.20
% 136.14/20.20 Sub-proof #322 shows that the following formulas are inconsistent:
% 136.14/20.20 ----------------------------------------------------------------
% 136.14/20.20 (1) ~ (all_4_2 = e2)
% 136.14/20.20 (2) ~ (all_4_2 = e1)
% 136.14/20.20 (3) ~ (all_4_2 = e3)
% 136.14/20.20 (4) all_54_15 = all_4_2
% 136.14/20.20 (5) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 136.14/20.20 (6) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2)
% 136.14/20.20 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 136.14/20.20 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25
% 136.14/20.20 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 136.14/20.20 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3)
% 136.14/20.20 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.14/20.20 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 136.14/20.20 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) &
% 136.14/20.20 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 &
% 136.14/20.20 all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~
% 136.14/20.20 (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) =
% 136.14/20.20 e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) =
% 136.14/20.20 all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23
% 136.14/20.20 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.14/20.20 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1,
% 136.14/20.20 e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 136.14/20.20 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.14/20.20 $i(all_56_29))
% 136.14/20.20 (7) all_56_31 = all_4_2
% 136.14/20.20
% 136.14/20.20 Begin of proof
% 136.14/20.20 |
% 136.14/20.20 | BETA: splitting (5) gives:
% 136.14/20.20 |
% 136.14/20.20 | Case 1:
% 136.14/20.20 | |
% 136.14/20.20 | | (8) all_54_15 = e3
% 136.14/20.20 | |
% 136.14/20.21 | | COMBINE_EQS: (4), (8) imply:
% 136.14/20.21 | | (9) all_4_2 = e3
% 136.14/20.21 | |
% 136.14/20.21 | | REDUCE: (3), (9) imply:
% 136.14/20.21 | | (10) $false
% 136.14/20.21 | |
% 136.14/20.21 | | CLOSE: (10) is inconsistent.
% 136.14/20.21 | |
% 136.14/20.21 | Case 2:
% 136.14/20.21 | |
% 136.14/20.21 | | (11) ~ (all_54_15 = e3)
% 136.14/20.21 | | (12) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 136.14/20.21 | |
% 136.14/20.21 | | BETA: splitting (6) gives:
% 136.14/20.21 | |
% 136.14/20.21 | | Case 1:
% 136.14/20.21 | | |
% 136.14/20.21 | | | (13) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 136.14/20.21 | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 136.14/20.21 | | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) =
% 136.14/20.21 | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 136.14/20.21 | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.14/20.21 | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 136.14/20.21 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.14/20.21 | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.14/20.21 | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.14/20.21 | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27))
% 136.14/20.21 | | |
% 136.14/20.21 | | | BETA: splitting (13) gives:
% 136.14/20.21 | | |
% 136.14/20.21 | | | Case 1:
% 136.14/20.21 | | | |
% 136.14/20.21 | | | | (14) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 136.14/20.21 | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 136.14/20.21 | | | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) =
% 136.14/20.21 | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 136.14/20.21 | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)
% 136.14/20.21 | | | |
% 136.14/20.21 | | | | ALPHA: (14) implies:
% 136.14/20.21 | | | | (15) all_56_31 = e3
% 136.14/20.21 | | | |
% 136.14/20.21 | | | | COMBINE_EQS: (7), (15) imply:
% 136.14/20.21 | | | | (16) all_4_2 = e3
% 136.14/20.21 | | | |
% 136.14/20.21 | | | | REDUCE: (3), (16) imply:
% 136.14/20.21 | | | | (17) $false
% 136.14/20.21 | | | |
% 136.14/20.21 | | | | CLOSE: (17) is inconsistent.
% 136.14/20.21 | | | |
% 136.14/20.21 | | | Case 2:
% 136.14/20.21 | | | |
% 136.14/20.21 | | | | (18) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 136.14/20.21 | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.14/20.21 | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.14/20.21 | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.14/20.21 | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)
% 136.14/20.21 | | | |
% 136.14/20.21 | | | | REF_CLOSE: (1), (7), (18) are inconsistent by sub-proof #765.
% 136.14/20.21 | | | |
% 136.14/20.21 | | | End of split
% 136.14/20.21 | | |
% 136.14/20.21 | | Case 2:
% 136.14/20.21 | | |
% 136.14/20.21 | | | (19) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.14/20.21 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.14/20.21 | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 136.14/20.21 | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 136.14/20.21 | | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 =
% 136.14/20.21 | | | e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 136.14/20.21 | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 136.14/20.21 | | | = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 136.14/20.21 | | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.14/20.21 | | | $i(all_56_29))
% 136.14/20.21 | | |
% 136.14/20.21 | | | BETA: splitting (19) gives:
% 136.14/20.21 | | |
% 136.14/20.21 | | | Case 1:
% 136.14/20.21 | | | |
% 136.14/20.21 | | | | (20) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.14/20.21 | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.14/20.21 | | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 136.14/20.21 | | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 136.14/20.21 | | | | $i(all_56_15) & $i(all_56_23)
% 136.14/20.21 | | | |
% 136.14/20.21 | | | | ALPHA: (20) implies:
% 136.14/20.21 | | | | (21) ~ (all_56_31 = e0)
% 136.14/20.21 | | | |
% 136.14/20.21 | | | | REDUCE: (7), (21) imply:
% 136.14/20.21 | | | | (22) ~ (all_4_2 = e0)
% 136.14/20.21 | | | |
% 136.14/20.21 | | | | REF_CLOSE: (1), (2), (4), (12), (22) are inconsistent by sub-proof #746.
% 136.14/20.21 | | | |
% 136.14/20.21 | | | Case 2:
% 136.14/20.21 | | | |
% 136.14/20.21 | | | | (23) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 136.14/20.21 | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 136.14/20.21 | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.14/20.21 | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 136.14/20.21 | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 136.14/20.21 | | | |
% 136.14/20.21 | | | | REF_CLOSE: (2), (7), (23) are inconsistent by sub-proof #745.
% 136.14/20.21 | | | |
% 136.14/20.21 | | | End of split
% 136.14/20.21 | | |
% 136.14/20.21 | | End of split
% 136.14/20.21 | |
% 136.14/20.21 | End of split
% 136.14/20.21 |
% 136.14/20.21 End of proof
% 136.14/20.21
% 136.14/20.21 Sub-proof #323 shows that the following formulas are inconsistent:
% 136.14/20.21 ----------------------------------------------------------------
% 136.14/20.21 (1) ~ (all_52_6 = e3)
% 136.14/20.21 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.21 (3) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3)
% 136.14/20.21 (4) op(e1, e2) = all_52_6
% 136.14/20.21 (5) ~ (all_52_2 = e3)
% 136.14/20.21 (6) op(e1, e3) = all_52_2
% 136.14/20.21
% 136.14/20.21 Begin of proof
% 136.14/20.21 |
% 136.14/20.21 | BETA: splitting (3) gives:
% 136.14/20.21 |
% 136.14/20.21 | Case 1:
% 136.14/20.21 | |
% 136.14/20.21 | | (7) all_57_6 = e3 & op(e1, e3) = e3
% 136.14/20.21 | |
% 136.14/20.21 | | REF_CLOSE: (2), (5), (6), (7) are inconsistent by sub-proof #761.
% 136.14/20.21 | |
% 136.14/20.21 | Case 2:
% 136.14/20.21 | |
% 136.14/20.21 | | (8) all_57_7 = e3 & op(e1, e2) = e3
% 136.14/20.21 | |
% 136.14/20.21 | | ALPHA: (8) implies:
% 136.14/20.21 | | (9) op(e1, e2) = e3
% 136.14/20.21 | |
% 136.14/20.21 | | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #654.
% 136.14/20.21 | |
% 136.14/20.21 | End of split
% 136.14/20.21 |
% 136.14/20.21 End of proof
% 136.14/20.21
% 136.14/20.21 Sub-proof #324 shows that the following formulas are inconsistent:
% 136.14/20.21 ----------------------------------------------------------------
% 136.14/20.21 (1) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2)
% 136.14/20.21 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 136.14/20.21 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25
% 136.14/20.21 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 136.14/20.21 $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~
% 136.14/20.21 (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 136.14/20.21 (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 136.14/20.21 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 136.14/20.21 = all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.14/20.21 $i(all_56_29))
% 136.14/20.21 (2) op(e1, e1) = all_6_2
% 136.14/20.21 (3) ~ (all_6_2 = e3)
% 136.14/20.21 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.21 (5) op(e2, e2) = e3
% 136.14/20.21 (6) ~ (e3 = e1)
% 136.14/20.21
% 136.14/20.21 Begin of proof
% 136.14/20.21 |
% 136.14/20.21 | BETA: splitting (1) gives:
% 136.14/20.21 |
% 136.14/20.21 | Case 1:
% 136.14/20.21 | |
% 136.14/20.21 | | (7) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.14/20.21 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.14/20.21 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.14/20.21 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1)
% 136.14/20.21 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)
% 136.14/20.21 | |
% 136.14/20.21 | | ALPHA: (7) implies:
% 136.14/20.21 | | (8) op(e1, e1) = e3
% 136.14/20.21 | |
% 136.14/20.21 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #771.
% 136.14/20.21 | |
% 136.14/20.21 | Case 2:
% 136.14/20.21 | |
% 136.14/20.21 | | (9) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13
% 136.14/20.21 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1
% 136.14/20.21 | | & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 136.14/20.21 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 136.14/20.21 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 136.14/20.21 | |
% 136.14/20.21 | | ALPHA: (9) implies:
% 136.14/20.21 | | (10) op(e2, e2) = e1
% 136.14/20.21 | |
% 136.14/20.21 | | REF_CLOSE: (4), (5), (6), (10) are inconsistent by sub-proof #325.
% 136.14/20.21 | |
% 136.14/20.21 | End of split
% 136.14/20.21 |
% 136.14/20.21 End of proof
% 136.14/20.21
% 136.14/20.21 Sub-proof #325 shows that the following formulas are inconsistent:
% 136.14/20.21 ----------------------------------------------------------------
% 136.14/20.21 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.21 (2) op(e2, e2) = e3
% 136.14/20.21 (3) op(e2, e2) = e1
% 136.14/20.21 (4) ~ (e3 = e1)
% 136.14/20.21
% 136.14/20.21 Begin of proof
% 136.14/20.21 |
% 136.14/20.21 | GROUND_INST: instantiating (1) with e3, e1, e2, e2, simplifying with (2), (3)
% 136.14/20.21 | gives:
% 136.14/20.21 | (5) e3 = e1
% 136.14/20.21 |
% 136.14/20.21 | REDUCE: (4), (5) imply:
% 136.14/20.21 | (6) $false
% 136.14/20.21 |
% 136.14/20.21 | CLOSE: (6) is inconsistent.
% 136.14/20.21 |
% 136.14/20.21 End of proof
% 136.14/20.21
% 136.14/20.21 Sub-proof #326 shows that the following formulas are inconsistent:
% 136.14/20.21 ----------------------------------------------------------------
% 136.14/20.21 (1) all_54_7 = all_52_13
% 136.14/20.21 (2) all_54_7 = e0
% 136.14/20.21 (3) ~ (all_52_13 = e0)
% 136.14/20.21
% 136.14/20.21 Begin of proof
% 136.14/20.21 |
% 136.14/20.21 | COMBINE_EQS: (1), (2) imply:
% 136.14/20.21 | (4) all_52_13 = e0
% 136.14/20.21 |
% 136.14/20.21 | SIMP: (4) implies:
% 136.14/20.21 | (5) all_52_13 = e0
% 136.14/20.21 |
% 136.14/20.21 | REDUCE: (3), (5) imply:
% 136.14/20.21 | (6) $false
% 136.14/20.21 |
% 136.14/20.21 | CLOSE: (6) is inconsistent.
% 136.14/20.21 |
% 136.14/20.21 End of proof
% 136.14/20.21
% 136.14/20.21 Sub-proof #327 shows that the following formulas are inconsistent:
% 136.14/20.21 ----------------------------------------------------------------
% 136.14/20.21 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.21 (2) op(e1, e0) = all_52_14
% 136.14/20.21 (3) op(e1, e0) = e1
% 136.14/20.21 (4) ~ (all_52_14 = e1)
% 136.14/20.21
% 136.14/20.21 Begin of proof
% 136.14/20.21 |
% 136.14/20.21 | GROUND_INST: instantiating (1) with all_52_14, e1, e0, e1, simplifying with
% 136.14/20.21 | (2), (3) gives:
% 136.14/20.21 | (5) all_52_14 = e1
% 136.14/20.21 |
% 136.14/20.21 | REDUCE: (4), (5) imply:
% 136.14/20.21 | (6) $false
% 136.14/20.21 |
% 136.14/20.21 | CLOSE: (6) is inconsistent.
% 136.14/20.21 |
% 136.14/20.21 End of proof
% 136.14/20.21
% 136.14/20.21 Sub-proof #328 shows that the following formulas are inconsistent:
% 136.14/20.21 ----------------------------------------------------------------
% 136.14/20.21 (1) op(e2, e0) = all_52_13
% 136.14/20.21 (2) ~ (all_52_14 = e3)
% 136.14/20.21 (3) op(e3, e3) = e2
% 136.14/20.21 (4) op(e3, e1) = all_56_17
% 136.14/20.21 (5) ( ~ (all_36_0 = e0) & op(e3, e1) = all_36_0 & $i(all_36_0)) | ( ~
% 136.14/20.21 (all_36_1 = e2) & op(e3, e3) = all_36_1 & $i(all_36_1))
% 136.14/20.21 (6) ~ (e2 = e0)
% 136.14/20.21 (7) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 136.14/20.21 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 136.14/20.21 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.21 (9) ~ (e2 = e1)
% 136.14/20.21 (10) ~ (e3 = e2)
% 136.14/20.21 (11) ~ (all_52_12 = e0)
% 136.14/20.21 (12) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 136.14/20.21 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 136.14/20.21 (13) op(e3, e0) = all_52_12
% 136.14/20.21 (14) ~ (all_52_13 = e3)
% 136.14/20.21 (15) op(e0, e0) = e2
% 136.14/20.21 (16) ~ (all_56_17 = e1)
% 136.14/20.21 (17) ~ (e3 = e1)
% 136.14/20.21 (18) ~ (e1 = e0)
% 136.14/20.21 (19) op(e1, e0) = all_52_14
% 136.14/20.21 (20) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 136.14/20.21 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 136.14/20.21
% 136.14/20.21 Begin of proof
% 136.14/20.21 |
% 136.14/20.21 | BETA: splitting (20) gives:
% 136.14/20.21 |
% 136.14/20.21 | Case 1:
% 136.14/20.21 | |
% 136.14/20.21 | | (21) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 136.14/20.21 | | e1)
% 136.14/20.21 | |
% 136.14/20.21 | | BETA: splitting (21) gives:
% 136.14/20.21 | |
% 136.14/20.21 | | Case 1:
% 136.14/20.21 | | |
% 136.14/20.21 | | | (22) all_57_0 = e1 & op(e3, e3) = e1
% 136.14/20.21 | | |
% 136.14/20.21 | | | ALPHA: (22) implies:
% 136.14/20.21 | | | (23) op(e3, e3) = e1
% 136.14/20.21 | | |
% 136.14/20.21 | | | REF_CLOSE: (3), (8), (9), (23) are inconsistent by sub-proof #743.
% 136.14/20.21 | | |
% 136.14/20.21 | | Case 2:
% 136.14/20.21 | | |
% 136.14/20.21 | | | (24) all_57_1 = e1 & op(e3, e2) = e1
% 136.14/20.21 | | |
% 136.14/20.21 | | | ALPHA: (24) implies:
% 136.14/20.21 | | | (25) op(e3, e2) = e1
% 136.14/20.21 | | |
% 136.14/20.21 | | | BETA: splitting (5) gives:
% 136.14/20.21 | | |
% 136.14/20.21 | | | Case 1:
% 136.14/20.21 | | | |
% 136.14/20.21 | | | | (26) ~ (all_36_0 = e0) & op(e3, e1) = all_36_0 & $i(all_36_0)
% 136.14/20.21 | | | |
% 136.14/20.21 | | | | ALPHA: (26) implies:
% 136.14/20.21 | | | | (27) ~ (all_36_0 = e0)
% 136.14/20.21 | | | | (28) op(e3, e1) = all_36_0
% 136.14/20.21 | | | |
% 136.14/20.21 | | | | BETA: splitting (7) gives:
% 136.14/20.21 | | | |
% 136.14/20.21 | | | | Case 1:
% 136.14/20.21 | | | | |
% 136.14/20.21 | | | | | (29) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3,
% 136.14/20.21 | | | | | e2) = e0)
% 136.14/20.21 | | | | |
% 136.14/20.21 | | | | | REF_CLOSE: (3), (6), (8), (18), (25), (29) are inconsistent by
% 136.14/20.21 | | | | | sub-proof #333.
% 136.14/20.21 | | | | |
% 136.14/20.21 | | | | Case 2:
% 136.14/20.21 | | | | |
% 136.14/20.21 | | | | | (30) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3,
% 136.14/20.21 | | | | | e0) = e0)
% 136.14/20.21 | | | | |
% 136.14/20.21 | | | | | BETA: splitting (30) gives:
% 136.14/20.21 | | | | |
% 136.14/20.21 | | | | | Case 1:
% 136.14/20.21 | | | | | |
% 136.14/20.21 | | | | | | (31) all_57_4 = e0 & op(e3, e1) = e0
% 136.14/20.21 | | | | | |
% 136.14/20.21 | | | | | | REF_CLOSE: (8), (27), (28), (31) are inconsistent by sub-proof #332.
% 136.14/20.21 | | | | | |
% 136.14/20.21 | | | | | Case 2:
% 136.14/20.21 | | | | | |
% 136.14/20.21 | | | | | | (32) all_57_9 = e0 & op(e3, e0) = e0
% 136.14/20.21 | | | | | |
% 136.14/20.21 | | | | | | REF_CLOSE: (8), (11), (13), (32) are inconsistent by sub-proof #618.
% 136.14/20.21 | | | | | |
% 136.14/20.21 | | | | | End of split
% 136.14/20.21 | | | | |
% 136.14/20.21 | | | | End of split
% 136.14/20.21 | | | |
% 136.14/20.21 | | | Case 2:
% 136.14/20.21 | | | |
% 136.14/20.21 | | | | (33) ~ (all_36_1 = e2) & op(e3, e3) = all_36_1 & $i(all_36_1)
% 136.14/20.21 | | | |
% 136.14/20.21 | | | | REF_CLOSE: (3), (8), (33) are inconsistent by sub-proof #342.
% 136.14/20.21 | | | |
% 136.14/20.21 | | | End of split
% 136.14/20.21 | | |
% 136.14/20.21 | | End of split
% 136.14/20.21 | |
% 136.14/20.21 | Case 2:
% 136.14/20.21 | |
% 136.14/20.21 | | (34) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 136.14/20.21 | | e1)
% 136.14/20.21 | |
% 136.14/20.21 | | BETA: splitting (34) gives:
% 136.14/20.21 | |
% 136.14/20.21 | | Case 1:
% 136.14/20.21 | | |
% 136.14/20.21 | | | (35) all_57_4 = e1 & op(e3, e1) = e1
% 136.14/20.21 | | |
% 136.14/20.21 | | | ALPHA: (35) implies:
% 136.14/20.21 | | | (36) op(e3, e1) = e1
% 136.14/20.21 | | |
% 136.14/20.21 | | | REF_CLOSE: (4), (8), (16), (36) are inconsistent by sub-proof #349.
% 136.14/20.21 | | |
% 136.14/20.21 | | Case 2:
% 136.14/20.21 | | |
% 136.14/20.21 | | | (37) all_57_9 = e1 & op(e3, e0) = e1
% 136.14/20.21 | | |
% 136.14/20.21 | | | ALPHA: (37) implies:
% 136.14/20.21 | | | (38) all_57_9 = e1
% 136.14/20.21 | | |
% 136.14/20.21 | | | REF_CLOSE: (1), (2), (8), (10), (12), (14), (15), (17), (19), (38) are
% 136.14/20.21 | | | inconsistent by sub-proof #329.
% 136.14/20.21 | | |
% 136.14/20.21 | | End of split
% 136.14/20.21 | |
% 136.14/20.21 | End of split
% 136.14/20.21 |
% 136.14/20.21 End of proof
% 136.14/20.21
% 136.14/20.21 Sub-proof #329 shows that the following formulas are inconsistent:
% 136.14/20.21 ----------------------------------------------------------------
% 136.14/20.21 (1) op(e2, e0) = all_52_13
% 136.14/20.21 (2) ~ (all_52_14 = e3)
% 136.14/20.21 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.21 (4) ~ (e3 = e2)
% 136.14/20.21 (5) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 136.14/20.21 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 136.14/20.21 (6) ~ (all_52_13 = e3)
% 136.14/20.21 (7) op(e0, e0) = e2
% 136.14/20.21 (8) all_57_9 = e1
% 136.14/20.21 (9) ~ (e3 = e1)
% 136.14/20.21 (10) op(e1, e0) = all_52_14
% 136.14/20.21
% 136.14/20.21 Begin of proof
% 136.14/20.21 |
% 136.14/20.21 | BETA: splitting (5) gives:
% 136.14/20.21 |
% 136.14/20.21 | Case 1:
% 136.14/20.21 | |
% 136.14/20.21 | | (11) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 136.14/20.21 | | e3)
% 136.14/20.21 | |
% 136.14/20.21 | | REF_CLOSE: (1), (3), (6), (8), (9), (11) are inconsistent by sub-proof #331.
% 136.14/20.21 | |
% 136.14/20.21 | Case 2:
% 136.14/20.21 | |
% 136.14/20.21 | | (12) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 136.14/20.21 | | e3)
% 136.14/20.21 | |
% 136.14/20.21 | | REF_CLOSE: (2), (3), (4), (7), (10), (12) are inconsistent by sub-proof
% 136.14/20.21 | | #330.
% 136.14/20.21 | |
% 136.14/20.21 | End of split
% 136.14/20.21 |
% 136.14/20.21 End of proof
% 136.14/20.21
% 136.14/20.21 Sub-proof #330 shows that the following formulas are inconsistent:
% 136.14/20.21 ----------------------------------------------------------------
% 136.14/20.21 (1) ~ (all_52_14 = e3)
% 136.14/20.21 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.21 (3) ~ (e3 = e2)
% 136.14/20.21 (4) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 136.14/20.21 (5) op(e0, e0) = e2
% 136.14/20.21 (6) op(e1, e0) = all_52_14
% 136.14/20.21
% 136.14/20.21 Begin of proof
% 136.14/20.21 |
% 136.14/20.21 | BETA: splitting (4) gives:
% 136.14/20.21 |
% 136.14/20.21 | Case 1:
% 136.14/20.21 | |
% 136.14/20.21 | | (7) all_57_11 = e3 & op(e1, e0) = e3
% 136.14/20.21 | |
% 136.14/20.21 | | REF_CLOSE: (1), (2), (6), (7) are inconsistent by sub-proof #750.
% 136.14/20.21 | |
% 136.14/20.21 | Case 2:
% 136.14/20.21 | |
% 136.14/20.21 | | (8) all_57_15 = e3 & op(e0, e0) = e3
% 136.14/20.21 | |
% 136.14/20.21 | | ALPHA: (8) implies:
% 136.14/20.21 | | (9) op(e0, e0) = e3
% 136.14/20.21 | |
% 136.14/20.21 | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #634.
% 136.14/20.21 | |
% 136.14/20.21 | End of split
% 136.14/20.21 |
% 136.14/20.21 End of proof
% 136.14/20.21
% 136.14/20.21 Sub-proof #331 shows that the following formulas are inconsistent:
% 136.14/20.21 ----------------------------------------------------------------
% 136.14/20.21 (1) op(e2, e0) = all_52_13
% 136.14/20.21 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.21 (3) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 136.14/20.21 (4) ~ (all_52_13 = e3)
% 136.14/20.21 (5) all_57_9 = e1
% 136.14/20.21 (6) ~ (e3 = e1)
% 136.14/20.21
% 136.14/20.21 Begin of proof
% 136.14/20.21 |
% 136.14/20.21 | BETA: splitting (3) gives:
% 136.14/20.21 |
% 136.14/20.21 | Case 1:
% 136.14/20.21 | |
% 136.14/20.21 | | (7) all_57_9 = e3 & op(e3, e0) = e3
% 136.14/20.21 | |
% 136.14/20.21 | | ALPHA: (7) implies:
% 136.14/20.21 | | (8) all_57_9 = e3
% 136.14/20.21 | |
% 136.14/20.21 | | REF_CLOSE: (5), (6), (8) are inconsistent by sub-proof #690.
% 136.14/20.21 | |
% 136.14/20.21 | Case 2:
% 136.14/20.21 | |
% 136.14/20.21 | | (9) all_57_10 = e3 & op(e2, e0) = e3
% 136.14/20.21 | |
% 136.14/20.21 | | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #749.
% 136.14/20.21 | |
% 136.14/20.21 | End of split
% 136.14/20.21 |
% 136.14/20.21 End of proof
% 136.14/20.21
% 136.14/20.21 Sub-proof #332 shows that the following formulas are inconsistent:
% 136.14/20.21 ----------------------------------------------------------------
% 136.14/20.21 (1) all_57_4 = e0 & op(e3, e1) = e0
% 136.14/20.21 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.21 (3) op(e3, e1) = all_36_0
% 136.14/20.21 (4) ~ (all_36_0 = e0)
% 136.14/20.21
% 136.14/20.21 Begin of proof
% 136.14/20.21 |
% 136.14/20.21 | ALPHA: (1) implies:
% 136.14/20.21 | (5) op(e3, e1) = e0
% 136.14/20.21 |
% 136.14/20.21 | GROUND_INST: instantiating (2) with e0, all_36_0, e1, e3, simplifying with
% 136.14/20.21 | (3), (5) gives:
% 136.14/20.21 | (6) all_36_0 = e0
% 136.14/20.21 |
% 136.14/20.21 | REDUCE: (4), (6) imply:
% 136.14/20.21 | (7) $false
% 136.14/20.21 |
% 136.14/20.21 | CLOSE: (7) is inconsistent.
% 136.14/20.21 |
% 136.14/20.21 End of proof
% 136.14/20.21
% 136.14/20.21 Sub-proof #333 shows that the following formulas are inconsistent:
% 136.14/20.21 ----------------------------------------------------------------
% 136.14/20.21 (1) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0)
% 136.14/20.21 (2) op(e3, e2) = e1
% 136.14/20.21 (3) op(e3, e3) = e2
% 136.14/20.21 (4) ~ (e2 = e0)
% 136.14/20.22 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.22 (6) ~ (e1 = e0)
% 136.14/20.22
% 136.14/20.22 Begin of proof
% 136.14/20.22 |
% 136.14/20.22 | BETA: splitting (1) gives:
% 136.14/20.22 |
% 136.14/20.22 | Case 1:
% 136.14/20.22 | |
% 136.14/20.22 | | (7) all_57_0 = e0 & op(e3, e3) = e0
% 136.14/20.22 | |
% 136.14/20.22 | | ALPHA: (7) implies:
% 136.14/20.22 | | (8) op(e3, e3) = e0
% 136.14/20.22 | |
% 136.14/20.22 | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #495.
% 136.14/20.22 | |
% 136.14/20.22 | Case 2:
% 136.14/20.22 | |
% 136.14/20.22 | | (9) all_57_1 = e0 & op(e3, e2) = e0
% 136.14/20.22 | |
% 136.14/20.22 | | ALPHA: (9) implies:
% 136.14/20.22 | | (10) op(e3, e2) = e0
% 136.14/20.22 | |
% 136.14/20.22 | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #730.
% 136.14/20.22 | |
% 136.14/20.22 | End of split
% 136.14/20.22 |
% 136.14/20.22 End of proof
% 136.14/20.22
% 136.14/20.22 Sub-proof #334 shows that the following formulas are inconsistent:
% 136.14/20.22 ----------------------------------------------------------------
% 136.14/20.22 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.22 (2) op(e2, e2) = all_26_1
% 136.14/20.22 (3) op(e2, e2) = e3
% 136.14/20.22 (4) ~ (all_26_1 = e3)
% 136.14/20.22
% 136.14/20.22 Begin of proof
% 136.14/20.22 |
% 136.14/20.22 | GROUND_INST: instantiating (1) with e3, all_26_1, e2, e2, simplifying with
% 136.14/20.22 | (2), (3) gives:
% 136.14/20.22 | (5) all_26_1 = e3
% 136.14/20.22 |
% 136.14/20.22 | REDUCE: (4), (5) imply:
% 136.14/20.22 | (6) $false
% 136.14/20.22 |
% 136.14/20.22 | CLOSE: (6) is inconsistent.
% 136.14/20.22 |
% 136.14/20.22 End of proof
% 136.14/20.22
% 136.14/20.22 Sub-proof #335 shows that the following formulas are inconsistent:
% 136.14/20.22 ----------------------------------------------------------------
% 136.14/20.22 (1) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2)
% 136.14/20.22 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3,
% 136.14/20.22 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 136.14/20.22 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 136.14/20.22 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 136.14/20.22 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.14/20.22 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) =
% 136.14/20.22 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.14/20.22 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 136.14/20.22 $i(all_56_21) & $i(all_56_29))
% 136.14/20.22 (2) op(e3, e3) = e2
% 136.14/20.22 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.22 (4) ~ (e2 = e1)
% 136.14/20.22 (5) op(e2, e3) = e3
% 136.14/20.22
% 136.14/20.22 Begin of proof
% 136.14/20.22 |
% 136.14/20.22 | BETA: splitting (1) gives:
% 136.14/20.22 |
% 136.14/20.22 | Case 1:
% 136.14/20.22 | |
% 136.14/20.22 | | (6) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 136.14/20.22 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 136.14/20.22 | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 136.14/20.22 | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 136.14/20.22 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)
% 136.14/20.22 | |
% 136.14/20.22 | | ALPHA: (6) implies:
% 136.14/20.22 | | (7) ~ (all_56_3 = e3)
% 136.14/20.22 | | (8) op(e2, e3) = all_56_3
% 136.14/20.22 | |
% 136.14/20.22 | | REF_CLOSE: (3), (5), (7), (8) are inconsistent by sub-proof #347.
% 136.14/20.22 | |
% 136.14/20.22 | Case 2:
% 136.14/20.22 | |
% 136.14/20.22 | | (9) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 136.14/20.22 | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 136.14/20.22 | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 136.14/20.22 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 136.14/20.22 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 136.14/20.22 | |
% 136.14/20.22 | | ALPHA: (9) implies:
% 136.14/20.22 | | (10) op(e3, e3) = e1
% 136.14/20.22 | |
% 136.14/20.22 | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #743.
% 136.14/20.22 | |
% 136.14/20.22 | End of split
% 136.14/20.22 |
% 136.14/20.22 End of proof
% 136.14/20.22
% 136.14/20.22 Sub-proof #336 shows that the following formulas are inconsistent:
% 136.14/20.22 ----------------------------------------------------------------
% 136.14/20.22 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.22 (2) op(e2, e0) = all_26_0
% 136.14/20.22 (3) op(e2, e0) = e1
% 136.14/20.22 (4) ~ (all_26_0 = e1)
% 136.14/20.22
% 136.14/20.22 Begin of proof
% 136.14/20.22 |
% 136.14/20.22 | GROUND_INST: instantiating (1) with e1, all_26_0, e0, e2, simplifying with
% 136.14/20.22 | (2), (3) gives:
% 136.14/20.22 | (5) all_26_0 = e1
% 136.14/20.22 |
% 136.14/20.22 | REDUCE: (4), (5) imply:
% 136.14/20.22 | (6) $false
% 136.14/20.22 |
% 136.14/20.22 | CLOSE: (6) is inconsistent.
% 136.14/20.22 |
% 136.14/20.22 End of proof
% 136.14/20.22
% 136.14/20.22 Sub-proof #337 shows that the following formulas are inconsistent:
% 136.14/20.22 ----------------------------------------------------------------
% 136.14/20.22 (1) all_54_7 = all_52_13
% 136.14/20.22 (2) all_54_7 = e2
% 136.14/20.22 (3) ~ (all_52_13 = e2)
% 136.14/20.22
% 136.14/20.22 Begin of proof
% 136.14/20.22 |
% 136.14/20.22 | COMBINE_EQS: (1), (2) imply:
% 136.14/20.22 | (4) all_52_13 = e2
% 136.14/20.22 |
% 136.14/20.22 | SIMP: (4) implies:
% 136.14/20.22 | (5) all_52_13 = e2
% 136.14/20.22 |
% 136.14/20.22 | REDUCE: (3), (5) imply:
% 136.14/20.22 | (6) $false
% 136.14/20.22 |
% 136.14/20.22 | CLOSE: (6) is inconsistent.
% 136.14/20.22 |
% 136.14/20.22 End of proof
% 136.14/20.22
% 136.14/20.22 Sub-proof #338 shows that the following formulas are inconsistent:
% 136.14/20.22 ----------------------------------------------------------------
% 136.14/20.22 (1) all_54_7 = all_52_13
% 136.14/20.22 (2) all_54_7 = e3
% 136.14/20.22 (3) ~ (all_52_13 = e3)
% 136.14/20.22
% 136.14/20.22 Begin of proof
% 136.14/20.22 |
% 136.14/20.22 | COMBINE_EQS: (1), (2) imply:
% 136.14/20.22 | (4) all_52_13 = e3
% 136.14/20.22 |
% 136.14/20.22 | SIMP: (4) implies:
% 136.14/20.22 | (5) all_52_13 = e3
% 136.14/20.22 |
% 136.14/20.22 | REDUCE: (3), (5) imply:
% 136.14/20.22 | (6) $false
% 136.14/20.22 |
% 136.14/20.22 | CLOSE: (6) is inconsistent.
% 136.14/20.22 |
% 136.14/20.22 End of proof
% 136.14/20.22
% 136.14/20.22 Sub-proof #339 shows that the following formulas are inconsistent:
% 136.14/20.22 ----------------------------------------------------------------
% 136.14/20.22 (1) all_54_5 = all_8_2
% 136.14/20.22 (2) all_54_5 = e1
% 136.14/20.22 (3) ~ (all_8_2 = e1)
% 136.14/20.22
% 136.14/20.22 Begin of proof
% 136.14/20.22 |
% 136.14/20.22 | COMBINE_EQS: (1), (2) imply:
% 136.14/20.22 | (4) all_8_2 = e1
% 136.14/20.22 |
% 136.14/20.22 | SIMP: (4) implies:
% 136.14/20.22 | (5) all_8_2 = e1
% 136.14/20.22 |
% 136.14/20.22 | REDUCE: (3), (5) imply:
% 136.14/20.22 | (6) $false
% 136.14/20.22 |
% 136.14/20.22 | CLOSE: (6) is inconsistent.
% 136.14/20.22 |
% 136.14/20.22 End of proof
% 136.14/20.22
% 136.14/20.22 Sub-proof #340 shows that the following formulas are inconsistent:
% 136.14/20.22 ----------------------------------------------------------------
% 136.14/20.22 (1) all_54_5 = all_8_2
% 136.14/20.22 (2) all_54_5 = e2
% 136.14/20.22 (3) ~ (all_8_2 = e2)
% 136.14/20.22
% 136.14/20.22 Begin of proof
% 136.14/20.22 |
% 136.14/20.22 | COMBINE_EQS: (1), (2) imply:
% 136.14/20.22 | (4) all_8_2 = e2
% 136.14/20.22 |
% 136.14/20.22 | SIMP: (4) implies:
% 136.14/20.22 | (5) all_8_2 = e2
% 136.14/20.22 |
% 136.14/20.22 | REDUCE: (3), (5) imply:
% 136.14/20.22 | (6) $false
% 136.14/20.22 |
% 136.14/20.22 | CLOSE: (6) is inconsistent.
% 136.14/20.22 |
% 136.14/20.22 End of proof
% 136.14/20.22
% 136.14/20.22 Sub-proof #341 shows that the following formulas are inconsistent:
% 136.14/20.22 ----------------------------------------------------------------
% 136.14/20.22 (1) all_57_6 = e2 & op(e1, e3) = e2
% 136.14/20.22 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.22 (3) op(e1, e3) = all_52_2
% 136.14/20.22 (4) ~ (all_52_2 = e2)
% 136.14/20.22
% 136.14/20.22 Begin of proof
% 136.14/20.22 |
% 136.14/20.22 | ALPHA: (1) implies:
% 136.14/20.22 | (5) op(e1, e3) = e2
% 136.14/20.22 |
% 136.14/20.22 | GROUND_INST: instantiating (2) with all_52_2, e2, e3, e1, simplifying with
% 136.14/20.22 | (3), (5) gives:
% 136.14/20.22 | (6) all_52_2 = e2
% 136.14/20.22 |
% 136.14/20.22 | REDUCE: (4), (6) imply:
% 136.14/20.22 | (7) $false
% 136.14/20.22 |
% 136.14/20.22 | CLOSE: (7) is inconsistent.
% 136.14/20.22 |
% 136.14/20.22 End of proof
% 136.14/20.22
% 136.14/20.22 Sub-proof #342 shows that the following formulas are inconsistent:
% 136.14/20.22 ----------------------------------------------------------------
% 136.14/20.22 (1) ~ (all_36_1 = e2) & op(e3, e3) = all_36_1 & $i(all_36_1)
% 136.14/20.22 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.22 (3) op(e3, e3) = e2
% 136.14/20.22
% 136.14/20.22 Begin of proof
% 136.14/20.22 |
% 136.14/20.22 | ALPHA: (1) implies:
% 136.14/20.22 | (4) ~ (all_36_1 = e2)
% 136.14/20.22 | (5) op(e3, e3) = all_36_1
% 136.14/20.22 |
% 136.14/20.22 | GROUND_INST: instantiating (2) with e2, all_36_1, e3, e3, simplifying with
% 136.14/20.22 | (3), (5) gives:
% 136.14/20.22 | (6) all_36_1 = e2
% 136.14/20.22 |
% 136.14/20.22 | REDUCE: (4), (6) imply:
% 136.14/20.22 | (7) $false
% 136.14/20.22 |
% 136.14/20.22 | CLOSE: (7) is inconsistent.
% 136.14/20.22 |
% 136.14/20.22 End of proof
% 136.14/20.22
% 136.14/20.22 Sub-proof #343 shows that the following formulas are inconsistent:
% 136.14/20.22 ----------------------------------------------------------------
% 136.14/20.22 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.22 (2) op(e3, e1) = e1
% 136.14/20.22 (3) op(e3, e1) = e0
% 136.14/20.22 (4) ~ (e1 = e0)
% 136.14/20.22
% 136.14/20.22 Begin of proof
% 136.14/20.22 |
% 136.14/20.22 | GROUND_INST: instantiating (1) with e0, e1, e1, e3, simplifying with (2), (3)
% 136.14/20.22 | gives:
% 136.14/20.22 | (5) e1 = e0
% 136.14/20.22 |
% 136.14/20.22 | REDUCE: (4), (5) imply:
% 136.14/20.22 | (6) $false
% 136.14/20.22 |
% 136.14/20.22 | CLOSE: (6) is inconsistent.
% 136.14/20.22 |
% 136.14/20.22 End of proof
% 136.14/20.22
% 136.14/20.22 Sub-proof #344 shows that the following formulas are inconsistent:
% 136.14/20.22 ----------------------------------------------------------------
% 136.14/20.22 (1) op(e3, e3) = e2
% 136.14/20.22 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.22 (3) ~ (e3 = e0)
% 136.14/20.22 (4) ~ (e3 = e2)
% 136.14/20.22 (5) op(e3, e1) = all_36_0
% 136.14/20.22 (6) all_57_1 = e0
% 136.14/20.22 (7) op(e3, e1) = all_52_8
% 136.14/20.22 (8) all_57_9 = e1
% 136.14/20.22 (9) ~ (e3 = e1)
% 136.14/20.22 (10) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 136.14/20.22 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 136.14/20.22 (11) ~ (all_52_8 = e3)
% 136.14/20.22
% 136.14/20.22 Begin of proof
% 136.14/20.22 |
% 136.14/20.22 | BETA: splitting (10) gives:
% 136.14/20.22 |
% 136.14/20.22 | Case 1:
% 136.14/20.22 | |
% 136.14/20.22 | | (12) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 136.14/20.22 | | e3)
% 136.14/20.22 | |
% 136.14/20.22 | | BETA: splitting (12) gives:
% 136.14/20.22 | |
% 136.14/20.22 | | Case 1:
% 136.14/20.22 | | |
% 136.14/20.22 | | | (13) all_57_0 = e3 & op(e3, e3) = e3
% 136.14/20.22 | | |
% 136.14/20.22 | | | ALPHA: (13) implies:
% 136.14/20.22 | | | (14) op(e3, e3) = e3
% 136.14/20.22 | | |
% 136.14/20.22 | | | REF_CLOSE: (1), (2), (4), (14) are inconsistent by sub-proof #778.
% 136.14/20.22 | | |
% 136.14/20.22 | | Case 2:
% 136.14/20.22 | | |
% 136.14/20.22 | | | (15) all_57_1 = e3 & op(e3, e2) = e3
% 136.14/20.22 | | |
% 136.14/20.22 | | | REF_CLOSE: (3), (6), (15) are inconsistent by sub-proof #376.
% 136.14/20.22 | | |
% 136.14/20.22 | | End of split
% 136.14/20.22 | |
% 136.14/20.22 | Case 2:
% 136.14/20.22 | |
% 136.14/20.22 | | (16) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 136.14/20.22 | | e3)
% 136.14/20.22 | |
% 136.14/20.22 | | BETA: splitting (16) gives:
% 136.14/20.22 | |
% 136.14/20.22 | | Case 1:
% 136.14/20.22 | | |
% 136.14/20.22 | | | (17) all_57_4 = e3 & op(e3, e1) = e3
% 136.14/20.22 | | |
% 136.14/20.22 | | | REF_CLOSE: (2), (5), (7), (11), (17) are inconsistent by sub-proof #379.
% 136.14/20.22 | | |
% 136.14/20.22 | | Case 2:
% 136.14/20.22 | | |
% 136.14/20.22 | | | (18) all_57_9 = e3 & op(e3, e0) = e3
% 136.14/20.22 | | |
% 136.14/20.22 | | | REF_CLOSE: (8), (9), (18) are inconsistent by sub-proof #345.
% 136.14/20.22 | | |
% 136.14/20.22 | | End of split
% 136.14/20.22 | |
% 136.14/20.22 | End of split
% 136.14/20.22 |
% 136.14/20.22 End of proof
% 136.14/20.22
% 136.14/20.22 Sub-proof #345 shows that the following formulas are inconsistent:
% 136.14/20.22 ----------------------------------------------------------------
% 136.14/20.22 (1) all_57_9 = e3 & op(e3, e0) = e3
% 136.14/20.22 (2) all_57_9 = e1
% 136.14/20.22 (3) ~ (e3 = e1)
% 136.14/20.22
% 136.14/20.22 Begin of proof
% 136.14/20.22 |
% 136.14/20.22 | ALPHA: (1) implies:
% 136.14/20.22 | (4) all_57_9 = e3
% 136.14/20.22 |
% 136.14/20.22 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.22 | (5) e3 = e1
% 136.14/20.22 |
% 136.14/20.22 | REDUCE: (3), (5) imply:
% 136.14/20.22 | (6) $false
% 136.14/20.22 |
% 136.14/20.22 | CLOSE: (6) is inconsistent.
% 136.14/20.22 |
% 136.14/20.22 End of proof
% 136.14/20.22
% 136.14/20.22 Sub-proof #346 shows that the following formulas are inconsistent:
% 136.14/20.22 ----------------------------------------------------------------
% 136.14/20.22 (1) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2)
% 136.14/20.22 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 136.14/20.22 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25
% 136.14/20.22 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 136.14/20.22 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3)
% 136.14/20.22 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.14/20.22 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 136.14/20.22 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) &
% 136.14/20.22 $i(all_56_11) & $i(all_56_19) & $i(all_56_27))
% 136.14/20.22 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.22 (3) op(e3, e1) = e1
% 136.14/20.22 (4) op(e2, e3) = e3
% 136.14/20.22
% 136.14/20.22 Begin of proof
% 136.14/20.22 |
% 136.14/20.22 | BETA: splitting (1) gives:
% 136.14/20.22 |
% 136.14/20.22 | Case 1:
% 136.14/20.22 | |
% 136.14/20.22 | | (5) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.14/20.22 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.14/20.22 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.14/20.22 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 136.14/20.22 | | $i(all_56_17) & $i(all_56_25)
% 136.14/20.22 | |
% 136.14/20.22 | | ALPHA: (5) implies:
% 136.14/20.22 | | (6) ~ (all_56_17 = e1)
% 136.14/20.22 | | (7) op(e3, e1) = all_56_17
% 136.14/20.22 | |
% 136.14/20.22 | | REF_CLOSE: (2), (3), (6), (7) are inconsistent by sub-proof #349.
% 136.14/20.22 | |
% 136.14/20.22 | Case 2:
% 136.14/20.22 | |
% 136.14/20.22 | | (8) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11
% 136.14/20.22 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 136.14/20.22 | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 136.14/20.22 | | e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 136.14/20.22 | | $i(all_56_19) & $i(all_56_27)
% 136.14/20.22 | |
% 136.14/20.22 | | ALPHA: (8) implies:
% 136.14/20.22 | | (9) ~ (all_56_3 = e3)
% 136.14/20.22 | | (10) op(e2, e3) = all_56_3
% 136.14/20.22 | |
% 136.14/20.22 | | REF_CLOSE: (2), (4), (9), (10) are inconsistent by sub-proof #347.
% 136.14/20.22 | |
% 136.14/20.22 | End of split
% 136.14/20.22 |
% 136.14/20.22 End of proof
% 136.14/20.22
% 136.14/20.22 Sub-proof #347 shows that the following formulas are inconsistent:
% 136.14/20.22 ----------------------------------------------------------------
% 136.14/20.22 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.22 (2) op(e2, e3) = all_56_3
% 136.14/20.22 (3) op(e2, e3) = e3
% 136.14/20.22 (4) ~ (all_56_3 = e3)
% 136.14/20.22
% 136.14/20.22 Begin of proof
% 136.14/20.22 |
% 136.14/20.22 | GROUND_INST: instantiating (1) with e3, all_56_3, e3, e2, simplifying with
% 136.14/20.22 | (2), (3) gives:
% 136.14/20.22 | (5) all_56_3 = e3
% 136.14/20.22 |
% 136.14/20.22 | REDUCE: (4), (5) imply:
% 136.14/20.22 | (6) $false
% 136.14/20.22 |
% 136.14/20.22 | CLOSE: (6) is inconsistent.
% 136.14/20.22 |
% 136.14/20.22 End of proof
% 136.14/20.22
% 136.14/20.22 Sub-proof #348 shows that the following formulas are inconsistent:
% 136.14/20.22 ----------------------------------------------------------------
% 136.14/20.22 (1) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2)
% 136.14/20.22 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 136.14/20.22 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25
% 136.14/20.22 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 136.14/20.22 $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~
% 136.14/20.22 (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 136.14/20.22 (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 136.14/20.22 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 136.14/20.22 = all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.14/20.22 $i(all_56_29))
% 136.14/20.22 (2) op(e3, e1) = e1
% 136.14/20.22 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.22 (4) ~ (all_52_9 = e2)
% 136.14/20.22 (5) op(e2, e1) = all_52_9
% 136.14/20.22
% 136.14/20.22 Begin of proof
% 136.14/20.22 |
% 136.14/20.22 | BETA: splitting (1) gives:
% 136.14/20.22 |
% 136.14/20.22 | Case 1:
% 136.14/20.22 | |
% 136.14/20.22 | | (6) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.14/20.22 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.14/20.22 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.14/20.22 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1)
% 136.14/20.22 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)
% 136.14/20.22 | |
% 136.14/20.22 | | ALPHA: (6) implies:
% 136.14/20.22 | | (7) ~ (all_56_17 = e1)
% 136.14/20.22 | | (8) op(e3, e1) = all_56_17
% 136.14/20.22 | |
% 136.14/20.22 | | REF_CLOSE: (2), (3), (7), (8) are inconsistent by sub-proof #349.
% 136.14/20.22 | |
% 136.14/20.22 | Case 2:
% 136.14/20.22 | |
% 136.14/20.22 | | (9) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13
% 136.14/20.22 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1
% 136.14/20.22 | | & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 136.14/20.22 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 136.14/20.22 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 136.14/20.22 | |
% 136.14/20.22 | | ALPHA: (9) implies:
% 136.14/20.22 | | (10) op(e2, e1) = e2
% 136.14/20.22 | |
% 136.14/20.22 | | REF_CLOSE: (3), (4), (5), (10) are inconsistent by sub-proof #770.
% 136.14/20.22 | |
% 136.14/20.22 | End of split
% 136.14/20.22 |
% 136.14/20.22 End of proof
% 136.14/20.22
% 136.14/20.22 Sub-proof #349 shows that the following formulas are inconsistent:
% 136.14/20.22 ----------------------------------------------------------------
% 136.14/20.22 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.22 (2) op(e3, e1) = all_56_17
% 136.14/20.22 (3) op(e3, e1) = e1
% 136.14/20.22 (4) ~ (all_56_17 = e1)
% 136.14/20.22
% 136.14/20.22 Begin of proof
% 136.14/20.22 |
% 136.14/20.22 | GROUND_INST: instantiating (1) with e1, all_56_17, e1, e3, simplifying with
% 136.14/20.22 | (2), (3) gives:
% 136.14/20.22 | (5) all_56_17 = e1
% 136.14/20.22 |
% 136.14/20.22 | REDUCE: (4), (5) imply:
% 136.14/20.22 | (6) $false
% 136.14/20.22 |
% 136.14/20.22 | CLOSE: (6) is inconsistent.
% 136.14/20.22 |
% 136.14/20.22 End of proof
% 136.14/20.22
% 136.14/20.22 Sub-proof #350 shows that the following formulas are inconsistent:
% 136.14/20.22 ----------------------------------------------------------------
% 136.14/20.22 (1) op(e0, e0) = all_4_2
% 136.14/20.22 (2) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 136.14/20.22 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.22 (4) ~ (e2 = e1)
% 136.14/20.22 (5) ~ (all_4_2 = e1)
% 136.14/20.22 (6) all_57_14 = e2
% 136.14/20.22
% 136.14/20.22 Begin of proof
% 136.14/20.22 |
% 136.14/20.22 | BETA: splitting (2) gives:
% 136.14/20.22 |
% 136.14/20.22 | Case 1:
% 136.14/20.22 | |
% 136.14/20.22 | | (7) all_57_14 = e1 & op(e0, e1) = e1
% 136.14/20.22 | |
% 136.14/20.22 | | ALPHA: (7) implies:
% 136.14/20.22 | | (8) all_57_14 = e1
% 136.14/20.22 | |
% 136.14/20.22 | | REF_CLOSE: (4), (6), (8) are inconsistent by sub-proof #560.
% 136.14/20.22 | |
% 136.14/20.22 | Case 2:
% 136.14/20.22 | |
% 136.14/20.22 | | (9) all_57_15 = e1 & op(e0, e0) = e1
% 136.14/20.22 | |
% 136.14/20.22 | | ALPHA: (9) implies:
% 136.14/20.22 | | (10) op(e0, e0) = e1
% 136.14/20.22 | |
% 136.14/20.22 | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #354.
% 136.14/20.22 | |
% 136.14/20.22 | End of split
% 136.14/20.22 |
% 136.14/20.22 End of proof
% 136.14/20.22
% 136.14/20.22 Sub-proof #351 shows that the following formulas are inconsistent:
% 136.14/20.22 ----------------------------------------------------------------
% 136.14/20.22 (1) ~ (all_52_11 = e1)
% 136.14/20.22 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.22 (3) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 136.14/20.22 (4) op(e0, e1) = all_52_11
% 136.14/20.22 (5) op(e0, e1) = e0
% 136.14/20.22 (6) ~ (all_52_11 = e0)
% 136.14/20.22 (7) all_54_14 = all_52_11
% 136.14/20.22
% 136.14/20.22 Begin of proof
% 136.14/20.22 |
% 136.14/20.22 | BETA: splitting (3) gives:
% 136.14/20.22 |
% 136.14/20.22 | Case 1:
% 136.14/20.22 | |
% 136.14/20.22 | | (8) all_54_14 = e2
% 136.14/20.22 | |
% 136.14/20.22 | | COMBINE_EQS: (7), (8) imply:
% 136.14/20.22 | | (9) all_52_11 = e2
% 136.14/20.22 | |
% 136.14/20.22 | | SIMP: (9) implies:
% 136.14/20.22 | | (10) all_52_11 = e2
% 136.14/20.22 | |
% 136.14/20.22 | | REDUCE: (6), (10) imply:
% 136.14/20.22 | | (11) ~ (e2 = e0)
% 136.14/20.22 | |
% 136.14/20.22 | | REDUCE: (4), (10) imply:
% 136.14/20.22 | | (12) op(e0, e1) = e2
% 136.14/20.22 | |
% 136.14/20.22 | | REF_CLOSE: (2), (5), (11), (12) are inconsistent by sub-proof #660.
% 136.14/20.22 | |
% 136.14/20.22 | Case 2:
% 136.14/20.22 | |
% 136.14/20.22 | | (13) all_54_14 = e1 | all_54_14 = e0
% 136.14/20.22 | |
% 136.14/20.22 | | REF_CLOSE: (1), (6), (7), (13) are inconsistent by sub-proof #755.
% 136.14/20.22 | |
% 136.14/20.22 | End of split
% 136.14/20.22 |
% 136.14/20.22 End of proof
% 136.14/20.22
% 136.14/20.22 Sub-proof #352 shows that the following formulas are inconsistent:
% 136.14/20.22 ----------------------------------------------------------------
% 136.14/20.22 (1) op(e0, e0) = all_4_2
% 136.14/20.22 (2) op(e1, e1) = all_6_2
% 136.14/20.22 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.22 (4) ~ (all_4_2 = e2)
% 136.14/20.22 (5) ~ (all_6_2 = e2)
% 136.14/20.22 (6) op(e0, e0) = e2
% 136.14/20.22 (7) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 136.14/20.22 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 136.14/20.22 all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0)
% 136.14/20.22 = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 136.14/20.22 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 136.14/20.22 all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~
% 136.14/20.22 (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 136.14/20.22 (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 &
% 136.14/20.22 op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 136.14/20.22 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.14/20.22 (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11
% 136.14/20.22 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 136.14/20.22 all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 136.14/20.22 e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11)
% 136.14/20.22 & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1
% 136.14/20.22 & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 136.14/20.22 ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3)
% 136.14/20.22 = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 136.14/20.22 $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 &
% 136.14/20.22 all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.14/20.22 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 136.14/20.22 op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 136.14/20.22 all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 136.14/20.22 $i(all_56_21) & $i(all_56_29))))
% 136.14/20.22
% 136.14/20.22 Begin of proof
% 136.14/20.22 |
% 136.14/20.22 | BETA: splitting (7) gives:
% 136.14/20.22 |
% 136.14/20.22 | Case 1:
% 136.14/20.22 | |
% 136.14/20.22 | | (8) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11
% 136.14/20.22 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 136.14/20.22 | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 136.14/20.22 | | e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3)
% 136.14/20.22 | | & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)
% 136.14/20.22 | |
% 136.14/20.22 | | ALPHA: (8) implies:
% 136.14/20.22 | | (9) op(e1, e1) = e2
% 136.14/20.22 | |
% 136.14/20.22 | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #767.
% 136.14/20.22 | |
% 136.14/20.22 | Case 2:
% 136.14/20.22 | |
% 136.14/20.22 | | (10) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31
% 136.14/20.22 | | = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 136.14/20.22 | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2)
% 136.14/20.22 | | = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 136.14/20.22 | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 136.14/20.22 | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3
% 136.14/20.22 | | = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 136.14/20.22 | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 136.14/20.22 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 136.14/20.22 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 136.14/20.22 | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7
% 136.14/20.22 | | = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 136.14/20.22 | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 136.14/20.22 | | e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) =
% 136.14/20.22 | | all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 136.14/20.22 | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 136.14/20.22 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 136.14/20.22 | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.14/20.22 | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 136.14/20.22 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)))
% 136.14/20.22 | |
% 136.14/20.22 | | ALPHA: (10) implies:
% 136.14/20.22 | | (11) op(e0, e0) = all_56_31
% 136.14/20.22 | |
% 136.14/20.22 | | REF_CLOSE: (1), (3), (4), (6), (11) are inconsistent by sub-proof #427.
% 136.14/20.22 | |
% 136.14/20.22 | End of split
% 136.14/20.22 |
% 136.14/20.22 End of proof
% 136.14/20.22
% 136.14/20.22 Sub-proof #353 shows that the following formulas are inconsistent:
% 136.14/20.22 ----------------------------------------------------------------
% 136.14/20.22 (1) op(e1, e0) = e2
% 136.14/20.22 (2) op(e0, e0) = all_4_2
% 136.14/20.22 (3) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 136.14/20.22 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.22 (5) ~ (e2 = e1)
% 136.14/20.22 (6) ~ (all_4_2 = e1)
% 136.14/20.22
% 136.14/20.22 Begin of proof
% 136.14/20.22 |
% 136.14/20.22 | BETA: splitting (3) gives:
% 136.14/20.22 |
% 136.14/20.22 | Case 1:
% 136.14/20.22 | |
% 136.14/20.22 | | (7) all_57_11 = e1 & op(e1, e0) = e1
% 136.14/20.22 | |
% 136.14/20.22 | | ALPHA: (7) implies:
% 136.14/20.22 | | (8) op(e1, e0) = e1
% 136.14/20.22 | |
% 136.14/20.22 | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #720.
% 136.14/20.22 | |
% 136.14/20.22 | Case 2:
% 136.14/20.22 | |
% 136.14/20.22 | | (9) all_57_15 = e1 & op(e0, e0) = e1
% 136.14/20.22 | |
% 136.14/20.22 | | ALPHA: (9) implies:
% 136.14/20.22 | | (10) op(e0, e0) = e1
% 136.14/20.22 | |
% 136.14/20.22 | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #354.
% 136.14/20.22 | |
% 136.14/20.22 | End of split
% 136.14/20.22 |
% 136.14/20.22 End of proof
% 136.14/20.22
% 136.14/20.22 Sub-proof #354 shows that the following formulas are inconsistent:
% 136.14/20.22 ----------------------------------------------------------------
% 136.14/20.22 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.22 (2) op(e0, e0) = all_4_2
% 136.14/20.22 (3) op(e0, e0) = e1
% 136.14/20.22 (4) ~ (all_4_2 = e1)
% 136.14/20.22
% 136.14/20.22 Begin of proof
% 136.14/20.22 |
% 136.14/20.22 | GROUND_INST: instantiating (1) with all_4_2, e1, e0, e0, simplifying with (2),
% 136.14/20.23 | (3) gives:
% 136.14/20.23 | (5) all_4_2 = e1
% 136.14/20.23 |
% 136.14/20.23 | REDUCE: (4), (5) imply:
% 136.14/20.23 | (6) $false
% 136.14/20.23 |
% 136.14/20.23 | CLOSE: (6) is inconsistent.
% 136.14/20.23 |
% 136.14/20.23 End of proof
% 136.14/20.23
% 136.14/20.23 Sub-proof #355 shows that the following formulas are inconsistent:
% 136.14/20.23 ----------------------------------------------------------------
% 136.14/20.23 (1) all_57_10 = e3 & op(e2, e0) = e3
% 136.14/20.23 (2) all_57_10 = e1
% 136.14/20.23 (3) ~ (e3 = e1)
% 136.14/20.23
% 136.14/20.23 Begin of proof
% 136.14/20.23 |
% 136.14/20.23 | ALPHA: (1) implies:
% 136.14/20.23 | (4) all_57_10 = e3
% 136.14/20.23 |
% 136.14/20.23 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.23 | (5) e3 = e1
% 136.14/20.23 |
% 136.14/20.23 | SIMP: (5) implies:
% 136.14/20.23 | (6) e3 = e1
% 136.14/20.23 |
% 136.14/20.23 | REDUCE: (3), (6) imply:
% 136.14/20.23 | (7) $false
% 136.14/20.23 |
% 136.14/20.23 | CLOSE: (7) is inconsistent.
% 136.14/20.23 |
% 136.14/20.23 End of proof
% 136.14/20.23
% 136.14/20.23 Sub-proof #356 shows that the following formulas are inconsistent:
% 136.14/20.23 ----------------------------------------------------------------
% 136.14/20.23 (1) op(e3, e3) = e2
% 136.14/20.23 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.23 (3) ~ (e2 = e1)
% 136.14/20.23 (4) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1)
% 136.14/20.23 (5) all_57_2 = e3
% 136.14/20.23 (6) ~ (e3 = e1)
% 136.14/20.23
% 136.14/20.23 Begin of proof
% 136.14/20.23 |
% 136.14/20.23 | BETA: splitting (4) gives:
% 136.14/20.23 |
% 136.14/20.23 | Case 1:
% 136.14/20.23 | |
% 136.14/20.23 | | (7) all_57_0 = e1 & op(e3, e3) = e1
% 136.14/20.23 | |
% 136.14/20.23 | | ALPHA: (7) implies:
% 136.14/20.23 | | (8) op(e3, e3) = e1
% 136.14/20.23 | |
% 136.14/20.23 | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #743.
% 136.14/20.23 | |
% 136.14/20.23 | Case 2:
% 136.14/20.23 | |
% 136.14/20.23 | | (9) all_57_2 = e1 & op(e2, e3) = e1
% 136.14/20.23 | |
% 136.14/20.23 | | REF_CLOSE: (5), (6), (9) are inconsistent by sub-proof #453.
% 136.14/20.23 | |
% 136.14/20.23 | End of split
% 136.14/20.23 |
% 136.14/20.23 End of proof
% 136.14/20.23
% 136.14/20.23 Sub-proof #357 shows that the following formulas are inconsistent:
% 136.14/20.23 ----------------------------------------------------------------
% 136.14/20.23 (1) ~ (e2 = e0)
% 136.14/20.23 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.23 (3) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 136.14/20.23 (all_57_11 = e0 & op(e1, e0) = e0)
% 136.14/20.23 (4) ~ (all_52_9 = e2)
% 136.14/20.23 (5) op(e2, e1) = all_52_9
% 136.14/20.23 (6) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 136.14/20.23 (7) all_57_11 = e2
% 136.14/20.23 (8) all_57_9 = e1
% 136.14/20.23 (9) ~ (e1 = e0)
% 136.14/20.23
% 136.14/20.23 Begin of proof
% 136.14/20.23 |
% 136.14/20.23 | BETA: splitting (6) gives:
% 136.14/20.23 |
% 136.14/20.23 | Case 1:
% 136.14/20.23 | |
% 136.14/20.23 | | (10) all_57_5 = e2 & op(e2, e1) = e2
% 136.14/20.23 | |
% 136.14/20.23 | | ALPHA: (10) implies:
% 136.14/20.23 | | (11) op(e2, e1) = e2
% 136.14/20.23 | |
% 136.14/20.23 | | REF_CLOSE: (2), (4), (5), (11) are inconsistent by sub-proof #770.
% 136.14/20.23 | |
% 136.14/20.23 | Case 2:
% 136.14/20.23 | |
% 136.14/20.23 | | (12) all_57_10 = e2 & op(e2, e0) = e2
% 136.14/20.23 | |
% 136.14/20.23 | | ALPHA: (12) implies:
% 136.14/20.23 | | (13) all_57_10 = e2
% 136.14/20.23 | |
% 136.14/20.23 | | BETA: splitting (3) gives:
% 136.14/20.23 | |
% 136.14/20.23 | | Case 1:
% 136.14/20.23 | | |
% 136.14/20.23 | | | (14) all_57_9 = e0 & op(e3, e0) = e0
% 136.14/20.23 | | |
% 136.14/20.23 | | | ALPHA: (14) implies:
% 136.14/20.23 | | | (15) all_57_9 = e0
% 136.14/20.23 | | |
% 136.14/20.23 | | | REF_CLOSE: (8), (9), (15) are inconsistent by sub-proof #383.
% 136.14/20.23 | | |
% 136.14/20.23 | | Case 2:
% 136.14/20.23 | | |
% 136.14/20.23 | | | (16) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 136.14/20.23 | | | = e0)
% 136.14/20.23 | | |
% 136.14/20.23 | | | BETA: splitting (16) gives:
% 136.14/20.23 | | |
% 136.14/20.23 | | | Case 1:
% 136.14/20.23 | | | |
% 136.14/20.23 | | | | (17) all_57_10 = e0 & op(e2, e0) = e0
% 136.14/20.23 | | | |
% 136.14/20.23 | | | | REF_CLOSE: (1), (13), (17) are inconsistent by sub-proof #363.
% 136.14/20.23 | | | |
% 136.14/20.23 | | | Case 2:
% 136.14/20.23 | | | |
% 136.14/20.23 | | | | (18) all_57_11 = e0 & op(e1, e0) = e0
% 136.14/20.23 | | | |
% 136.14/20.23 | | | | REF_CLOSE: (1), (7), (18) are inconsistent by sub-proof #656.
% 136.14/20.23 | | | |
% 136.14/20.23 | | | End of split
% 136.14/20.23 | | |
% 136.14/20.23 | | End of split
% 136.14/20.23 | |
% 136.14/20.23 | End of split
% 136.14/20.23 |
% 136.14/20.23 End of proof
% 136.14/20.23
% 136.14/20.23 Sub-proof #358 shows that the following formulas are inconsistent:
% 136.14/20.23 ----------------------------------------------------------------
% 136.14/20.23 (1) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 136.14/20.23 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 136.14/20.23 (2) op(e2, e0) = all_52_13
% 136.14/20.23 (3) op(e3, e3) = e2
% 136.14/20.23 (4) ~ (e2 = e0)
% 136.14/20.23 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.23 (6) ~ (e3 = e0)
% 136.14/20.23 (7) ~ (all_52_9 = e2)
% 136.14/20.23 (8) ~ (all_52_13 = e2)
% 136.14/20.23 (9) op(e2, e1) = all_52_9
% 136.14/20.23 (10) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 136.14/20.23 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 136.14/20.23 (11) ~ (all_52_1 = e2)
% 136.14/20.23 (12) all_57_2 = e3
% 136.14/20.23 (13) op(e2, e3) = all_52_1
% 136.14/20.23 (14) ~ (e1 = e0)
% 136.14/20.23 (15) all_57_3 = e2
% 136.14/20.23 (16) all_57_6 = e2
% 136.14/20.23 (17) all_57_12 = e1
% 136.14/20.23
% 136.14/20.23 Begin of proof
% 136.14/20.23 |
% 136.14/20.23 | BETA: splitting (10) gives:
% 136.14/20.23 |
% 136.14/20.23 | Case 1:
% 136.14/20.23 | |
% 136.14/20.23 | | (18) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 136.14/20.23 | | e0)
% 136.14/20.23 | |
% 136.14/20.23 | | REF_CLOSE: (3), (4), (5), (6), (12), (18) are inconsistent by sub-proof
% 136.14/20.23 | | #426.
% 136.14/20.23 | |
% 136.14/20.23 | Case 2:
% 136.14/20.23 | |
% 136.14/20.23 | | (19) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 136.14/20.23 | | e0)
% 136.14/20.23 | |
% 136.14/20.23 | | BETA: splitting (19) gives:
% 136.14/20.23 | |
% 136.14/20.23 | | Case 1:
% 136.14/20.23 | | |
% 136.14/20.23 | | | (20) all_57_6 = e0 & op(e1, e3) = e0
% 136.14/20.23 | | |
% 136.14/20.23 | | | ALPHA: (20) implies:
% 136.14/20.23 | | | (21) all_57_6 = e0
% 136.14/20.23 | | |
% 136.14/20.23 | | | COMBINE_EQS: (16), (21) imply:
% 136.14/20.23 | | | (22) e2 = e0
% 136.14/20.23 | | |
% 136.14/20.23 | | | SIMP: (22) implies:
% 136.14/20.23 | | | (23) e2 = e0
% 136.14/20.23 | | |
% 136.14/20.23 | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (11), (13), (15), (23) are
% 136.14/20.23 | | | inconsistent by sub-proof #359.
% 136.14/20.23 | | |
% 136.14/20.23 | | Case 2:
% 136.14/20.23 | | |
% 136.14/20.23 | | | (24) all_57_12 = e0 & op(e0, e3) = e0
% 136.14/20.23 | | |
% 136.14/20.23 | | | ALPHA: (24) implies:
% 136.14/20.23 | | | (25) all_57_12 = e0
% 136.14/20.23 | | |
% 136.14/20.23 | | | REF_CLOSE: (14), (17), (25) are inconsistent by sub-proof #581.
% 136.14/20.23 | | |
% 136.14/20.23 | | End of split
% 136.14/20.23 | |
% 136.14/20.23 | End of split
% 136.14/20.23 |
% 136.14/20.23 End of proof
% 136.14/20.23
% 136.14/20.23 Sub-proof #359 shows that the following formulas are inconsistent:
% 136.14/20.23 ----------------------------------------------------------------
% 136.14/20.23 (1) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 136.14/20.23 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 136.14/20.23 (2) op(e2, e0) = all_52_13
% 136.14/20.23 (3) ~ (e2 = e0)
% 136.14/20.23 (4) e2 = e0
% 136.14/20.23 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.23 (6) ~ (all_52_9 = e2)
% 136.14/20.23 (7) ~ (all_52_13 = e2)
% 136.14/20.23 (8) op(e2, e1) = all_52_9
% 136.14/20.23 (9) ~ (all_52_1 = e2)
% 136.14/20.23 (10) op(e2, e3) = all_52_1
% 136.14/20.23 (11) all_57_3 = e2
% 136.14/20.23
% 136.14/20.23 Begin of proof
% 136.14/20.23 |
% 136.14/20.23 | COMBINE_EQS: (4), (11) imply:
% 136.14/20.23 | (12) all_57_3 = e0
% 136.14/20.23 |
% 136.14/20.23 | BETA: splitting (1) gives:
% 136.14/20.23 |
% 136.14/20.23 | Case 1:
% 136.14/20.23 | |
% 136.14/20.23 | | (13) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 136.14/20.23 | | e2)
% 136.14/20.23 | |
% 136.14/20.23 | | BETA: splitting (13) gives:
% 136.14/20.23 | |
% 136.14/20.23 | | Case 1:
% 136.14/20.23 | | |
% 136.14/20.23 | | | (14) all_57_2 = e2 & op(e2, e3) = e2
% 136.14/20.23 | | |
% 136.14/20.23 | | | ALPHA: (14) implies:
% 136.14/20.23 | | | (15) op(e2, e3) = e2
% 136.14/20.23 | | |
% 136.14/20.23 | | | REF_CLOSE: (5), (9), (10), (15) are inconsistent by sub-proof #779.
% 136.14/20.23 | | |
% 136.14/20.23 | | Case 2:
% 136.14/20.23 | | |
% 136.14/20.23 | | | (16) all_57_3 = e2 & op(e2, e2) = e2
% 136.14/20.23 | | |
% 136.14/20.23 | | | REF_CLOSE: (3), (11), (12) are inconsistent by sub-proof #679.
% 136.14/20.23 | | |
% 136.14/20.23 | | End of split
% 136.14/20.23 | |
% 136.14/20.23 | Case 2:
% 136.14/20.23 | |
% 136.14/20.23 | | (17) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 136.14/20.23 | | e2)
% 136.14/20.23 | |
% 136.14/20.23 | | REF_CLOSE: (2), (5), (6), (7), (8), (17) are inconsistent by sub-proof #625.
% 136.14/20.23 | |
% 136.14/20.23 | End of split
% 136.14/20.23 |
% 136.14/20.23 End of proof
% 136.14/20.23
% 136.14/20.23 Sub-proof #360 shows that the following formulas are inconsistent:
% 136.14/20.23 ----------------------------------------------------------------
% 136.14/20.23 (1) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 136.14/20.23 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 136.14/20.23 (2) op(e3, e3) = e2
% 136.14/20.23 (3) ~ (e2 = e0)
% 136.14/20.23 (4) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 136.14/20.23 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 136.14/20.23 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.23 (6) ~ (e2 = e1)
% 136.14/20.23 (7) ~ (e3 = e0)
% 136.14/20.23 (8) ~ (e3 = e2)
% 136.14/20.23 (9) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 136.14/20.23 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 136.14/20.23 (10) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 136.14/20.23 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 136.14/20.23 (11) all_57_3 = e3
% 136.14/20.23 (12) ~ (e3 = e1)
% 136.14/20.23 (13) ~ (e1 = e0)
% 136.14/20.23 (14) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 136.14/20.23 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 136.14/20.23 (15) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 136.14/20.23 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 136.14/20.23 (16) all_57_6 = e2
% 136.14/20.23
% 136.14/20.23 Begin of proof
% 136.14/20.23 |
% 136.14/20.23 | BETA: splitting (1) gives:
% 136.14/20.23 |
% 136.14/20.23 | Case 1:
% 136.14/20.23 | |
% 136.14/20.23 | | (17) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 136.14/20.23 | | e2)
% 136.14/20.23 | |
% 136.14/20.23 | | BETA: splitting (17) gives:
% 136.14/20.23 | |
% 136.14/20.23 | | Case 1:
% 136.14/20.23 | | |
% 136.14/20.23 | | | (18) all_57_2 = e2 & op(e2, e3) = e2
% 136.14/20.23 | | |
% 136.14/20.23 | | | ALPHA: (18) implies:
% 136.14/20.23 | | | (19) all_57_2 = e2
% 136.14/20.23 | | |
% 136.14/20.23 | | | REF_CLOSE: (2), (4), (5), (6), (8), (9), (12), (16), (19) are inconsistent
% 136.14/20.23 | | | by sub-proof #393.
% 136.14/20.23 | | |
% 136.14/20.23 | | Case 2:
% 136.14/20.23 | | |
% 136.14/20.23 | | | (20) all_57_3 = e2 & op(e2, e2) = e2
% 136.14/20.23 | | |
% 136.14/20.23 | | | REF_CLOSE: (8), (11), (20) are inconsistent by sub-proof #375.
% 136.14/20.23 | | |
% 136.14/20.23 | | End of split
% 136.14/20.23 | |
% 136.14/20.23 | Case 2:
% 136.14/20.23 | |
% 136.14/20.23 | | (21) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 136.14/20.23 | | e2)
% 136.14/20.23 | |
% 136.14/20.23 | | BETA: splitting (21) gives:
% 136.14/20.23 | |
% 136.14/20.23 | | Case 1:
% 136.14/20.23 | | |
% 136.14/20.23 | | | (22) all_57_5 = e2 & op(e2, e1) = e2
% 136.14/20.23 | | |
% 136.14/20.23 | | | ALPHA: (22) implies:
% 136.14/20.23 | | | (23) all_57_5 = e2
% 136.14/20.23 | | |
% 136.14/20.23 | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 136.14/20.23 | | | (14), (15), (16), (23) are inconsistent by sub-proof #366.
% 136.14/20.23 | | |
% 136.14/20.23 | | Case 2:
% 136.14/20.23 | | |
% 136.14/20.23 | | | (24) all_57_10 = e2 & op(e2, e0) = e2
% 136.14/20.23 | | |
% 136.14/20.23 | | | ALPHA: (24) implies:
% 136.14/20.23 | | | (25) all_57_10 = e2
% 136.14/20.23 | | |
% 136.14/20.23 | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 136.14/20.23 | | | (14), (15), (16), (25) are inconsistent by sub-proof #361.
% 136.14/20.23 | | |
% 136.14/20.23 | | End of split
% 136.14/20.23 | |
% 136.14/20.23 | End of split
% 136.14/20.23 |
% 136.14/20.23 End of proof
% 136.14/20.23
% 136.14/20.23 Sub-proof #361 shows that the following formulas are inconsistent:
% 136.14/20.23 ----------------------------------------------------------------
% 136.14/20.23 (1) op(e3, e3) = e2
% 136.14/20.23 (2) ~ (e2 = e0)
% 136.14/20.23 (3) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 136.14/20.23 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 136.14/20.23 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.23 (5) ~ (e2 = e1)
% 136.14/20.23 (6) ~ (e3 = e0)
% 136.14/20.23 (7) ~ (e3 = e2)
% 136.14/20.23 (8) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 136.14/20.23 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 136.14/20.23 (9) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 136.14/20.23 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 136.14/20.23 (10) all_57_3 = e3
% 136.14/20.23 (11) ~ (e3 = e1)
% 136.14/20.23 (12) ~ (e1 = e0)
% 136.14/20.23 (13) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 136.14/20.23 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 136.14/20.23 (14) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 136.14/20.23 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 136.14/20.23 (15) all_57_6 = e2
% 136.14/20.23 (16) all_57_10 = e2
% 136.14/20.23
% 136.14/20.23 Begin of proof
% 136.14/20.23 |
% 136.14/20.23 | BETA: splitting (8) gives:
% 136.14/20.23 |
% 136.14/20.23 | Case 1:
% 136.14/20.23 | |
% 136.14/20.23 | | (17) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 136.14/20.23 | | e3)
% 136.14/20.23 | |
% 136.14/20.23 | | BETA: splitting (17) gives:
% 136.14/20.23 | |
% 136.14/20.23 | | Case 1:
% 136.14/20.23 | | |
% 136.14/20.23 | | | (18) all_57_0 = e3 & op(e3, e3) = e3
% 136.14/20.23 | | |
% 136.14/20.23 | | | ALPHA: (18) implies:
% 136.14/20.23 | | | (19) op(e3, e3) = e3
% 136.14/20.23 | | |
% 136.14/20.23 | | | REF_CLOSE: (1), (4), (7), (19) are inconsistent by sub-proof #778.
% 136.14/20.23 | | |
% 136.14/20.23 | | Case 2:
% 136.14/20.23 | | |
% 136.14/20.23 | | | (20) all_57_2 = e3 & op(e2, e3) = e3
% 136.14/20.23 | | |
% 136.14/20.23 | | | ALPHA: (20) implies:
% 136.14/20.23 | | | (21) all_57_2 = e3
% 136.14/20.23 | | |
% 136.14/20.23 | | | REF_CLOSE: (2), (5), (6), (10), (11), (12), (13), (14), (16), (21) are
% 136.14/20.23 | | | inconsistent by sub-proof #362.
% 136.14/20.23 | | |
% 136.14/20.23 | | End of split
% 136.14/20.23 | |
% 136.14/20.23 | Case 2:
% 136.14/20.23 | |
% 136.14/20.23 | | (22) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 136.14/20.23 | | e3)
% 136.14/20.23 | |
% 136.14/20.23 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (11), (12), (15), (22)
% 136.14/20.23 | | are inconsistent by sub-proof #367.
% 136.14/20.23 | |
% 136.14/20.23 | End of split
% 136.14/20.23 |
% 136.14/20.23 End of proof
% 136.14/20.23
% 136.14/20.23 Sub-proof #362 shows that the following formulas are inconsistent:
% 136.14/20.23 ----------------------------------------------------------------
% 136.14/20.23 (1) ~ (e2 = e0)
% 136.14/20.23 (2) ~ (e2 = e1)
% 136.14/20.23 (3) ~ (e3 = e0)
% 136.14/20.23 (4) all_57_2 = e3
% 136.14/20.23 (5) all_57_3 = e3
% 136.14/20.23 (6) ~ (e3 = e1)
% 136.14/20.23 (7) ~ (e1 = e0)
% 136.14/20.23 (8) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 136.14/20.23 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 136.14/20.23 (9) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 136.14/20.23 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 136.14/20.23 (10) all_57_10 = e2
% 136.14/20.23
% 136.14/20.23 Begin of proof
% 136.14/20.23 |
% 136.14/20.23 | BETA: splitting (9) gives:
% 136.14/20.23 |
% 136.14/20.23 | Case 1:
% 136.14/20.23 | |
% 136.14/20.23 | | (11) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 136.14/20.23 | | e0)
% 136.14/20.23 | |
% 136.14/20.23 | | REF_CLOSE: (3), (4), (5), (11) are inconsistent by sub-proof #373.
% 136.14/20.23 | |
% 136.14/20.23 | Case 2:
% 136.14/20.23 | |
% 136.14/20.23 | | (12) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 136.14/20.23 | | e0)
% 136.14/20.23 | |
% 136.14/20.23 | | BETA: splitting (12) gives:
% 136.14/20.23 | |
% 136.14/20.23 | | Case 1:
% 136.14/20.23 | | |
% 136.14/20.23 | | | (13) all_57_5 = e0 & op(e2, e1) = e0
% 136.14/20.23 | | |
% 136.14/20.23 | | | ALPHA: (13) implies:
% 136.14/20.23 | | | (14) all_57_5 = e0
% 136.14/20.23 | | |
% 136.14/20.23 | | | BETA: splitting (8) gives:
% 136.14/20.23 | | |
% 136.14/20.23 | | | Case 1:
% 136.14/20.23 | | | |
% 136.14/20.23 | | | | (15) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2)
% 136.14/20.23 | | | | = e1)
% 136.14/20.23 | | | |
% 136.14/20.23 | | | | BETA: splitting (15) gives:
% 136.14/20.23 | | | |
% 136.14/20.23 | | | | Case 1:
% 136.14/20.23 | | | | |
% 136.14/20.23 | | | | | (16) all_57_2 = e1 & op(e2, e3) = e1
% 136.14/20.23 | | | | |
% 136.14/20.23 | | | | | REF_CLOSE: (4), (6), (16) are inconsistent by sub-proof #371.
% 136.14/20.23 | | | | |
% 136.14/20.23 | | | | Case 2:
% 136.14/20.23 | | | | |
% 136.14/20.23 | | | | | (17) all_57_3 = e1 & op(e2, e2) = e1
% 136.14/20.23 | | | | |
% 136.14/20.23 | | | | | REF_CLOSE: (5), (6), (17) are inconsistent by sub-proof #370.
% 136.14/20.23 | | | | |
% 136.14/20.23 | | | | End of split
% 136.14/20.23 | | | |
% 136.14/20.23 | | | Case 2:
% 136.14/20.23 | | | |
% 136.14/20.23 | | | | (18) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0)
% 136.14/20.23 | | | | = e1)
% 136.14/20.23 | | | |
% 136.14/20.23 | | | | REF_CLOSE: (2), (7), (10), (14), (18) are inconsistent by sub-proof
% 136.14/20.23 | | | | #364.
% 136.14/20.23 | | | |
% 136.14/20.23 | | | End of split
% 136.14/20.23 | | |
% 136.14/20.23 | | Case 2:
% 136.14/20.23 | | |
% 136.14/20.23 | | | (19) all_57_10 = e0 & op(e2, e0) = e0
% 136.14/20.23 | | |
% 136.14/20.23 | | | REF_CLOSE: (1), (10), (19) are inconsistent by sub-proof #363.
% 136.14/20.23 | | |
% 136.14/20.23 | | End of split
% 136.14/20.23 | |
% 136.14/20.23 | End of split
% 136.14/20.23 |
% 136.14/20.23 End of proof
% 136.14/20.23
% 136.14/20.23 Sub-proof #363 shows that the following formulas are inconsistent:
% 136.14/20.23 ----------------------------------------------------------------
% 136.14/20.23 (1) all_57_10 = e0 & op(e2, e0) = e0
% 136.14/20.23 (2) all_57_10 = e2
% 136.14/20.23 (3) ~ (e2 = e0)
% 136.14/20.23
% 136.14/20.23 Begin of proof
% 136.14/20.23 |
% 136.14/20.23 | ALPHA: (1) implies:
% 136.14/20.23 | (4) all_57_10 = e0
% 136.14/20.23 |
% 136.14/20.23 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.23 | (5) e2 = e0
% 136.14/20.23 |
% 136.14/20.23 | SIMP: (5) implies:
% 136.14/20.23 | (6) e2 = e0
% 136.14/20.23 |
% 136.14/20.23 | REDUCE: (3), (6) imply:
% 136.14/20.23 | (7) $false
% 136.14/20.23 |
% 136.14/20.23 | CLOSE: (7) is inconsistent.
% 136.14/20.23 |
% 136.14/20.23 End of proof
% 136.14/20.23
% 136.14/20.23 Sub-proof #364 shows that the following formulas are inconsistent:
% 136.14/20.23 ----------------------------------------------------------------
% 136.14/20.23 (1) ~ (e2 = e1)
% 136.14/20.23 (2) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 136.14/20.23 (3) ~ (e1 = e0)
% 136.14/20.23 (4) all_57_5 = e0
% 136.14/20.23 (5) all_57_10 = e2
% 136.14/20.23
% 136.14/20.23 Begin of proof
% 136.14/20.23 |
% 136.14/20.23 | BETA: splitting (2) gives:
% 136.14/20.23 |
% 136.14/20.23 | Case 1:
% 136.14/20.23 | |
% 136.14/20.23 | | (6) all_57_5 = e1 & op(e2, e1) = e1
% 136.14/20.23 | |
% 136.14/20.23 | | REF_CLOSE: (3), (4), (6) are inconsistent by sub-proof #365.
% 136.14/20.23 | |
% 136.14/20.23 | Case 2:
% 136.14/20.23 | |
% 136.14/20.23 | | (7) all_57_10 = e1 & op(e2, e0) = e1
% 136.14/20.23 | |
% 136.14/20.23 | | ALPHA: (7) implies:
% 136.14/20.23 | | (8) all_57_10 = e1
% 136.14/20.23 | |
% 136.14/20.23 | | REF_CLOSE: (1), (5), (8) are inconsistent by sub-proof #414.
% 136.14/20.23 | |
% 136.14/20.23 | End of split
% 136.14/20.23 |
% 136.14/20.23 End of proof
% 136.14/20.23
% 136.14/20.23 Sub-proof #365 shows that the following formulas are inconsistent:
% 136.14/20.23 ----------------------------------------------------------------
% 136.14/20.23 (1) all_57_5 = e1 & op(e2, e1) = e1
% 136.14/20.23 (2) all_57_5 = e0
% 136.14/20.23 (3) ~ (e1 = e0)
% 136.14/20.23
% 136.14/20.23 Begin of proof
% 136.14/20.23 |
% 136.14/20.23 | ALPHA: (1) implies:
% 136.14/20.23 | (4) all_57_5 = e1
% 136.14/20.23 |
% 136.14/20.23 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.23 | (5) e1 = e0
% 136.14/20.23 |
% 136.14/20.23 | REDUCE: (3), (5) imply:
% 136.14/20.23 | (6) $false
% 136.14/20.23 |
% 136.14/20.23 | CLOSE: (6) is inconsistent.
% 136.14/20.23 |
% 136.14/20.23 End of proof
% 136.14/20.23
% 136.14/20.23 Sub-proof #366 shows that the following formulas are inconsistent:
% 136.14/20.23 ----------------------------------------------------------------
% 136.14/20.23 (1) op(e3, e3) = e2
% 136.14/20.23 (2) ~ (e2 = e0)
% 136.14/20.23 (3) all_57_5 = e2
% 136.14/20.23 (4) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 136.14/20.23 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 136.14/20.23 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.23 (6) ~ (e2 = e1)
% 136.14/20.23 (7) ~ (e3 = e0)
% 136.14/20.23 (8) ~ (e3 = e2)
% 136.14/20.23 (9) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 136.14/20.23 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 136.14/20.23 (10) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 136.14/20.23 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 136.14/20.23 (11) all_57_3 = e3
% 136.14/20.23 (12) ~ (e3 = e1)
% 136.14/20.23 (13) ~ (e1 = e0)
% 136.14/20.23 (14) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 136.14/20.23 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 136.14/20.23 (15) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 136.14/20.23 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 136.14/20.23 (16) all_57_6 = e2
% 136.14/20.23
% 136.14/20.23 Begin of proof
% 136.14/20.23 |
% 136.14/20.23 | BETA: splitting (9) gives:
% 136.14/20.23 |
% 136.14/20.23 | Case 1:
% 136.14/20.23 | |
% 136.14/20.23 | | (17) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 136.14/20.23 | | e3)
% 136.14/20.23 | |
% 136.14/20.23 | | BETA: splitting (17) gives:
% 136.14/20.23 | |
% 136.14/20.23 | | Case 1:
% 136.14/20.23 | | |
% 136.14/20.23 | | | (18) all_57_0 = e3 & op(e3, e3) = e3
% 136.14/20.23 | | |
% 136.14/20.23 | | | ALPHA: (18) implies:
% 136.14/20.23 | | | (19) op(e3, e3) = e3
% 136.14/20.23 | | |
% 136.14/20.23 | | | REF_CLOSE: (1), (5), (8), (19) are inconsistent by sub-proof #778.
% 136.14/20.23 | | |
% 136.14/20.23 | | Case 2:
% 136.14/20.23 | | |
% 136.14/20.23 | | | (20) all_57_2 = e3 & op(e2, e3) = e3
% 136.14/20.23 | | |
% 136.14/20.23 | | | ALPHA: (20) implies:
% 136.14/20.23 | | | (21) all_57_2 = e3
% 136.14/20.23 | | |
% 136.14/20.23 | | | REF_CLOSE: (2), (3), (6), (7), (11), (12), (13), (14), (15), (21) are
% 136.14/20.23 | | | inconsistent by sub-proof #368.
% 136.14/20.23 | | |
% 136.14/20.23 | | End of split
% 136.14/20.23 | |
% 136.14/20.23 | Case 2:
% 136.14/20.23 | |
% 136.14/20.23 | | (22) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 136.14/20.23 | | e3)
% 136.14/20.23 | |
% 136.14/20.23 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (12), (13), (16), (22)
% 136.14/20.23 | | are inconsistent by sub-proof #367.
% 136.14/20.23 | |
% 136.14/20.23 | End of split
% 136.14/20.23 |
% 136.14/20.23 End of proof
% 136.14/20.23
% 136.14/20.23 Sub-proof #367 shows that the following formulas are inconsistent:
% 136.14/20.23 ----------------------------------------------------------------
% 136.14/20.23 (1) op(e3, e3) = e2
% 136.14/20.23 (2) ~ (e2 = e0)
% 136.14/20.23 (3) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 136.14/20.23 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 136.14/20.23 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.23 (5) ~ (e2 = e1)
% 136.14/20.23 (6) ~ (e3 = e0)
% 136.14/20.23 (7) ~ (e3 = e2)
% 136.14/20.23 (8) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 136.14/20.23 (9) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 136.14/20.23 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 136.14/20.23 (10) ~ (e3 = e1)
% 136.14/20.23 (11) ~ (e1 = e0)
% 136.14/20.23 (12) all_57_6 = e2
% 136.14/20.23
% 136.14/20.23 Begin of proof
% 136.14/20.23 |
% 136.14/20.23 | BETA: splitting (8) gives:
% 136.14/20.23 |
% 136.14/20.23 | Case 1:
% 136.14/20.23 | |
% 136.14/20.23 | | (13) all_57_6 = e3 & op(e1, e3) = e3
% 136.14/20.23 | |
% 136.14/20.23 | | ALPHA: (13) implies:
% 136.14/20.23 | | (14) all_57_6 = e3
% 136.14/20.23 | |
% 136.14/20.23 | | REF_CLOSE: (7), (12), (14) are inconsistent by sub-proof #592.
% 136.14/20.23 | |
% 136.14/20.23 | Case 2:
% 136.14/20.23 | |
% 136.14/20.23 | | (15) all_57_12 = e3 & op(e0, e3) = e3
% 136.14/20.23 | |
% 136.14/20.23 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (10), (11), (12), (15) are
% 136.14/20.23 | | inconsistent by sub-proof #391.
% 136.14/20.23 | |
% 136.14/20.23 | End of split
% 136.14/20.23 |
% 136.14/20.23 End of proof
% 136.14/20.23
% 136.14/20.23 Sub-proof #368 shows that the following formulas are inconsistent:
% 136.14/20.23 ----------------------------------------------------------------
% 136.14/20.23 (1) ~ (e2 = e0)
% 136.14/20.23 (2) all_57_5 = e2
% 136.14/20.23 (3) ~ (e2 = e1)
% 136.14/20.23 (4) ~ (e3 = e0)
% 136.14/20.23 (5) all_57_2 = e3
% 136.14/20.23 (6) all_57_3 = e3
% 136.14/20.23 (7) ~ (e3 = e1)
% 136.14/20.23 (8) ~ (e1 = e0)
% 136.14/20.23 (9) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 136.14/20.23 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 136.14/20.23 (10) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 136.14/20.23 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 136.14/20.23
% 136.14/20.23 Begin of proof
% 136.14/20.23 |
% 136.14/20.23 | BETA: splitting (10) gives:
% 136.14/20.23 |
% 136.14/20.23 | Case 1:
% 136.14/20.23 | |
% 136.14/20.23 | | (11) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 136.14/20.23 | | e0)
% 136.14/20.23 | |
% 136.14/20.23 | | REF_CLOSE: (4), (5), (6), (11) are inconsistent by sub-proof #373.
% 136.14/20.23 | |
% 136.14/20.23 | Case 2:
% 136.14/20.23 | |
% 136.14/20.23 | | (12) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 136.14/20.23 | | e0)
% 136.14/20.23 | |
% 136.14/20.23 | | BETA: splitting (12) gives:
% 136.14/20.23 | |
% 136.14/20.23 | | Case 1:
% 136.14/20.23 | | |
% 136.14/20.23 | | | (13) all_57_5 = e0 & op(e2, e1) = e0
% 136.14/20.23 | | |
% 136.14/20.23 | | | ALPHA: (13) implies:
% 136.14/20.23 | | | (14) all_57_5 = e0
% 136.14/20.23 | | |
% 136.14/20.23 | | | REF_CLOSE: (1), (2), (14) are inconsistent by sub-proof #372.
% 136.14/20.23 | | |
% 136.14/20.23 | | Case 2:
% 136.14/20.23 | | |
% 136.14/20.23 | | | (15) all_57_10 = e0 & op(e2, e0) = e0
% 136.14/20.23 | | |
% 136.14/20.23 | | | ALPHA: (15) implies:
% 136.14/20.23 | | | (16) all_57_10 = e0
% 136.14/20.23 | | |
% 136.14/20.23 | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (16) are inconsistent by
% 136.14/20.23 | | | sub-proof #369.
% 136.14/20.23 | | |
% 136.14/20.23 | | End of split
% 136.14/20.23 | |
% 136.14/20.23 | End of split
% 136.14/20.23 |
% 136.14/20.23 End of proof
% 136.14/20.23
% 136.14/20.23 Sub-proof #369 shows that the following formulas are inconsistent:
% 136.14/20.23 ----------------------------------------------------------------
% 136.14/20.23 (1) all_57_5 = e2
% 136.14/20.23 (2) ~ (e2 = e1)
% 136.14/20.23 (3) all_57_10 = e0
% 136.14/20.23 (4) all_57_2 = e3
% 136.14/20.24 (5) all_57_3 = e3
% 136.14/20.24 (6) ~ (e3 = e1)
% 136.14/20.24 (7) ~ (e1 = e0)
% 136.14/20.24 (8) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 136.14/20.24 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 136.14/20.24
% 136.14/20.24 Begin of proof
% 136.14/20.24 |
% 136.14/20.24 | BETA: splitting (8) gives:
% 136.14/20.24 |
% 136.14/20.24 | Case 1:
% 136.14/20.24 | |
% 136.14/20.24 | | (9) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 136.14/20.24 | |
% 136.14/20.24 | | BETA: splitting (9) gives:
% 136.14/20.24 | |
% 136.14/20.24 | | Case 1:
% 136.14/20.24 | | |
% 136.14/20.24 | | | (10) all_57_2 = e1 & op(e2, e3) = e1
% 136.14/20.24 | | |
% 136.14/20.24 | | | REF_CLOSE: (4), (6), (10) are inconsistent by sub-proof #371.
% 136.14/20.24 | | |
% 136.14/20.24 | | Case 2:
% 136.14/20.24 | | |
% 136.14/20.24 | | | (11) all_57_3 = e1 & op(e2, e2) = e1
% 136.14/20.24 | | |
% 136.14/20.24 | | | REF_CLOSE: (5), (6), (11) are inconsistent by sub-proof #370.
% 136.14/20.24 | | |
% 136.14/20.24 | | End of split
% 136.14/20.24 | |
% 136.14/20.24 | Case 2:
% 136.14/20.24 | |
% 136.14/20.24 | | (12) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 136.14/20.24 | | e1)
% 136.14/20.24 | |
% 136.14/20.24 | | BETA: splitting (12) gives:
% 136.14/20.24 | |
% 136.14/20.24 | | Case 1:
% 136.14/20.24 | | |
% 136.14/20.24 | | | (13) all_57_5 = e1 & op(e2, e1) = e1
% 136.14/20.24 | | |
% 136.14/20.24 | | | ALPHA: (13) implies:
% 136.14/20.24 | | | (14) all_57_5 = e1
% 136.14/20.24 | | |
% 136.14/20.24 | | | REF_CLOSE: (1), (2), (14) are inconsistent by sub-proof #418.
% 136.14/20.24 | | |
% 136.14/20.24 | | Case 2:
% 136.14/20.24 | | |
% 136.14/20.24 | | | (15) all_57_10 = e1 & op(e2, e0) = e1
% 136.14/20.24 | | |
% 136.14/20.24 | | | ALPHA: (15) implies:
% 136.14/20.24 | | | (16) all_57_10 = e1
% 136.14/20.24 | | |
% 136.14/20.24 | | | COMBINE_EQS: (3), (16) imply:
% 136.14/20.24 | | | (17) e1 = e0
% 136.14/20.24 | | |
% 136.14/20.24 | | | REDUCE: (7), (17) imply:
% 136.14/20.24 | | | (18) $false
% 136.14/20.24 | | |
% 136.14/20.24 | | | CLOSE: (18) is inconsistent.
% 136.14/20.24 | | |
% 136.14/20.24 | | End of split
% 136.14/20.24 | |
% 136.14/20.24 | End of split
% 136.14/20.24 |
% 136.14/20.24 End of proof
% 136.14/20.24
% 136.14/20.24 Sub-proof #370 shows that the following formulas are inconsistent:
% 136.14/20.24 ----------------------------------------------------------------
% 136.14/20.24 (1) all_57_3 = e1 & op(e2, e2) = e1
% 136.14/20.24 (2) all_57_3 = e3
% 136.14/20.24 (3) ~ (e3 = e1)
% 136.14/20.24
% 136.14/20.24 Begin of proof
% 136.14/20.24 |
% 136.14/20.24 | ALPHA: (1) implies:
% 136.14/20.24 | (4) all_57_3 = e1
% 136.14/20.24 |
% 136.14/20.24 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.24 | (5) e3 = e1
% 136.14/20.24 |
% 136.14/20.24 | REDUCE: (3), (5) imply:
% 136.14/20.24 | (6) $false
% 136.14/20.24 |
% 136.14/20.24 | CLOSE: (6) is inconsistent.
% 136.14/20.24 |
% 136.14/20.24 End of proof
% 136.14/20.24
% 136.14/20.24 Sub-proof #371 shows that the following formulas are inconsistent:
% 136.14/20.24 ----------------------------------------------------------------
% 136.14/20.24 (1) all_57_2 = e1 & op(e2, e3) = e1
% 136.14/20.24 (2) all_57_2 = e3
% 136.14/20.24 (3) ~ (e3 = e1)
% 136.14/20.24
% 136.14/20.24 Begin of proof
% 136.14/20.24 |
% 136.14/20.24 | ALPHA: (1) implies:
% 136.14/20.24 | (4) all_57_2 = e1
% 136.14/20.24 |
% 136.14/20.24 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.24 | (5) e3 = e1
% 136.14/20.24 |
% 136.14/20.24 | SIMP: (5) implies:
% 136.14/20.24 | (6) e3 = e1
% 136.14/20.24 |
% 136.14/20.24 | REDUCE: (3), (6) imply:
% 136.14/20.24 | (7) $false
% 136.14/20.24 |
% 136.14/20.24 | CLOSE: (7) is inconsistent.
% 136.14/20.24 |
% 136.14/20.24 End of proof
% 136.14/20.24
% 136.14/20.24 Sub-proof #372 shows that the following formulas are inconsistent:
% 136.14/20.24 ----------------------------------------------------------------
% 136.14/20.24 (1) all_57_5 = e2
% 136.14/20.24 (2) all_57_5 = e0
% 136.14/20.24 (3) ~ (e2 = e0)
% 136.14/20.24
% 136.14/20.24 Begin of proof
% 136.14/20.24 |
% 136.14/20.24 | COMBINE_EQS: (1), (2) imply:
% 136.14/20.24 | (4) e2 = e0
% 136.14/20.24 |
% 136.14/20.24 | SIMP: (4) implies:
% 136.14/20.24 | (5) e2 = e0
% 136.14/20.24 |
% 136.14/20.24 | REDUCE: (3), (5) imply:
% 136.14/20.24 | (6) $false
% 136.14/20.24 |
% 136.14/20.24 | CLOSE: (6) is inconsistent.
% 136.14/20.24 |
% 136.14/20.24 End of proof
% 136.14/20.24
% 136.14/20.24 Sub-proof #373 shows that the following formulas are inconsistent:
% 136.14/20.24 ----------------------------------------------------------------
% 136.14/20.24 (1) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 136.14/20.24 (2) all_57_2 = e3
% 136.14/20.24 (3) ~ (e3 = e0)
% 136.14/20.24 (4) all_57_3 = e3
% 136.14/20.24
% 136.14/20.24 Begin of proof
% 136.14/20.24 |
% 136.14/20.24 | BETA: splitting (1) gives:
% 136.14/20.24 |
% 136.14/20.24 | Case 1:
% 136.14/20.24 | |
% 136.14/20.24 | | (5) all_57_2 = e0 & op(e2, e3) = e0
% 136.14/20.24 | |
% 136.14/20.24 | | ALPHA: (5) implies:
% 136.14/20.24 | | (6) all_57_2 = e0
% 136.14/20.24 | |
% 136.14/20.24 | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #593.
% 136.14/20.24 | |
% 136.14/20.24 | Case 2:
% 136.14/20.24 | |
% 136.14/20.24 | | (7) all_57_3 = e0 & op(e2, e2) = e0
% 136.14/20.24 | |
% 136.14/20.24 | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #374.
% 136.14/20.24 | |
% 136.14/20.24 | End of split
% 136.14/20.24 |
% 136.14/20.24 End of proof
% 136.14/20.24
% 136.14/20.24 Sub-proof #374 shows that the following formulas are inconsistent:
% 136.14/20.24 ----------------------------------------------------------------
% 136.14/20.24 (1) all_57_3 = e0 & op(e2, e2) = e0
% 136.14/20.24 (2) all_57_3 = e3
% 136.14/20.24 (3) ~ (e3 = e0)
% 136.14/20.24
% 136.14/20.24 Begin of proof
% 136.14/20.24 |
% 136.14/20.24 | ALPHA: (1) implies:
% 136.14/20.24 | (4) all_57_3 = e0
% 136.14/20.24 |
% 136.14/20.24 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.24 | (5) e3 = e0
% 136.14/20.24 |
% 136.14/20.24 | REDUCE: (3), (5) imply:
% 136.14/20.24 | (6) $false
% 136.14/20.24 |
% 136.14/20.24 | CLOSE: (6) is inconsistent.
% 136.14/20.24 |
% 136.14/20.24 End of proof
% 136.14/20.24
% 136.14/20.24 Sub-proof #375 shows that the following formulas are inconsistent:
% 136.14/20.24 ----------------------------------------------------------------
% 136.14/20.24 (1) all_57_3 = e2 & op(e2, e2) = e2
% 136.14/20.24 (2) all_57_3 = e3
% 136.14/20.24 (3) ~ (e3 = e2)
% 136.14/20.24
% 136.14/20.24 Begin of proof
% 136.14/20.24 |
% 136.14/20.24 | ALPHA: (1) implies:
% 136.14/20.24 | (4) all_57_3 = e2
% 136.14/20.24 |
% 136.14/20.24 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.24 | (5) e3 = e2
% 136.14/20.24 |
% 136.14/20.24 | REDUCE: (3), (5) imply:
% 136.14/20.24 | (6) $false
% 136.14/20.24 |
% 136.14/20.24 | CLOSE: (6) is inconsistent.
% 136.14/20.24 |
% 136.14/20.24 End of proof
% 136.14/20.24
% 136.14/20.24 Sub-proof #376 shows that the following formulas are inconsistent:
% 136.14/20.24 ----------------------------------------------------------------
% 136.14/20.24 (1) all_57_1 = e3 & op(e3, e2) = e3
% 136.14/20.24 (2) all_57_1 = e0
% 136.14/20.24 (3) ~ (e3 = e0)
% 136.14/20.24
% 136.14/20.24 Begin of proof
% 136.14/20.24 |
% 136.14/20.24 | ALPHA: (1) implies:
% 136.14/20.24 | (4) all_57_1 = e3
% 136.14/20.24 |
% 136.14/20.24 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.24 | (5) e3 = e0
% 136.14/20.24 |
% 136.14/20.24 | SIMP: (5) implies:
% 136.14/20.24 | (6) e3 = e0
% 136.14/20.24 |
% 136.14/20.24 | REDUCE: (3), (6) imply:
% 136.14/20.24 | (7) $false
% 136.14/20.24 |
% 136.14/20.24 | CLOSE: (7) is inconsistent.
% 136.14/20.24 |
% 136.14/20.24 End of proof
% 136.14/20.24
% 136.14/20.24 Sub-proof #377 shows that the following formulas are inconsistent:
% 136.14/20.24 ----------------------------------------------------------------
% 136.14/20.24 (1) all_57_10 = e3 & op(e2, e0) = e3
% 136.14/20.24 (2) all_57_10 = e0
% 136.14/20.24 (3) ~ (e3 = e0)
% 136.14/20.24
% 136.14/20.24 Begin of proof
% 136.14/20.24 |
% 136.14/20.24 | ALPHA: (1) implies:
% 136.14/20.24 | (4) all_57_10 = e3
% 136.14/20.24 |
% 136.14/20.24 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.24 | (5) e3 = e0
% 136.14/20.24 |
% 136.14/20.24 | REDUCE: (3), (5) imply:
% 136.14/20.24 | (6) $false
% 136.14/20.24 |
% 136.14/20.24 | CLOSE: (6) is inconsistent.
% 136.14/20.24 |
% 136.14/20.24 End of proof
% 136.14/20.24
% 136.14/20.24 Sub-proof #378 shows that the following formulas are inconsistent:
% 136.14/20.24 ----------------------------------------------------------------
% 136.14/20.24 (1) op(e3, e3) = e2
% 136.14/20.24 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.24 (3) ~ (e2 = e1)
% 136.14/20.24 (4) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1)
% 136.14/20.24 (5) op(e3, e2) = all_52_4
% 136.14/20.24 (6) ~ (all_52_4 = e1)
% 136.14/20.24
% 136.14/20.24 Begin of proof
% 136.14/20.24 |
% 136.14/20.24 | BETA: splitting (4) gives:
% 136.14/20.24 |
% 136.14/20.24 | Case 1:
% 136.14/20.24 | |
% 136.14/20.24 | | (7) all_57_0 = e1 & op(e3, e3) = e1
% 136.14/20.24 | |
% 136.14/20.24 | | ALPHA: (7) implies:
% 136.14/20.24 | | (8) op(e3, e3) = e1
% 136.14/20.24 | |
% 136.14/20.24 | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #743.
% 136.14/20.24 | |
% 136.14/20.24 | Case 2:
% 136.14/20.24 | |
% 136.14/20.24 | | (9) all_57_1 = e1 & op(e3, e2) = e1
% 136.14/20.24 | |
% 136.14/20.24 | | REF_CLOSE: (2), (5), (6), (9) are inconsistent by sub-proof #684.
% 136.14/20.24 | |
% 136.14/20.24 | End of split
% 136.14/20.24 |
% 136.14/20.24 End of proof
% 136.14/20.24
% 136.14/20.24 Sub-proof #379 shows that the following formulas are inconsistent:
% 136.14/20.24 ----------------------------------------------------------------
% 136.14/20.24 (1) all_57_4 = e3 & op(e3, e1) = e3
% 136.14/20.24 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.24 (3) op(e3, e1) = all_36_0
% 136.14/20.24 (4) op(e3, e1) = all_52_8
% 136.14/20.24 (5) ~ (all_52_8 = e3)
% 136.14/20.24
% 136.14/20.24 Begin of proof
% 136.14/20.24 |
% 136.14/20.24 | ALPHA: (1) implies:
% 136.14/20.24 | (6) op(e3, e1) = e3
% 136.14/20.24 |
% 136.14/20.24 | GROUND_INST: instantiating (2) with all_52_8, e3, e1, e3, simplifying with
% 136.14/20.24 | (4), (6) gives:
% 136.14/20.24 | (7) all_52_8 = e3
% 136.14/20.24 |
% 136.14/20.24 | GROUND_INST: instantiating (2) with all_52_8, all_36_0, e1, e3, simplifying
% 136.14/20.24 | with (3), (4) gives:
% 136.14/20.24 | (8) all_52_8 = all_36_0
% 136.14/20.24 |
% 136.14/20.24 | COMBINE_EQS: (7), (8) imply:
% 136.14/20.24 | (9) all_36_0 = e3
% 136.14/20.24 |
% 136.14/20.24 | REDUCE: (5), (7) imply:
% 136.14/20.24 | (10) $false
% 136.14/20.24 |
% 136.14/20.24 | CLOSE: (10) is inconsistent.
% 136.14/20.24 |
% 136.14/20.24 End of proof
% 136.14/20.24
% 136.14/20.24 Sub-proof #380 shows that the following formulas are inconsistent:
% 136.14/20.24 ----------------------------------------------------------------
% 136.14/20.24 (1) ~ (all_16_1 = e0) & op(e2, e2) = all_16_1 & $i(all_16_1)
% 136.14/20.24 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.24 (3) op(e2, e2) = e0
% 136.14/20.24
% 136.14/20.24 Begin of proof
% 136.14/20.24 |
% 136.14/20.24 | ALPHA: (1) implies:
% 136.14/20.24 | (4) ~ (all_16_1 = e0)
% 136.14/20.24 | (5) op(e2, e2) = all_16_1
% 136.14/20.24 |
% 136.14/20.24 | GROUND_INST: instantiating (2) with e0, all_16_1, e2, e2, simplifying with
% 136.14/20.24 | (3), (5) gives:
% 136.14/20.24 | (6) all_16_1 = e0
% 136.14/20.24 |
% 136.14/20.24 | REDUCE: (4), (6) imply:
% 136.14/20.24 | (7) $false
% 136.14/20.24 |
% 136.14/20.24 | CLOSE: (7) is inconsistent.
% 136.14/20.24 |
% 136.14/20.24 End of proof
% 136.14/20.24
% 136.14/20.24 Sub-proof #381 shows that the following formulas are inconsistent:
% 136.14/20.24 ----------------------------------------------------------------
% 136.14/20.24 (1) ~ (all_16_0 = e0)
% 136.14/20.24 (2) ~ (all_16_0 = e1)
% 136.14/20.24 (3) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 136.14/20.24 (4) ~ (all_16_0 = e2)
% 136.14/20.24 (5) all_54_4 = all_16_0
% 136.14/20.24
% 136.14/20.24 Begin of proof
% 136.14/20.24 |
% 136.14/20.24 | BETA: splitting (3) gives:
% 136.14/20.24 |
% 136.14/20.24 | Case 1:
% 136.14/20.24 | |
% 136.14/20.24 | | (6) all_54_4 = e2
% 136.14/20.24 | |
% 136.14/20.24 | | COMBINE_EQS: (5), (6) imply:
% 136.14/20.24 | | (7) all_16_0 = e2
% 136.14/20.24 | |
% 136.14/20.24 | | REDUCE: (4), (7) imply:
% 136.14/20.24 | | (8) $false
% 136.14/20.24 | |
% 136.14/20.24 | | CLOSE: (8) is inconsistent.
% 136.14/20.24 | |
% 136.14/20.24 | Case 2:
% 136.14/20.24 | |
% 136.14/20.24 | | (9) all_54_4 = e1 | all_54_4 = e0
% 136.14/20.24 | |
% 136.14/20.24 | | BETA: splitting (9) gives:
% 136.14/20.24 | |
% 136.14/20.24 | | Case 1:
% 136.14/20.24 | | |
% 136.14/20.24 | | | (10) all_54_4 = e1
% 136.14/20.24 | | |
% 136.14/20.24 | | | COMBINE_EQS: (5), (10) imply:
% 136.14/20.24 | | | (11) all_16_0 = e1
% 136.14/20.24 | | |
% 136.14/20.24 | | | REDUCE: (2), (11) imply:
% 136.14/20.24 | | | (12) $false
% 136.14/20.24 | | |
% 136.14/20.24 | | | CLOSE: (12) is inconsistent.
% 136.14/20.24 | | |
% 136.14/20.24 | | Case 2:
% 136.14/20.24 | | |
% 136.14/20.24 | | | (13) all_54_4 = e0
% 136.14/20.24 | | |
% 136.14/20.24 | | | COMBINE_EQS: (5), (13) imply:
% 136.14/20.24 | | | (14) all_16_0 = e0
% 136.14/20.24 | | |
% 136.14/20.24 | | | REDUCE: (1), (14) imply:
% 136.14/20.24 | | | (15) $false
% 136.14/20.24 | | |
% 136.14/20.24 | | | CLOSE: (15) is inconsistent.
% 136.14/20.24 | | |
% 136.14/20.24 | | End of split
% 136.14/20.24 | |
% 136.14/20.24 | End of split
% 136.14/20.24 |
% 136.14/20.24 End of proof
% 136.14/20.24
% 136.14/20.24 Sub-proof #382 shows that the following formulas are inconsistent:
% 136.14/20.24 ----------------------------------------------------------------
% 136.14/20.24 (1) all_57_4 = e1 & op(e3, e1) = e1
% 136.14/20.24 (2) all_57_4 = e3
% 136.14/20.24 (3) ~ (e3 = e1)
% 136.14/20.24
% 136.14/20.24 Begin of proof
% 136.14/20.24 |
% 136.14/20.24 | ALPHA: (1) implies:
% 136.14/20.24 | (4) all_57_4 = e1
% 136.14/20.24 |
% 136.14/20.24 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.24 | (5) e3 = e1
% 136.14/20.24 |
% 136.14/20.24 | REDUCE: (3), (5) imply:
% 136.14/20.24 | (6) $false
% 136.14/20.24 |
% 136.14/20.24 | CLOSE: (6) is inconsistent.
% 136.14/20.24 |
% 136.14/20.24 End of proof
% 136.14/20.24
% 136.14/20.24 Sub-proof #383 shows that the following formulas are inconsistent:
% 136.14/20.24 ----------------------------------------------------------------
% 136.14/20.24 (1) all_57_9 = e1
% 136.14/20.24 (2) all_57_9 = e0
% 136.14/20.24 (3) ~ (e1 = e0)
% 136.14/20.24
% 136.14/20.24 Begin of proof
% 136.14/20.24 |
% 136.14/20.24 | COMBINE_EQS: (1), (2) imply:
% 136.14/20.24 | (4) e1 = e0
% 136.14/20.24 |
% 136.14/20.24 | SIMP: (4) implies:
% 136.14/20.24 | (5) e1 = e0
% 136.14/20.24 |
% 136.14/20.24 | REDUCE: (3), (5) imply:
% 136.14/20.24 | (6) $false
% 136.14/20.24 |
% 136.14/20.24 | CLOSE: (6) is inconsistent.
% 136.14/20.24 |
% 136.14/20.24 End of proof
% 136.14/20.24
% 136.14/20.24 Sub-proof #384 shows that the following formulas are inconsistent:
% 136.14/20.24 ----------------------------------------------------------------
% 136.14/20.24 (1) all_57_4 = e0 & op(e3, e1) = e0
% 136.14/20.24 (2) all_57_4 = e3
% 136.14/20.24 (3) ~ (e3 = e0)
% 136.14/20.24
% 136.14/20.24 Begin of proof
% 136.14/20.24 |
% 136.14/20.24 | ALPHA: (1) implies:
% 136.14/20.24 | (4) all_57_4 = e0
% 136.14/20.24 |
% 136.14/20.24 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.24 | (5) e3 = e0
% 136.14/20.24 |
% 136.14/20.24 | REDUCE: (3), (5) imply:
% 136.14/20.24 | (6) $false
% 136.14/20.24 |
% 136.14/20.24 | CLOSE: (6) is inconsistent.
% 136.14/20.24 |
% 136.14/20.24 End of proof
% 136.14/20.24
% 136.14/20.24 Sub-proof #385 shows that the following formulas are inconsistent:
% 136.14/20.24 ----------------------------------------------------------------
% 136.14/20.24 (1) all_57_7 = e2 & op(e1, e2) = e2
% 136.14/20.24 (2) all_57_7 = e3
% 136.14/20.24 (3) ~ (e3 = e2)
% 136.14/20.24
% 136.14/20.24 Begin of proof
% 136.14/20.24 |
% 136.14/20.24 | ALPHA: (1) implies:
% 136.14/20.24 | (4) all_57_7 = e2
% 136.14/20.24 |
% 136.14/20.24 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.24 | (5) e3 = e2
% 136.14/20.24 |
% 136.14/20.24 | REDUCE: (3), (5) imply:
% 136.14/20.24 | (6) $false
% 136.14/20.24 |
% 136.14/20.24 | CLOSE: (6) is inconsistent.
% 136.14/20.24 |
% 136.14/20.24 End of proof
% 136.14/20.24
% 136.14/20.24 Sub-proof #386 shows that the following formulas are inconsistent:
% 136.14/20.24 ----------------------------------------------------------------
% 136.14/20.24 (1) op(e0, e0) = e0
% 136.14/20.24 (2) op(e2, e0) = all_52_13
% 136.14/20.24 (3) ~ (all_52_14 = e3)
% 136.14/20.24 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.24 (5) ~ (e3 = e0)
% 136.14/20.24 (6) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 136.14/20.24 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 136.14/20.24 (7) ~ (all_52_13 = e3)
% 136.14/20.24 (8) op(e1, e0) = all_52_14
% 136.14/20.24 (9) all_57_9 = e0
% 136.14/20.24
% 136.14/20.24 Begin of proof
% 136.14/20.24 |
% 136.14/20.24 | BETA: splitting (6) gives:
% 136.14/20.24 |
% 136.14/20.24 | Case 1:
% 136.14/20.24 | |
% 136.14/20.24 | | (10) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 136.14/20.24 | | e3)
% 136.14/20.24 | |
% 136.14/20.24 | | BETA: splitting (10) gives:
% 136.14/20.24 | |
% 136.14/20.24 | | Case 1:
% 136.14/20.24 | | |
% 136.14/20.24 | | | (11) all_57_9 = e3 & op(e3, e0) = e3
% 136.14/20.24 | | |
% 136.14/20.24 | | | ALPHA: (11) implies:
% 136.14/20.24 | | | (12) all_57_9 = e3
% 136.14/20.24 | | |
% 136.14/20.24 | | | REF_CLOSE: (5), (9), (12) are inconsistent by sub-proof #670.
% 136.14/20.24 | | |
% 136.14/20.24 | | Case 2:
% 136.14/20.24 | | |
% 136.14/20.24 | | | (13) all_57_10 = e3 & op(e2, e0) = e3
% 136.14/20.24 | | |
% 136.14/20.24 | | | REF_CLOSE: (2), (4), (7), (13) are inconsistent by sub-proof #749.
% 136.14/20.24 | | |
% 136.14/20.24 | | End of split
% 136.14/20.24 | |
% 136.14/20.24 | Case 2:
% 136.14/20.24 | |
% 136.14/20.24 | | (14) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 136.14/20.24 | | e3)
% 136.14/20.24 | |
% 136.14/20.24 | | REF_CLOSE: (1), (3), (4), (5), (8), (14) are inconsistent by sub-proof #387.
% 136.14/20.24 | |
% 136.14/20.24 | End of split
% 136.14/20.24 |
% 136.14/20.24 End of proof
% 136.14/20.24
% 136.14/20.24 Sub-proof #387 shows that the following formulas are inconsistent:
% 136.14/20.24 ----------------------------------------------------------------
% 136.14/20.24 (1) op(e0, e0) = e0
% 136.14/20.24 (2) ~ (all_52_14 = e3)
% 136.14/20.24 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.24 (4) ~ (e3 = e0)
% 136.14/20.24 (5) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 136.14/20.24 (6) op(e1, e0) = all_52_14
% 136.14/20.24
% 136.14/20.24 Begin of proof
% 136.14/20.24 |
% 136.14/20.24 | BETA: splitting (5) gives:
% 136.14/20.24 |
% 136.14/20.24 | Case 1:
% 136.14/20.24 | |
% 136.14/20.24 | | (7) all_57_11 = e3 & op(e1, e0) = e3
% 136.14/20.24 | |
% 136.14/20.24 | | REF_CLOSE: (2), (3), (6), (7) are inconsistent by sub-proof #750.
% 136.14/20.24 | |
% 136.14/20.24 | Case 2:
% 136.14/20.24 | |
% 136.14/20.24 | | (8) all_57_15 = e3 & op(e0, e0) = e3
% 136.14/20.24 | |
% 136.14/20.24 | | ALPHA: (8) implies:
% 136.14/20.24 | | (9) op(e0, e0) = e3
% 136.14/20.24 | |
% 136.14/20.24 | | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #715.
% 136.14/20.24 | |
% 136.14/20.24 | End of split
% 136.14/20.24 |
% 136.14/20.24 End of proof
% 136.14/20.24
% 136.14/20.24 Sub-proof #388 shows that the following formulas are inconsistent:
% 136.14/20.24 ----------------------------------------------------------------
% 136.14/20.24 (1) ~ (e2 = e0)
% 136.14/20.24 (2) all_57_3 = e0
% 136.14/20.24 (3) ~ (e2 = e1)
% 136.14/20.24 (4) ~ (e3 = e2)
% 136.14/20.24 (5) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 136.14/20.24 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 136.14/20.24 (6) all_57_13 = e3 & op(e0, e2) = e3
% 136.14/20.24 (7) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 136.14/20.24 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 136.14/20.24 (8) all_57_7 = e3
% 136.14/20.24 (9) ~ (e3 = e1)
% 136.14/20.24 (10) ~ (e1 = e0)
% 136.14/20.24
% 136.14/20.24 Begin of proof
% 136.14/20.24 |
% 136.14/20.24 | ALPHA: (6) implies:
% 136.14/20.24 | (11) all_57_13 = e3
% 136.14/20.24 |
% 136.14/20.24 | BETA: splitting (5) gives:
% 136.14/20.24 |
% 136.14/20.24 | Case 1:
% 136.14/20.24 | |
% 136.14/20.24 | | (12) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 136.14/20.24 | | e2)
% 136.14/20.24 | |
% 136.14/20.24 | | BETA: splitting (12) gives:
% 136.14/20.24 | |
% 136.14/20.24 | | Case 1:
% 136.14/20.24 | | |
% 136.14/20.24 | | | (13) all_57_1 = e2 & op(e3, e2) = e2
% 136.14/20.24 | | |
% 136.14/20.24 | | | ALPHA: (13) implies:
% 136.14/20.24 | | | (14) all_57_1 = e2
% 136.14/20.24 | | |
% 136.14/20.24 | | | BETA: splitting (7) gives:
% 136.14/20.24 | | |
% 136.14/20.24 | | | Case 1:
% 136.14/20.24 | | | |
% 136.14/20.24 | | | | (15) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2)
% 136.14/20.24 | | | | = e1)
% 136.14/20.24 | | | |
% 136.14/20.24 | | | | BETA: splitting (15) gives:
% 136.14/20.24 | | | |
% 136.14/20.24 | | | | Case 1:
% 136.14/20.24 | | | | |
% 136.14/20.24 | | | | | (16) all_57_1 = e1 & op(e3, e2) = e1
% 136.14/20.24 | | | | |
% 136.14/20.24 | | | | | REF_CLOSE: (3), (14), (16) are inconsistent by sub-proof #465.
% 136.14/20.24 | | | | |
% 136.14/20.24 | | | | Case 2:
% 136.14/20.24 | | | | |
% 136.14/20.24 | | | | | (17) all_57_3 = e1 & op(e2, e2) = e1
% 136.14/20.24 | | | | |
% 136.14/20.24 | | | | | REF_CLOSE: (2), (10), (17) are inconsistent by sub-proof #449.
% 136.14/20.24 | | | | |
% 136.14/20.24 | | | | End of split
% 136.14/20.24 | | | |
% 136.14/20.24 | | | Case 2:
% 136.14/20.24 | | | |
% 136.14/20.24 | | | | (18) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2)
% 136.14/20.24 | | | | = e1)
% 136.14/20.24 | | | |
% 136.14/20.24 | | | | BETA: splitting (18) gives:
% 136.14/20.24 | | | |
% 136.14/20.24 | | | | Case 1:
% 136.14/20.24 | | | | |
% 136.14/20.24 | | | | | (19) all_57_7 = e1 & op(e1, e2) = e1
% 136.14/20.24 | | | | |
% 136.14/20.24 | | | | | ALPHA: (19) implies:
% 136.14/20.24 | | | | | (20) all_57_7 = e1
% 136.14/20.24 | | | | |
% 136.14/20.24 | | | | | REF_CLOSE: (8), (9), (20) are inconsistent by sub-proof #390.
% 136.14/20.24 | | | | |
% 136.14/20.24 | | | | Case 2:
% 136.14/20.24 | | | | |
% 136.14/20.24 | | | | | (21) all_57_13 = e1 & op(e0, e2) = e1
% 136.14/20.24 | | | | |
% 136.14/20.24 | | | | | REF_CLOSE: (9), (11), (21) are inconsistent by sub-proof #389.
% 136.14/20.24 | | | | |
% 136.14/20.24 | | | | End of split
% 136.14/20.24 | | | |
% 136.14/20.24 | | | End of split
% 136.14/20.24 | | |
% 136.14/20.24 | | Case 2:
% 136.14/20.24 | | |
% 136.14/20.24 | | | (22) all_57_3 = e2 & op(e2, e2) = e2
% 136.14/20.24 | | |
% 136.14/20.24 | | | ALPHA: (22) implies:
% 136.14/20.24 | | | (23) all_57_3 = e2
% 136.14/20.24 | | |
% 136.14/20.24 | | | REF_CLOSE: (1), (2), (23) are inconsistent by sub-proof #679.
% 136.14/20.24 | | |
% 136.14/20.24 | | End of split
% 136.14/20.24 | |
% 136.14/20.24 | Case 2:
% 136.14/20.24 | |
% 136.14/20.24 | | (24) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 136.14/20.24 | | e2)
% 136.14/20.24 | |
% 136.14/20.24 | | BETA: splitting (24) gives:
% 136.14/20.24 | |
% 136.14/20.24 | | Case 1:
% 136.14/20.24 | | |
% 136.14/20.24 | | | (25) all_57_7 = e2 & op(e1, e2) = e2
% 136.14/20.24 | | |
% 136.14/20.24 | | | ALPHA: (25) implies:
% 136.14/20.24 | | | (26) all_57_7 = e2
% 136.14/20.24 | | |
% 136.14/20.24 | | | REF_CLOSE: (4), (8), (26) are inconsistent by sub-proof #486.
% 136.14/20.24 | | |
% 136.14/20.24 | | Case 2:
% 136.14/20.24 | | |
% 136.14/20.24 | | | (27) all_57_13 = e2 & op(e0, e2) = e2
% 136.14/20.24 | | |
% 136.14/20.24 | | | ALPHA: (27) implies:
% 136.14/20.24 | | | (28) all_57_13 = e2
% 136.14/20.24 | | |
% 136.14/20.24 | | | REF_CLOSE: (4), (11), (28) are inconsistent by sub-proof #408.
% 136.14/20.24 | | |
% 136.14/20.24 | | End of split
% 136.14/20.24 | |
% 136.14/20.24 | End of split
% 136.14/20.24 |
% 136.14/20.24 End of proof
% 136.14/20.24
% 136.14/20.24 Sub-proof #389 shows that the following formulas are inconsistent:
% 136.14/20.24 ----------------------------------------------------------------
% 136.14/20.24 (1) all_57_13 = e1 & op(e0, e2) = e1
% 136.14/20.24 (2) all_57_13 = e3
% 136.14/20.24 (3) ~ (e3 = e1)
% 136.14/20.24
% 136.14/20.24 Begin of proof
% 136.14/20.24 |
% 136.14/20.24 | ALPHA: (1) implies:
% 136.14/20.24 | (4) all_57_13 = e1
% 136.14/20.24 |
% 136.14/20.24 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.24 | (5) e3 = e1
% 136.14/20.24 |
% 136.14/20.24 | SIMP: (5) implies:
% 136.14/20.24 | (6) e3 = e1
% 136.14/20.24 |
% 136.14/20.24 | REDUCE: (3), (6) imply:
% 136.14/20.24 | (7) $false
% 136.14/20.24 |
% 136.14/20.24 | CLOSE: (7) is inconsistent.
% 136.14/20.24 |
% 136.14/20.24 End of proof
% 136.14/20.24
% 136.14/20.24 Sub-proof #390 shows that the following formulas are inconsistent:
% 136.14/20.24 ----------------------------------------------------------------
% 136.14/20.24 (1) all_57_7 = e3
% 136.14/20.24 (2) all_57_7 = e1
% 136.14/20.24 (3) ~ (e3 = e1)
% 136.14/20.24
% 136.14/20.24 Begin of proof
% 136.14/20.24 |
% 136.14/20.24 | COMBINE_EQS: (1), (2) imply:
% 136.14/20.24 | (4) e3 = e1
% 136.14/20.24 |
% 136.14/20.24 | SIMP: (4) implies:
% 136.14/20.24 | (5) e3 = e1
% 136.14/20.24 |
% 136.14/20.24 | REDUCE: (3), (5) imply:
% 136.14/20.24 | (6) $false
% 136.14/20.24 |
% 136.14/20.24 | CLOSE: (6) is inconsistent.
% 136.14/20.24 |
% 136.14/20.24 End of proof
% 136.14/20.24
% 136.14/20.24 Sub-proof #391 shows that the following formulas are inconsistent:
% 136.14/20.24 ----------------------------------------------------------------
% 136.14/20.24 (1) op(e3, e3) = e2
% 136.14/20.24 (2) ~ (e2 = e0)
% 136.14/20.24 (3) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 136.14/20.24 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 136.14/20.24 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.24 (5) ~ (e2 = e1)
% 136.14/20.24 (6) ~ (e3 = e0)
% 136.14/20.24 (7) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 136.14/20.24 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 136.14/20.24 (8) all_57_12 = e3 & op(e0, e3) = e3
% 136.14/20.24 (9) ~ (e3 = e1)
% 136.14/20.24 (10) ~ (e1 = e0)
% 136.14/20.24 (11) all_57_6 = e2
% 136.14/20.24
% 136.14/20.24 Begin of proof
% 136.14/20.24 |
% 136.14/20.24 | ALPHA: (8) implies:
% 136.14/20.24 | (12) all_57_12 = e3
% 136.14/20.24 |
% 136.14/20.24 | BETA: splitting (3) gives:
% 136.14/20.24 |
% 136.14/20.24 | Case 1:
% 136.14/20.24 | |
% 136.14/20.24 | | (13) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 136.14/20.24 | | e1)
% 136.14/20.24 | |
% 136.14/20.24 | | BETA: splitting (13) gives:
% 136.14/20.24 | |
% 136.14/20.24 | | Case 1:
% 136.14/20.24 | | |
% 136.14/20.24 | | | (14) all_57_0 = e1 & op(e3, e3) = e1
% 136.14/20.24 | | |
% 136.14/20.24 | | | ALPHA: (14) implies:
% 136.14/20.24 | | | (15) op(e3, e3) = e1
% 136.14/20.24 | | |
% 136.14/20.24 | | | REF_CLOSE: (1), (4), (5), (15) are inconsistent by sub-proof #743.
% 136.14/20.24 | | |
% 136.14/20.24 | | Case 2:
% 136.14/20.24 | | |
% 136.14/20.24 | | | (16) all_57_2 = e1 & op(e2, e3) = e1
% 136.14/20.24 | | |
% 136.14/20.24 | | | ALPHA: (16) implies:
% 136.14/20.24 | | | (17) all_57_2 = e1
% 136.14/20.24 | | |
% 136.14/20.24 | | | REF_CLOSE: (1), (2), (4), (6), (7), (10), (11), (12), (17) are
% 136.14/20.24 | | | inconsistent by sub-proof #392.
% 136.14/20.24 | | |
% 136.14/20.24 | | End of split
% 136.14/20.24 | |
% 136.14/20.24 | Case 2:
% 136.14/20.24 | |
% 136.14/20.24 | | (18) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 136.14/20.24 | | e1)
% 136.14/20.24 | |
% 136.14/20.24 | | BETA: splitting (18) gives:
% 136.14/20.24 | |
% 136.14/20.24 | | Case 1:
% 136.14/20.24 | | |
% 136.14/20.24 | | | (19) all_57_6 = e1 & op(e1, e3) = e1
% 136.14/20.24 | | |
% 136.14/20.24 | | | ALPHA: (19) implies:
% 136.14/20.24 | | | (20) all_57_6 = e1
% 136.14/20.24 | | |
% 136.14/20.24 | | | COMBINE_EQS: (11), (20) imply:
% 136.14/20.24 | | | (21) e2 = e1
% 136.14/20.24 | | |
% 136.14/20.24 | | | SIMP: (21) implies:
% 136.14/20.24 | | | (22) e2 = e1
% 136.14/20.24 | | |
% 136.14/20.24 | | | REDUCE: (5), (22) imply:
% 136.14/20.24 | | | (23) $false
% 136.14/20.24 | | |
% 136.14/20.24 | | | CLOSE: (23) is inconsistent.
% 136.14/20.24 | | |
% 136.14/20.24 | | Case 2:
% 136.14/20.24 | | |
% 136.14/20.24 | | | (24) all_57_12 = e1 & op(e0, e3) = e1
% 136.14/20.24 | | |
% 136.14/20.24 | | | ALPHA: (24) implies:
% 136.14/20.24 | | | (25) all_57_12 = e1
% 136.14/20.24 | | |
% 136.14/20.24 | | | REF_CLOSE: (9), (12), (25) are inconsistent by sub-proof #591.
% 136.14/20.24 | | |
% 136.14/20.24 | | End of split
% 136.14/20.24 | |
% 136.14/20.24 | End of split
% 136.14/20.24 |
% 136.14/20.24 End of proof
% 136.14/20.24
% 136.14/20.24 Sub-proof #392 shows that the following formulas are inconsistent:
% 136.14/20.24 ----------------------------------------------------------------
% 136.14/20.24 (1) all_57_2 = e1
% 136.14/20.24 (2) op(e3, e3) = e2
% 136.14/20.24 (3) ~ (e2 = e0)
% 136.14/20.24 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.24 (5) ~ (e3 = e0)
% 136.14/20.24 (6) all_57_12 = e3
% 136.14/20.24 (7) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 136.14/20.24 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 136.14/20.24 (8) ~ (e1 = e0)
% 136.14/20.24 (9) all_57_6 = e2
% 136.14/20.24
% 136.14/20.24 Begin of proof
% 136.14/20.24 |
% 136.14/20.24 | BETA: splitting (7) gives:
% 136.14/20.24 |
% 136.14/20.24 | Case 1:
% 136.14/20.24 | |
% 136.14/20.24 | | (10) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 136.14/20.24 | | e0)
% 136.14/20.24 | |
% 136.14/20.24 | | BETA: splitting (10) gives:
% 136.14/20.24 | |
% 136.14/20.24 | | Case 1:
% 136.14/20.24 | | |
% 136.14/20.24 | | | (11) all_57_0 = e0 & op(e3, e3) = e0
% 136.14/20.24 | | |
% 136.14/20.24 | | | ALPHA: (11) implies:
% 136.14/20.24 | | | (12) op(e3, e3) = e0
% 136.14/20.24 | | |
% 136.14/20.24 | | | REF_CLOSE: (2), (3), (4), (12) are inconsistent by sub-proof #495.
% 136.14/20.24 | | |
% 136.14/20.24 | | Case 2:
% 136.14/20.24 | | |
% 136.14/20.24 | | | (13) all_57_2 = e0 & op(e2, e3) = e0
% 136.14/20.24 | | |
% 136.14/20.24 | | | ALPHA: (13) implies:
% 136.14/20.24 | | | (14) all_57_2 = e0
% 136.14/20.24 | | |
% 136.14/20.24 | | | REF_CLOSE: (1), (8), (14) are inconsistent by sub-proof #646.
% 136.14/20.24 | | |
% 136.14/20.24 | | End of split
% 136.14/20.24 | |
% 136.14/20.24 | Case 2:
% 136.14/20.24 | |
% 136.14/20.24 | | (15) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 136.14/20.24 | | e0)
% 136.14/20.24 | |
% 136.14/20.24 | | BETA: splitting (15) gives:
% 136.14/20.24 | |
% 136.14/20.24 | | Case 1:
% 136.14/20.24 | | |
% 136.14/20.24 | | | (16) all_57_6 = e0 & op(e1, e3) = e0
% 136.14/20.24 | | |
% 136.14/20.24 | | | ALPHA: (16) implies:
% 136.14/20.24 | | | (17) all_57_6 = e0
% 136.14/20.24 | | |
% 136.14/20.24 | | | REF_CLOSE: (3), (9), (17) are inconsistent by sub-proof #586.
% 136.14/20.24 | | |
% 136.14/20.24 | | Case 2:
% 136.14/20.24 | | |
% 136.14/20.24 | | | (18) all_57_12 = e0 & op(e0, e3) = e0
% 136.14/20.24 | | |
% 136.14/20.24 | | | REF_CLOSE: (5), (6), (18) are inconsistent by sub-proof #436.
% 136.14/20.24 | | |
% 136.14/20.24 | | End of split
% 136.14/20.24 | |
% 136.14/20.24 | End of split
% 136.14/20.24 |
% 136.14/20.24 End of proof
% 136.14/20.24
% 136.14/20.24 Sub-proof #393 shows that the following formulas are inconsistent:
% 136.14/20.24 ----------------------------------------------------------------
% 136.14/20.24 (1) op(e3, e3) = e2
% 136.14/20.24 (2) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 136.14/20.24 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 136.14/20.24 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.24 (4) ~ (e2 = e1)
% 136.14/20.25 (5) ~ (e3 = e2)
% 136.14/20.25 (6) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 136.14/20.25 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 136.14/20.25 (7) all_57_2 = e2
% 136.14/20.25 (8) ~ (e3 = e1)
% 136.14/20.25 (9) all_57_6 = e2
% 136.14/20.25
% 136.14/20.25 Begin of proof
% 136.14/20.25 |
% 136.14/20.25 | BETA: splitting (2) gives:
% 136.14/20.25 |
% 136.14/20.25 | Case 1:
% 136.14/20.25 | |
% 136.14/20.25 | | (10) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 136.14/20.25 | | e1)
% 136.14/20.25 | |
% 136.14/20.25 | | REF_CLOSE: (1), (3), (4), (7), (10) are inconsistent by sub-proof #496.
% 136.14/20.25 | |
% 136.14/20.25 | Case 2:
% 136.14/20.25 | |
% 136.14/20.25 | | (11) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 136.14/20.25 | | e1)
% 136.14/20.25 | |
% 136.14/20.25 | | BETA: splitting (11) gives:
% 136.14/20.25 | |
% 136.14/20.25 | | Case 1:
% 136.14/20.25 | | |
% 136.14/20.25 | | | (12) all_57_6 = e1 & op(e1, e3) = e1
% 136.14/20.25 | | |
% 136.14/20.25 | | | ALPHA: (12) implies:
% 136.14/20.25 | | | (13) all_57_6 = e1
% 136.14/20.25 | | |
% 136.14/20.25 | | | COMBINE_EQS: (9), (13) imply:
% 136.14/20.25 | | | (14) e2 = e1
% 136.14/20.25 | | |
% 136.14/20.25 | | | REDUCE: (4), (14) imply:
% 136.14/20.25 | | | (15) $false
% 136.14/20.25 | | |
% 136.14/20.25 | | | CLOSE: (15) is inconsistent.
% 136.14/20.25 | | |
% 136.14/20.25 | | Case 2:
% 136.14/20.25 | | |
% 136.14/20.25 | | | (16) all_57_12 = e1 & op(e0, e3) = e1
% 136.14/20.25 | | |
% 136.14/20.25 | | | ALPHA: (16) implies:
% 136.14/20.25 | | | (17) all_57_12 = e1
% 136.14/20.25 | | |
% 136.14/20.25 | | | BETA: splitting (6) gives:
% 136.14/20.25 | | |
% 136.14/20.25 | | | Case 1:
% 136.14/20.25 | | | |
% 136.14/20.25 | | | | (18) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3)
% 136.14/20.25 | | | | = e3)
% 136.14/20.25 | | | |
% 136.14/20.25 | | | | BETA: splitting (18) gives:
% 136.14/20.25 | | | |
% 136.14/20.25 | | | | Case 1:
% 136.14/20.25 | | | | |
% 136.14/20.25 | | | | | (19) all_57_0 = e3 & op(e3, e3) = e3
% 136.14/20.25 | | | | |
% 136.14/20.25 | | | | | ALPHA: (19) implies:
% 136.14/20.25 | | | | | (20) op(e3, e3) = e3
% 136.14/20.25 | | | | |
% 136.14/20.25 | | | | | REF_CLOSE: (1), (3), (5), (20) are inconsistent by sub-proof #778.
% 136.14/20.25 | | | | |
% 136.14/20.25 | | | | Case 2:
% 136.14/20.25 | | | | |
% 136.14/20.25 | | | | | (21) all_57_2 = e3 & op(e2, e3) = e3
% 136.14/20.25 | | | | |
% 136.14/20.25 | | | | | REF_CLOSE: (5), (7), (21) are inconsistent by sub-proof #590.
% 136.14/20.25 | | | | |
% 136.14/20.25 | | | | End of split
% 136.14/20.25 | | | |
% 136.14/20.25 | | | Case 2:
% 136.14/20.25 | | | |
% 136.14/20.25 | | | | (22) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3)
% 136.14/20.25 | | | | = e3)
% 136.14/20.25 | | | |
% 136.14/20.25 | | | | BETA: splitting (22) gives:
% 136.14/20.25 | | | |
% 136.14/20.25 | | | | Case 1:
% 136.14/20.25 | | | | |
% 136.14/20.25 | | | | | (23) all_57_6 = e3 & op(e1, e3) = e3
% 136.14/20.25 | | | | |
% 136.14/20.25 | | | | | ALPHA: (23) implies:
% 136.14/20.25 | | | | | (24) all_57_6 = e3
% 136.14/20.25 | | | | |
% 136.14/20.25 | | | | | REF_CLOSE: (5), (9), (24) are inconsistent by sub-proof #592.
% 136.14/20.25 | | | | |
% 136.14/20.25 | | | | Case 2:
% 136.14/20.25 | | | | |
% 136.14/20.25 | | | | | (25) all_57_12 = e3 & op(e0, e3) = e3
% 136.14/20.25 | | | | |
% 136.14/20.25 | | | | | REF_CLOSE: (8), (17), (25) are inconsistent by sub-proof #394.
% 136.14/20.25 | | | | |
% 136.14/20.25 | | | | End of split
% 136.14/20.25 | | | |
% 136.14/20.25 | | | End of split
% 136.14/20.25 | | |
% 136.14/20.25 | | End of split
% 136.14/20.25 | |
% 136.14/20.25 | End of split
% 136.14/20.25 |
% 136.14/20.25 End of proof
% 136.14/20.25
% 136.14/20.25 Sub-proof #394 shows that the following formulas are inconsistent:
% 136.14/20.25 ----------------------------------------------------------------
% 136.14/20.25 (1) all_57_12 = e3 & op(e0, e3) = e3
% 136.14/20.25 (2) all_57_12 = e1
% 136.14/20.25 (3) ~ (e3 = e1)
% 136.14/20.25
% 136.14/20.25 Begin of proof
% 136.14/20.25 |
% 136.14/20.25 | ALPHA: (1) implies:
% 136.14/20.25 | (4) all_57_12 = e3
% 136.14/20.25 |
% 136.14/20.25 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.25 | (5) e3 = e1
% 136.14/20.25 |
% 136.14/20.25 | REDUCE: (3), (5) imply:
% 136.14/20.25 | (6) $false
% 136.14/20.25 |
% 136.14/20.25 | CLOSE: (6) is inconsistent.
% 136.14/20.25 |
% 136.14/20.25 End of proof
% 136.14/20.25
% 136.14/20.25 Sub-proof #395 shows that the following formulas are inconsistent:
% 136.14/20.25 ----------------------------------------------------------------
% 136.14/20.25 (1) ~ (all_52_4 = e0)
% 136.14/20.25 (2) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 136.14/20.25 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 136.14/20.25 (3) ~ (e2 = e0)
% 136.14/20.25 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.25 (5) op(e0, e2) = all_52_7
% 136.14/20.25 (6) ~ (all_52_6 = e0)
% 136.14/20.25 (7) op(e1, e2) = all_52_6
% 136.14/20.25 (8) ~ (all_52_7 = e0)
% 136.14/20.25 (9) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 136.14/20.25 (10) ~ (all_52_4 = e2)
% 136.14/20.25 (11) op(e3, e2) = all_52_4
% 136.14/20.25
% 136.14/20.25 Begin of proof
% 136.14/20.25 |
% 136.14/20.25 | BETA: splitting (9) gives:
% 136.14/20.25 |
% 136.14/20.25 | Case 1:
% 136.14/20.25 | |
% 136.14/20.25 | | (12) all_57_1 = e2 & op(e3, e2) = e2
% 136.14/20.25 | |
% 136.14/20.25 | | REF_CLOSE: (4), (10), (11), (12) are inconsistent by sub-proof #396.
% 136.14/20.25 | |
% 136.14/20.25 | Case 2:
% 136.14/20.25 | |
% 136.14/20.25 | | (13) all_57_3 = e2 & op(e2, e2) = e2
% 136.14/20.25 | |
% 136.14/20.25 | | ALPHA: (13) implies:
% 136.14/20.25 | | (14) all_57_3 = e2
% 136.14/20.25 | |
% 136.14/20.25 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (11), (14) are
% 136.14/20.25 | | inconsistent by sub-proof #503.
% 136.14/20.25 | |
% 136.14/20.25 | End of split
% 136.14/20.25 |
% 136.14/20.25 End of proof
% 136.14/20.25
% 136.14/20.25 Sub-proof #396 shows that the following formulas are inconsistent:
% 136.14/20.25 ----------------------------------------------------------------
% 136.14/20.25 (1) all_57_1 = e2 & op(e3, e2) = e2
% 136.14/20.25 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.25 (3) op(e3, e2) = all_52_4
% 136.14/20.25 (4) ~ (all_52_4 = e2)
% 136.14/20.25
% 136.14/20.25 Begin of proof
% 136.14/20.25 |
% 136.14/20.25 | ALPHA: (1) implies:
% 136.14/20.25 | (5) op(e3, e2) = e2
% 136.14/20.25 |
% 136.14/20.25 | GROUND_INST: instantiating (2) with all_52_4, e2, e2, e3, simplifying with
% 136.14/20.25 | (3), (5) gives:
% 136.14/20.25 | (6) all_52_4 = e2
% 136.14/20.25 |
% 136.14/20.25 | REDUCE: (4), (6) imply:
% 136.14/20.25 | (7) $false
% 136.14/20.25 |
% 136.14/20.25 | CLOSE: (7) is inconsistent.
% 136.14/20.25 |
% 136.14/20.25 End of proof
% 136.14/20.25
% 136.14/20.25 Sub-proof #397 shows that the following formulas are inconsistent:
% 136.14/20.25 ----------------------------------------------------------------
% 136.14/20.25 (1) all_57_14 = e2 & op(e0, e1) = e2
% 136.14/20.25 (2) all_57_14 = e3
% 136.14/20.25 (3) ~ (e3 = e2)
% 136.14/20.25
% 136.14/20.25 Begin of proof
% 136.14/20.25 |
% 136.14/20.25 | ALPHA: (1) implies:
% 136.14/20.25 | (4) all_57_14 = e2
% 136.14/20.25 |
% 136.14/20.25 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.25 | (5) e3 = e2
% 136.14/20.25 |
% 136.14/20.25 | REDUCE: (3), (5) imply:
% 136.14/20.25 | (6) $false
% 136.14/20.25 |
% 136.14/20.25 | CLOSE: (6) is inconsistent.
% 136.14/20.25 |
% 136.14/20.25 End of proof
% 136.14/20.25
% 136.14/20.25 Sub-proof #398 shows that the following formulas are inconsistent:
% 136.14/20.25 ----------------------------------------------------------------
% 136.14/20.25 (1) ~ (e2 = e0)
% 136.14/20.25 (2) ~ (e3 = e0)
% 136.14/20.25 (3) all_57_15 = e2
% 136.14/20.25 (4) all_57_13 = e2
% 136.14/20.25 (5) all_57_14 = e3
% 136.14/20.25 (6) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 136.14/20.25 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 136.14/20.25 e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 136.14/20.25 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 136.14/20.25 (7) ~ (e1 = e0)
% 136.14/20.25 (8) all_57_12 = e1
% 136.14/20.25
% 136.14/20.25 Begin of proof
% 136.14/20.25 |
% 136.14/20.25 | BETA: splitting (6) gives:
% 136.14/20.25 |
% 136.14/20.25 | Case 1:
% 136.14/20.25 | |
% 136.14/20.25 | | (9) all_57_15 = e0 & op(e0, e0) = e0
% 136.14/20.25 | |
% 136.14/20.25 | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #437.
% 136.14/20.25 | |
% 136.14/20.25 | Case 2:
% 136.14/20.25 | |
% 136.14/20.25 | | (10) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 136.14/20.25 | | e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 136.14/20.25 | | op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 136.14/20.25 | | (all_57_14 = e0 & op(e0, e1) = e0))
% 136.14/20.25 | |
% 136.14/20.25 | | ALPHA: (10) implies:
% 136.14/20.25 | | (11) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 136.14/20.25 | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 136.14/20.25 | |
% 136.14/20.25 | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (11) are inconsistent by sub-proof
% 136.14/20.25 | | #399.
% 136.14/20.25 | |
% 136.14/20.25 | End of split
% 136.14/20.25 |
% 136.14/20.25 End of proof
% 136.14/20.25
% 136.14/20.25 Sub-proof #399 shows that the following formulas are inconsistent:
% 136.14/20.25 ----------------------------------------------------------------
% 136.14/20.25 (1) ~ (e2 = e0)
% 136.14/20.25 (2) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 136.14/20.25 (all_57_14 = e0 & op(e0, e1) = e0)
% 136.14/20.25 (3) ~ (e3 = e0)
% 136.14/20.25 (4) all_57_13 = e2
% 136.14/20.25 (5) all_57_14 = e3
% 136.14/20.25 (6) ~ (e1 = e0)
% 136.14/20.25 (7) all_57_12 = e1
% 136.14/20.25
% 136.14/20.25 Begin of proof
% 136.14/20.25 |
% 136.14/20.25 | BETA: splitting (2) gives:
% 136.14/20.25 |
% 136.14/20.25 | Case 1:
% 136.14/20.25 | |
% 136.14/20.25 | | (8) all_57_12 = e0 & op(e0, e3) = e0
% 136.14/20.25 | |
% 136.14/20.25 | | ALPHA: (8) implies:
% 136.14/20.25 | | (9) all_57_12 = e0
% 136.14/20.25 | |
% 136.14/20.25 | | REF_CLOSE: (6), (7), (9) are inconsistent by sub-proof #581.
% 136.14/20.25 | |
% 136.14/20.25 | Case 2:
% 136.14/20.25 | |
% 136.14/20.25 | | (10) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 136.14/20.25 | | e0)
% 136.14/20.25 | |
% 136.14/20.25 | | BETA: splitting (10) gives:
% 136.14/20.25 | |
% 136.14/20.25 | | Case 1:
% 136.14/20.25 | | |
% 136.14/20.25 | | | (11) all_57_13 = e0 & op(e0, e2) = e0
% 136.14/20.25 | | |
% 136.14/20.25 | | | REF_CLOSE: (1), (4), (11) are inconsistent by sub-proof #411.
% 136.14/20.25 | | |
% 136.14/20.25 | | Case 2:
% 136.14/20.25 | | |
% 136.14/20.25 | | | (12) all_57_14 = e0 & op(e0, e1) = e0
% 136.14/20.25 | | |
% 136.14/20.25 | | | ALPHA: (12) implies:
% 136.14/20.25 | | | (13) all_57_14 = e0
% 136.14/20.25 | | |
% 136.14/20.25 | | | REF_CLOSE: (3), (5), (13) are inconsistent by sub-proof #400.
% 136.14/20.25 | | |
% 136.14/20.25 | | End of split
% 136.14/20.25 | |
% 136.14/20.25 | End of split
% 136.14/20.25 |
% 136.14/20.25 End of proof
% 136.14/20.25
% 136.14/20.25 Sub-proof #400 shows that the following formulas are inconsistent:
% 136.14/20.25 ----------------------------------------------------------------
% 136.14/20.25 (1) all_57_14 = e3
% 136.14/20.25 (2) all_57_14 = e0
% 136.14/20.25 (3) ~ (e3 = e0)
% 136.14/20.25
% 136.14/20.25 Begin of proof
% 136.14/20.25 |
% 136.14/20.25 | COMBINE_EQS: (1), (2) imply:
% 136.14/20.25 | (4) e3 = e0
% 136.14/20.25 |
% 136.14/20.25 | SIMP: (4) implies:
% 136.14/20.25 | (5) e3 = e0
% 136.14/20.25 |
% 136.14/20.25 | REDUCE: (3), (5) imply:
% 136.14/20.25 | (6) $false
% 136.14/20.25 |
% 136.14/20.25 | CLOSE: (6) is inconsistent.
% 136.14/20.25 |
% 136.14/20.25 End of proof
% 136.14/20.25
% 136.14/20.25 Sub-proof #401 shows that the following formulas are inconsistent:
% 136.14/20.25 ----------------------------------------------------------------
% 136.14/20.25 (1) ~ (e2 = e0)
% 136.14/20.25 (2) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 136.14/20.25 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 136.14/20.25 (3) ~ (e2 = e1)
% 136.14/20.25 (4) ~ (e3 = e0)
% 136.14/20.25 (5) ~ (e3 = e2)
% 136.14/20.25 (6) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 136.14/20.25 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 136.14/20.25 (7) all_57_13 = e2
% 136.14/20.25 (8) all_57_14 = e2
% 136.14/20.25 (9) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 136.14/20.25 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 136.14/20.25 e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 136.14/20.25 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 136.14/20.25 (10) ~ (e3 = e1)
% 136.14/20.25 (11) ~ (e1 = e0)
% 136.14/20.25
% 136.14/20.25 Begin of proof
% 136.14/20.25 |
% 136.14/20.25 | BETA: splitting (2) gives:
% 136.14/20.25 |
% 136.14/20.25 | Case 1:
% 136.14/20.25 | |
% 136.14/20.25 | | (12) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 136.14/20.25 | | e3)
% 136.14/20.25 | |
% 136.14/20.25 | | BETA: splitting (12) gives:
% 136.14/20.25 | |
% 136.14/20.25 | | Case 1:
% 136.14/20.25 | | |
% 136.14/20.25 | | | (13) all_57_12 = e3 & op(e0, e3) = e3
% 136.14/20.25 | | |
% 136.14/20.25 | | | ALPHA: (13) implies:
% 136.14/20.25 | | | (14) all_57_12 = e3
% 136.14/20.25 | | |
% 136.14/20.25 | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11), (14) are
% 136.14/20.25 | | | inconsistent by sub-proof #409.
% 136.14/20.25 | | |
% 136.14/20.25 | | Case 2:
% 136.14/20.25 | | |
% 136.14/20.25 | | | (15) all_57_13 = e3 & op(e0, e2) = e3
% 136.14/20.25 | | |
% 136.14/20.25 | | | ALPHA: (15) implies:
% 136.14/20.25 | | | (16) all_57_13 = e3
% 136.14/20.25 | | |
% 136.14/20.25 | | | REF_CLOSE: (5), (7), (16) are inconsistent by sub-proof #408.
% 136.14/20.25 | | |
% 136.14/20.25 | | End of split
% 136.14/20.25 | |
% 136.14/20.25 | Case 2:
% 136.14/20.25 | |
% 136.14/20.25 | | (17) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 136.14/20.25 | | e3)
% 136.14/20.25 | |
% 136.14/20.25 | | BETA: splitting (17) gives:
% 136.14/20.25 | |
% 136.14/20.25 | | Case 1:
% 136.14/20.25 | | |
% 136.14/20.25 | | | (18) all_57_14 = e3 & op(e0, e1) = e3
% 136.14/20.25 | | |
% 136.14/20.25 | | | ALPHA: (18) implies:
% 136.14/20.25 | | | (19) all_57_14 = e3
% 136.14/20.25 | | |
% 136.14/20.25 | | | REF_CLOSE: (5), (8), (19) are inconsistent by sub-proof #407.
% 136.14/20.25 | | |
% 136.14/20.25 | | Case 2:
% 136.14/20.25 | | |
% 136.14/20.25 | | | (20) all_57_15 = e3 & op(e0, e0) = e3
% 136.14/20.25 | | |
% 136.14/20.25 | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11), (20) are
% 136.14/20.25 | | | inconsistent by sub-proof #402.
% 136.14/20.25 | | |
% 136.14/20.25 | | End of split
% 136.14/20.25 | |
% 136.14/20.25 | End of split
% 136.14/20.25 |
% 136.14/20.25 End of proof
% 136.14/20.25
% 136.14/20.25 Sub-proof #402 shows that the following formulas are inconsistent:
% 136.14/20.25 ----------------------------------------------------------------
% 136.14/20.25 (1) ~ (e2 = e0)
% 136.14/20.25 (2) ~ (e2 = e1)
% 136.14/20.25 (3) ~ (e3 = e0)
% 136.14/20.25 (4) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 136.14/20.25 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 136.14/20.25 (5) all_57_13 = e2
% 136.14/20.25 (6) all_57_14 = e2
% 136.14/20.25 (7) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 136.14/20.25 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 136.14/20.25 e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 136.14/20.25 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 136.14/20.25 (8) ~ (e3 = e1)
% 136.14/20.25 (9) ~ (e1 = e0)
% 136.14/20.25 (10) all_57_15 = e3 & op(e0, e0) = e3
% 136.14/20.25
% 136.14/20.25 Begin of proof
% 136.14/20.25 |
% 136.14/20.25 | ALPHA: (10) implies:
% 136.14/20.25 | (11) all_57_15 = e3
% 136.14/20.25 |
% 136.14/20.25 | BETA: splitting (7) gives:
% 136.14/20.25 |
% 136.14/20.25 | Case 1:
% 136.14/20.25 | |
% 136.14/20.25 | | (12) all_57_15 = e0 & op(e0, e0) = e0
% 136.14/20.25 | |
% 136.14/20.25 | | REF_CLOSE: (3), (11), (12) are inconsistent by sub-proof #406.
% 136.14/20.25 | |
% 136.14/20.25 | Case 2:
% 136.14/20.25 | |
% 136.14/20.25 | | (13) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 136.14/20.25 | | e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 136.14/20.25 | | op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 136.14/20.25 | | (all_57_14 = e0 & op(e0, e1) = e0))
% 136.14/20.25 | |
% 136.14/20.25 | | ALPHA: (13) implies:
% 136.14/20.25 | | (14) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 136.14/20.25 | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 136.14/20.25 | |
% 136.14/20.25 | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (11), (14) are inconsistent by
% 136.14/20.25 | | sub-proof #403.
% 136.14/20.25 | |
% 136.14/20.25 | End of split
% 136.14/20.25 |
% 136.14/20.25 End of proof
% 136.14/20.25
% 136.14/20.25 Sub-proof #403 shows that the following formulas are inconsistent:
% 136.14/20.25 ----------------------------------------------------------------
% 136.14/20.25 (1) ~ (e2 = e0)
% 136.14/20.25 (2) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 136.14/20.25 (all_57_14 = e0 & op(e0, e1) = e0)
% 136.14/20.25 (3) ~ (e2 = e1)
% 136.14/20.25 (4) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 136.14/20.25 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 136.14/20.25 (5) all_57_15 = e3
% 136.14/20.25 (6) all_57_13 = e2
% 136.14/20.25 (7) all_57_14 = e2
% 136.14/20.25 (8) ~ (e3 = e1)
% 136.14/20.25 (9) ~ (e1 = e0)
% 136.14/20.25
% 136.14/20.25 Begin of proof
% 136.14/20.25 |
% 136.14/20.25 | BETA: splitting (2) gives:
% 136.14/20.25 |
% 136.14/20.25 | Case 1:
% 136.14/20.25 | |
% 136.14/20.25 | | (10) all_57_12 = e0 & op(e0, e3) = e0
% 136.14/20.25 | |
% 136.14/20.25 | | ALPHA: (10) implies:
% 136.14/20.25 | | (11) all_57_12 = e0
% 136.14/20.25 | |
% 136.14/20.25 | | BETA: splitting (4) gives:
% 136.14/20.25 | |
% 136.14/20.25 | | Case 1:
% 136.14/20.25 | | |
% 136.14/20.25 | | | (12) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2)
% 136.14/20.25 | | | = e1)
% 136.14/20.25 | | |
% 136.14/20.25 | | | BETA: splitting (12) gives:
% 136.14/20.25 | | |
% 136.14/20.25 | | | Case 1:
% 136.14/20.25 | | | |
% 136.14/20.25 | | | | (13) all_57_12 = e1 & op(e0, e3) = e1
% 136.14/20.25 | | | |
% 136.14/20.25 | | | | REF_CLOSE: (9), (11), (13) are inconsistent by sub-proof #405.
% 136.14/20.25 | | | |
% 136.14/20.25 | | | Case 2:
% 136.14/20.25 | | | |
% 136.14/20.25 | | | | (14) all_57_13 = e1 & op(e0, e2) = e1
% 136.14/20.25 | | | |
% 136.14/20.25 | | | | ALPHA: (14) implies:
% 136.14/20.25 | | | | (15) all_57_13 = e1
% 136.14/20.25 | | | |
% 136.14/20.25 | | | | REF_CLOSE: (3), (6), (15) are inconsistent by sub-proof #567.
% 136.14/20.25 | | | |
% 136.14/20.25 | | | End of split
% 136.14/20.25 | | |
% 136.14/20.25 | | Case 2:
% 136.14/20.25 | | |
% 136.14/20.25 | | | (16) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0)
% 136.14/20.25 | | | = e1)
% 136.14/20.25 | | |
% 136.14/20.25 | | | BETA: splitting (16) gives:
% 136.14/20.25 | | |
% 136.14/20.25 | | | Case 1:
% 136.14/20.25 | | | |
% 136.14/20.25 | | | | (17) all_57_14 = e1 & op(e0, e1) = e1
% 136.14/20.25 | | | |
% 136.14/20.25 | | | | ALPHA: (17) implies:
% 136.14/20.25 | | | | (18) all_57_14 = e1
% 136.14/20.25 | | | |
% 136.14/20.25 | | | | REF_CLOSE: (3), (7), (18) are inconsistent by sub-proof #560.
% 136.14/20.25 | | | |
% 136.14/20.25 | | | Case 2:
% 136.14/20.25 | | | |
% 136.14/20.25 | | | | (19) all_57_15 = e1 & op(e0, e0) = e1
% 136.14/20.25 | | | |
% 136.14/20.25 | | | | ALPHA: (19) implies:
% 136.14/20.25 | | | | (20) all_57_15 = e1
% 136.14/20.25 | | | |
% 136.14/20.25 | | | | COMBINE_EQS: (5), (20) imply:
% 136.14/20.25 | | | | (21) e3 = e1
% 136.14/20.25 | | | |
% 136.14/20.25 | | | | REDUCE: (8), (21) imply:
% 136.14/20.25 | | | | (22) $false
% 136.14/20.25 | | | |
% 136.14/20.25 | | | | CLOSE: (22) is inconsistent.
% 136.14/20.25 | | | |
% 136.14/20.25 | | | End of split
% 136.14/20.25 | | |
% 136.14/20.25 | | End of split
% 136.14/20.25 | |
% 136.14/20.25 | Case 2:
% 136.14/20.25 | |
% 136.14/20.25 | | (23) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 136.14/20.25 | | e0)
% 136.14/20.25 | |
% 136.14/20.25 | | BETA: splitting (23) gives:
% 136.14/20.25 | |
% 136.14/20.25 | | Case 1:
% 136.14/20.25 | | |
% 136.14/20.25 | | | (24) all_57_13 = e0 & op(e0, e2) = e0
% 136.14/20.25 | | |
% 136.14/20.25 | | | ALPHA: (24) implies:
% 136.14/20.25 | | | (25) all_57_13 = e0
% 136.14/20.25 | | |
% 136.14/20.25 | | | REF_CLOSE: (1), (6), (25) are inconsistent by sub-proof #404.
% 136.14/20.25 | | |
% 136.14/20.25 | | Case 2:
% 136.14/20.25 | | |
% 136.14/20.25 | | | (26) all_57_14 = e0 & op(e0, e1) = e0
% 136.14/20.25 | | |
% 136.14/20.25 | | | REF_CLOSE: (1), (7), (26) are inconsistent by sub-proof #580.
% 136.14/20.25 | | |
% 136.14/20.25 | | End of split
% 136.14/20.25 | |
% 136.14/20.25 | End of split
% 136.14/20.25 |
% 136.14/20.25 End of proof
% 136.14/20.25
% 136.14/20.25 Sub-proof #404 shows that the following formulas are inconsistent:
% 136.14/20.25 ----------------------------------------------------------------
% 136.14/20.25 (1) all_57_13 = e2
% 136.14/20.25 (2) all_57_13 = e0
% 136.14/20.25 (3) ~ (e2 = e0)
% 136.14/20.25
% 136.14/20.25 Begin of proof
% 136.14/20.25 |
% 136.14/20.25 | COMBINE_EQS: (1), (2) imply:
% 136.14/20.25 | (4) e2 = e0
% 136.14/20.25 |
% 136.14/20.25 | SIMP: (4) implies:
% 136.14/20.25 | (5) e2 = e0
% 136.14/20.25 |
% 136.14/20.25 | REDUCE: (3), (5) imply:
% 136.14/20.25 | (6) $false
% 136.14/20.25 |
% 136.14/20.25 | CLOSE: (6) is inconsistent.
% 136.14/20.25 |
% 136.14/20.25 End of proof
% 136.14/20.25
% 136.14/20.25 Sub-proof #405 shows that the following formulas are inconsistent:
% 136.14/20.25 ----------------------------------------------------------------
% 136.14/20.25 (1) all_57_12 = e1 & op(e0, e3) = e1
% 136.14/20.25 (2) all_57_12 = e0
% 136.14/20.25 (3) ~ (e1 = e0)
% 136.14/20.25
% 136.14/20.25 Begin of proof
% 136.14/20.25 |
% 136.14/20.25 | ALPHA: (1) implies:
% 136.14/20.25 | (4) all_57_12 = e1
% 136.14/20.25 |
% 136.14/20.25 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.25 | (5) e1 = e0
% 136.14/20.25 |
% 136.14/20.25 | REDUCE: (3), (5) imply:
% 136.14/20.25 | (6) $false
% 136.14/20.25 |
% 136.14/20.25 | CLOSE: (6) is inconsistent.
% 136.14/20.25 |
% 136.14/20.25 End of proof
% 136.14/20.25
% 136.14/20.25 Sub-proof #406 shows that the following formulas are inconsistent:
% 136.14/20.25 ----------------------------------------------------------------
% 136.14/20.25 (1) all_57_15 = e0 & op(e0, e0) = e0
% 136.14/20.25 (2) all_57_15 = e3
% 136.14/20.25 (3) ~ (e3 = e0)
% 136.14/20.25
% 136.14/20.25 Begin of proof
% 136.14/20.25 |
% 136.14/20.25 | ALPHA: (1) implies:
% 136.14/20.25 | (4) all_57_15 = e0
% 136.14/20.25 |
% 136.14/20.25 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.25 | (5) e3 = e0
% 136.14/20.25 |
% 136.14/20.25 | SIMP: (5) implies:
% 136.14/20.25 | (6) e3 = e0
% 136.14/20.25 |
% 136.14/20.25 | REDUCE: (3), (6) imply:
% 136.14/20.25 | (7) $false
% 136.14/20.25 |
% 136.14/20.25 | CLOSE: (7) is inconsistent.
% 136.14/20.25 |
% 136.14/20.25 End of proof
% 136.14/20.25
% 136.14/20.25 Sub-proof #407 shows that the following formulas are inconsistent:
% 136.14/20.25 ----------------------------------------------------------------
% 136.14/20.25 (1) all_57_14 = e3
% 136.14/20.25 (2) all_57_14 = e2
% 136.14/20.25 (3) ~ (e3 = e2)
% 136.14/20.25
% 136.14/20.25 Begin of proof
% 136.14/20.25 |
% 136.14/20.25 | COMBINE_EQS: (1), (2) imply:
% 136.14/20.25 | (4) e3 = e2
% 136.14/20.25 |
% 136.14/20.25 | SIMP: (4) implies:
% 136.14/20.25 | (5) e3 = e2
% 136.14/20.25 |
% 136.14/20.25 | REDUCE: (3), (5) imply:
% 136.14/20.25 | (6) $false
% 136.14/20.25 |
% 136.14/20.25 | CLOSE: (6) is inconsistent.
% 136.14/20.25 |
% 136.14/20.25 End of proof
% 136.14/20.25
% 136.14/20.25 Sub-proof #408 shows that the following formulas are inconsistent:
% 136.14/20.25 ----------------------------------------------------------------
% 136.14/20.25 (1) all_57_13 = e3
% 136.14/20.25 (2) all_57_13 = e2
% 136.14/20.25 (3) ~ (e3 = e2)
% 136.14/20.25
% 136.14/20.25 Begin of proof
% 136.14/20.25 |
% 136.14/20.25 | COMBINE_EQS: (1), (2) imply:
% 136.14/20.25 | (4) e3 = e2
% 136.14/20.25 |
% 136.14/20.25 | SIMP: (4) implies:
% 136.14/20.25 | (5) e3 = e2
% 136.14/20.25 |
% 136.14/20.25 | REDUCE: (3), (5) imply:
% 136.14/20.25 | (6) $false
% 136.14/20.25 |
% 136.14/20.25 | CLOSE: (6) is inconsistent.
% 136.14/20.25 |
% 136.14/20.25 End of proof
% 136.14/20.25
% 136.14/20.25 Sub-proof #409 shows that the following formulas are inconsistent:
% 136.14/20.25 ----------------------------------------------------------------
% 136.14/20.25 (1) ~ (e2 = e0)
% 136.14/20.25 (2) ~ (e2 = e1)
% 136.14/20.25 (3) ~ (e3 = e0)
% 136.14/20.25 (4) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 136.14/20.25 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 136.14/20.25 (5) all_57_13 = e2
% 136.14/20.25 (6) all_57_12 = e3
% 136.14/20.25 (7) all_57_14 = e2
% 136.14/20.25 (8) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 136.14/20.25 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 136.14/20.25 e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 136.14/20.25 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 136.14/20.25 (9) ~ (e3 = e1)
% 136.14/20.25 (10) ~ (e1 = e0)
% 136.14/20.25
% 136.14/20.25 Begin of proof
% 136.14/20.25 |
% 136.14/20.25 | BETA: splitting (4) gives:
% 136.14/20.25 |
% 136.14/20.25 | Case 1:
% 136.14/20.25 | |
% 136.14/20.25 | | (11) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 136.14/20.25 | | e1)
% 136.14/20.25 | |
% 136.14/20.25 | | BETA: splitting (11) gives:
% 136.14/20.25 | |
% 136.14/20.25 | | Case 1:
% 136.14/20.25 | | |
% 136.14/20.25 | | | (12) all_57_12 = e1 & op(e0, e3) = e1
% 136.14/20.25 | | |
% 136.14/20.25 | | | REF_CLOSE: (6), (9), (12) are inconsistent by sub-proof #490.
% 136.14/20.25 | | |
% 136.14/20.25 | | Case 2:
% 136.14/20.25 | | |
% 136.14/20.25 | | | (13) all_57_13 = e1 & op(e0, e2) = e1
% 136.14/20.25 | | |
% 136.14/20.25 | | | ALPHA: (13) implies:
% 136.14/20.25 | | | (14) all_57_13 = e1
% 136.14/20.25 | | |
% 136.14/20.25 | | | REF_CLOSE: (2), (5), (14) are inconsistent by sub-proof #567.
% 136.14/20.25 | | |
% 136.14/20.25 | | End of split
% 136.14/20.25 | |
% 136.14/20.25 | Case 2:
% 136.14/20.25 | |
% 136.14/20.25 | | (15) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 136.14/20.25 | | e1)
% 136.14/20.25 | |
% 136.14/20.25 | | BETA: splitting (15) gives:
% 136.14/20.25 | |
% 136.14/20.25 | | Case 1:
% 136.14/20.25 | | |
% 136.14/20.25 | | | (16) all_57_14 = e1 & op(e0, e1) = e1
% 136.14/20.25 | | |
% 136.14/20.25 | | | ALPHA: (16) implies:
% 136.14/20.25 | | | (17) all_57_14 = e1
% 136.14/20.25 | | |
% 136.14/20.25 | | | REF_CLOSE: (2), (7), (17) are inconsistent by sub-proof #560.
% 136.14/20.25 | | |
% 136.14/20.25 | | Case 2:
% 136.14/20.25 | | |
% 136.14/20.25 | | | (18) all_57_15 = e1 & op(e0, e0) = e1
% 136.14/20.25 | | |
% 136.14/20.25 | | | ALPHA: (18) implies:
% 136.14/20.25 | | | (19) all_57_15 = e1
% 136.14/20.25 | | |
% 136.14/20.25 | | | BETA: splitting (8) gives:
% 136.14/20.25 | | |
% 136.14/20.25 | | | Case 1:
% 136.14/20.25 | | | |
% 136.14/20.25 | | | | (20) all_57_15 = e0 & op(e0, e0) = e0
% 136.14/20.25 | | | |
% 136.14/20.25 | | | | REF_CLOSE: (10), (19), (20) are inconsistent by sub-proof #412.
% 136.14/20.25 | | | |
% 136.14/20.25 | | | Case 2:
% 136.14/20.25 | | | |
% 136.14/20.25 | | | | (21) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 136.14/20.25 | | | | e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 136.14/20.25 | | | | ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 136.14/20.25 | | | | e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 136.14/20.25 | | | |
% 136.14/20.25 | | | | ALPHA: (21) implies:
% 136.14/20.25 | | | | (22) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 136.14/20.25 | | | | e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 136.14/20.25 | | | |
% 136.14/20.25 | | | | REF_CLOSE: (1), (3), (5), (6), (7), (22) are inconsistent by sub-proof
% 136.14/20.25 | | | | #410.
% 136.14/20.25 | | | |
% 136.14/20.25 | | | End of split
% 136.14/20.25 | | |
% 136.14/20.25 | | End of split
% 136.14/20.25 | |
% 136.14/20.25 | End of split
% 136.14/20.25 |
% 136.14/20.25 End of proof
% 136.14/20.25
% 136.14/20.25 Sub-proof #410 shows that the following formulas are inconsistent:
% 136.14/20.25 ----------------------------------------------------------------
% 136.14/20.25 (1) ~ (e2 = e0)
% 136.14/20.25 (2) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 136.14/20.25 (all_57_14 = e0 & op(e0, e1) = e0)
% 136.14/20.25 (3) ~ (e3 = e0)
% 136.14/20.25 (4) all_57_13 = e2
% 136.14/20.25 (5) all_57_12 = e3
% 136.14/20.25 (6) all_57_14 = e2
% 136.14/20.25
% 136.14/20.25 Begin of proof
% 136.14/20.25 |
% 136.14/20.25 | BETA: splitting (2) gives:
% 136.14/20.25 |
% 136.14/20.25 | Case 1:
% 136.14/20.25 | |
% 136.14/20.25 | | (7) all_57_12 = e0 & op(e0, e3) = e0
% 136.14/20.25 | |
% 136.14/20.25 | | REF_CLOSE: (3), (5), (7) are inconsistent by sub-proof #436.
% 136.14/20.25 | |
% 136.14/20.25 | Case 2:
% 136.14/20.25 | |
% 136.14/20.25 | | (8) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 136.14/20.25 | | e0)
% 136.14/20.25 | |
% 136.14/20.25 | | BETA: splitting (8) gives:
% 136.14/20.25 | |
% 136.14/20.25 | | Case 1:
% 136.14/20.25 | | |
% 136.14/20.25 | | | (9) all_57_13 = e0 & op(e0, e2) = e0
% 136.14/20.25 | | |
% 136.14/20.25 | | | REF_CLOSE: (1), (4), (9) are inconsistent by sub-proof #411.
% 136.14/20.25 | | |
% 136.14/20.25 | | Case 2:
% 136.14/20.25 | | |
% 136.14/20.25 | | | (10) all_57_14 = e0 & op(e0, e1) = e0
% 136.14/20.25 | | |
% 136.14/20.25 | | | REF_CLOSE: (1), (6), (10) are inconsistent by sub-proof #580.
% 136.14/20.25 | | |
% 136.14/20.25 | | End of split
% 136.14/20.25 | |
% 136.14/20.25 | End of split
% 136.14/20.25 |
% 136.14/20.25 End of proof
% 136.14/20.25
% 136.14/20.25 Sub-proof #411 shows that the following formulas are inconsistent:
% 136.14/20.25 ----------------------------------------------------------------
% 136.14/20.25 (1) all_57_13 = e0 & op(e0, e2) = e0
% 136.14/20.25 (2) all_57_13 = e2
% 136.14/20.25 (3) ~ (e2 = e0)
% 136.14/20.25
% 136.14/20.25 Begin of proof
% 136.14/20.25 |
% 136.14/20.25 | ALPHA: (1) implies:
% 136.14/20.25 | (4) all_57_13 = e0
% 136.14/20.25 |
% 136.14/20.25 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.25 | (5) e2 = e0
% 136.14/20.25 |
% 136.14/20.25 | REDUCE: (3), (5) imply:
% 136.14/20.25 | (6) $false
% 136.14/20.25 |
% 136.14/20.25 | CLOSE: (6) is inconsistent.
% 136.14/20.25 |
% 136.14/20.25 End of proof
% 136.14/20.25
% 136.14/20.25 Sub-proof #412 shows that the following formulas are inconsistent:
% 136.14/20.25 ----------------------------------------------------------------
% 136.14/20.25 (1) all_57_15 = e0 & op(e0, e0) = e0
% 136.14/20.25 (2) all_57_15 = e1
% 136.14/20.25 (3) ~ (e1 = e0)
% 136.14/20.25
% 136.14/20.25 Begin of proof
% 136.14/20.25 |
% 136.14/20.25 | ALPHA: (1) implies:
% 136.14/20.25 | (4) all_57_15 = e0
% 136.14/20.25 |
% 136.14/20.25 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.25 | (5) e1 = e0
% 136.14/20.25 |
% 136.14/20.25 | SIMP: (5) implies:
% 136.14/20.25 | (6) e1 = e0
% 136.14/20.25 |
% 136.14/20.25 | REDUCE: (3), (6) imply:
% 136.14/20.25 | (7) $false
% 136.14/20.25 |
% 136.14/20.25 | CLOSE: (7) is inconsistent.
% 136.14/20.25 |
% 136.14/20.25 End of proof
% 136.14/20.25
% 136.14/20.25 Sub-proof #413 shows that the following formulas are inconsistent:
% 136.14/20.25 ----------------------------------------------------------------
% 136.14/20.25 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.25 (2) op(e3, e2) = e3
% 136.14/20.25 (3) op(e3, e2) = e1
% 136.14/20.25 (4) ~ (e3 = e1)
% 136.14/20.25
% 136.14/20.25 Begin of proof
% 136.14/20.25 |
% 136.14/20.25 | GROUND_INST: instantiating (1) with e1, e3, e2, e3, simplifying with (2), (3)
% 136.14/20.25 | gives:
% 136.14/20.25 | (5) e3 = e1
% 136.14/20.25 |
% 136.14/20.25 | REDUCE: (4), (5) imply:
% 136.14/20.25 | (6) $false
% 136.14/20.25 |
% 136.14/20.25 | CLOSE: (6) is inconsistent.
% 136.14/20.25 |
% 136.14/20.25 End of proof
% 136.14/20.25
% 136.14/20.25 Sub-proof #414 shows that the following formulas are inconsistent:
% 136.14/20.25 ----------------------------------------------------------------
% 136.14/20.25 (1) all_57_10 = e2
% 136.14/20.25 (2) all_57_10 = e1
% 136.14/20.25 (3) ~ (e2 = e1)
% 136.14/20.25
% 136.14/20.25 Begin of proof
% 136.14/20.25 |
% 136.14/20.25 | COMBINE_EQS: (1), (2) imply:
% 136.14/20.25 | (4) e2 = e1
% 136.14/20.25 |
% 136.14/20.25 | SIMP: (4) implies:
% 136.14/20.25 | (5) e2 = e1
% 136.14/20.25 |
% 136.14/20.25 | REDUCE: (3), (5) imply:
% 136.14/20.25 | (6) $false
% 136.14/20.25 |
% 136.14/20.25 | CLOSE: (6) is inconsistent.
% 136.14/20.25 |
% 136.14/20.25 End of proof
% 136.14/20.25
% 136.14/20.25 Sub-proof #415 shows that the following formulas are inconsistent:
% 136.14/20.25 ----------------------------------------------------------------
% 136.14/20.25 (1) op(e2, e2) = e0
% 136.14/20.25 (2) ~ (all_16_0 = e1)
% 136.14/20.25 (3) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 136.14/20.25 (4) op(e2, e3) = all_16_0
% 136.14/20.25 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.25 (6) ~ (e1 = e0)
% 136.14/20.25
% 136.14/20.25 Begin of proof
% 136.14/20.25 |
% 136.14/20.25 | BETA: splitting (3) gives:
% 136.14/20.25 |
% 136.14/20.25 | Case 1:
% 136.14/20.25 | |
% 136.14/20.25 | | (7) all_57_2 = e1 & op(e2, e3) = e1
% 136.14/20.25 | |
% 136.14/20.25 | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #425.
% 136.14/20.25 | |
% 136.14/20.25 | Case 2:
% 136.14/20.25 | |
% 136.14/20.25 | | (8) all_57_3 = e1 & op(e2, e2) = e1
% 136.14/20.25 | |
% 136.14/20.25 | | ALPHA: (8) implies:
% 136.14/20.26 | | (9) op(e2, e2) = e1
% 136.14/20.26 | |
% 136.14/20.26 | | REF_CLOSE: (1), (5), (6), (9) are inconsistent by sub-proof #675.
% 136.14/20.26 | |
% 136.14/20.26 | End of split
% 136.14/20.26 |
% 136.14/20.26 End of proof
% 136.14/20.26
% 136.14/20.26 Sub-proof #416 shows that the following formulas are inconsistent:
% 136.14/20.26 ----------------------------------------------------------------
% 136.14/20.26 (1) all_57_6 = e0
% 136.14/20.26 (2) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 136.14/20.26 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 136.14/20.26 (3) ~ (e2 = e1)
% 136.14/20.26 (4) all_57_0 = e2
% 136.14/20.26 (5) all_57_2 = e3
% 136.14/20.26 (6) ~ (e3 = e1)
% 136.14/20.26 (7) ~ (e1 = e0)
% 136.14/20.26 (8) all_57_12 = e2
% 136.14/20.26
% 136.14/20.26 Begin of proof
% 136.14/20.26 |
% 136.14/20.26 | BETA: splitting (2) gives:
% 136.14/20.26 |
% 136.14/20.26 | Case 1:
% 136.14/20.26 | |
% 136.14/20.26 | | (9) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1)
% 136.14/20.26 | |
% 136.14/20.26 | | BETA: splitting (9) gives:
% 136.14/20.26 | |
% 136.14/20.26 | | Case 1:
% 136.14/20.26 | | |
% 136.14/20.26 | | | (10) all_57_0 = e1 & op(e3, e3) = e1
% 136.14/20.26 | | |
% 136.14/20.26 | | | ALPHA: (10) implies:
% 136.14/20.26 | | | (11) all_57_0 = e1
% 136.14/20.26 | | |
% 136.14/20.26 | | | COMBINE_EQS: (4), (11) imply:
% 136.14/20.26 | | | (12) e2 = e1
% 136.14/20.26 | | |
% 136.14/20.26 | | | REDUCE: (3), (12) imply:
% 136.14/20.26 | | | (13) $false
% 136.14/20.26 | | |
% 136.14/20.26 | | | CLOSE: (13) is inconsistent.
% 136.14/20.26 | | |
% 136.14/20.26 | | Case 2:
% 136.14/20.26 | | |
% 136.14/20.26 | | | (14) all_57_2 = e1 & op(e2, e3) = e1
% 136.14/20.26 | | |
% 136.14/20.26 | | | REF_CLOSE: (5), (6), (14) are inconsistent by sub-proof #453.
% 136.14/20.26 | | |
% 136.14/20.26 | | End of split
% 136.14/20.26 | |
% 136.14/20.26 | Case 2:
% 136.14/20.26 | |
% 136.14/20.26 | | (15) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 136.14/20.26 | | e1)
% 136.14/20.26 | |
% 136.14/20.26 | | REF_CLOSE: (1), (3), (7), (8), (15) are inconsistent by sub-proof #417.
% 136.14/20.26 | |
% 136.14/20.26 | End of split
% 136.14/20.26 |
% 136.14/20.26 End of proof
% 136.14/20.26
% 136.14/20.26 Sub-proof #417 shows that the following formulas are inconsistent:
% 136.14/20.26 ----------------------------------------------------------------
% 136.14/20.26 (1) all_57_6 = e0
% 136.14/20.26 (2) ~ (e2 = e1)
% 136.14/20.26 (3) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 136.14/20.26 (4) ~ (e1 = e0)
% 136.14/20.26 (5) all_57_12 = e2
% 136.14/20.26
% 136.14/20.26 Begin of proof
% 136.14/20.26 |
% 136.14/20.26 | BETA: splitting (3) gives:
% 136.14/20.26 |
% 136.14/20.26 | Case 1:
% 136.14/20.26 | |
% 136.14/20.26 | | (6) all_57_6 = e1 & op(e1, e3) = e1
% 136.14/20.26 | |
% 136.14/20.26 | | ALPHA: (6) implies:
% 136.14/20.26 | | (7) all_57_6 = e1
% 136.14/20.26 | |
% 136.14/20.26 | | REF_CLOSE: (1), (4), (7) are inconsistent by sub-proof #493.
% 136.14/20.26 | |
% 136.14/20.26 | Case 2:
% 136.14/20.26 | |
% 136.14/20.26 | | (8) all_57_12 = e1 & op(e0, e3) = e1
% 136.14/20.26 | |
% 136.14/20.26 | | ALPHA: (8) implies:
% 136.14/20.26 | | (9) all_57_12 = e1
% 136.14/20.26 | |
% 136.14/20.26 | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #644.
% 136.14/20.26 | |
% 136.14/20.26 | End of split
% 136.14/20.26 |
% 136.14/20.26 End of proof
% 136.14/20.26
% 136.14/20.26 Sub-proof #418 shows that the following formulas are inconsistent:
% 136.14/20.26 ----------------------------------------------------------------
% 136.14/20.26 (1) all_57_5 = e2
% 136.14/20.26 (2) all_57_5 = e1
% 136.14/20.26 (3) ~ (e2 = e1)
% 136.14/20.26
% 136.14/20.26 Begin of proof
% 136.14/20.26 |
% 136.14/20.26 | COMBINE_EQS: (1), (2) imply:
% 136.14/20.26 | (4) e2 = e1
% 136.14/20.26 |
% 136.14/20.26 | SIMP: (4) implies:
% 136.14/20.26 | (5) e2 = e1
% 136.14/20.26 |
% 136.14/20.26 | REDUCE: (3), (5) imply:
% 136.14/20.26 | (6) $false
% 136.14/20.26 |
% 136.14/20.26 | CLOSE: (6) is inconsistent.
% 136.14/20.26 |
% 136.14/20.26 End of proof
% 136.14/20.26
% 136.14/20.26 Sub-proof #419 shows that the following formulas are inconsistent:
% 136.14/20.26 ----------------------------------------------------------------
% 136.14/20.26 (1) all_57_4 = e1 & op(e3, e1) = e1
% 136.14/20.26 (2) all_57_4 = e0
% 136.14/20.26 (3) ~ (e1 = e0)
% 136.14/20.26
% 136.14/20.26 Begin of proof
% 136.14/20.26 |
% 136.14/20.26 | ALPHA: (1) implies:
% 136.14/20.26 | (4) all_57_4 = e1
% 136.14/20.26 |
% 136.14/20.26 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.26 | (5) e1 = e0
% 136.14/20.26 |
% 136.14/20.26 | SIMP: (5) implies:
% 136.14/20.26 | (6) e1 = e0
% 136.14/20.26 |
% 136.14/20.26 | REDUCE: (3), (6) imply:
% 136.14/20.26 | (7) $false
% 136.14/20.26 |
% 136.14/20.26 | CLOSE: (7) is inconsistent.
% 136.14/20.26 |
% 136.14/20.26 End of proof
% 136.14/20.26
% 136.14/20.26 Sub-proof #420 shows that the following formulas are inconsistent:
% 136.14/20.26 ----------------------------------------------------------------
% 136.14/20.26 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.26 (2) ~ (e3 = e0)
% 136.14/20.26 (3) ~ (all_52_9 = e3)
% 136.14/20.26 (4) op(e2, e1) = all_52_9
% 136.14/20.26 (5) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3)
% 136.14/20.26 (6) op(e3, e1) = all_52_8
% 136.14/20.26 (7) op(e3, e1) = e0
% 136.14/20.26
% 136.14/20.26 Begin of proof
% 136.14/20.26 |
% 136.14/20.26 | BETA: splitting (5) gives:
% 136.14/20.26 |
% 136.14/20.26 | Case 1:
% 136.14/20.26 | |
% 136.14/20.26 | | (8) all_57_4 = e3 & op(e3, e1) = e3
% 136.14/20.26 | |
% 136.14/20.26 | | ALPHA: (8) implies:
% 136.14/20.26 | | (9) op(e3, e1) = e3
% 136.14/20.26 | |
% 136.14/20.26 | | REF_CLOSE: (1), (2), (6), (7), (9) are inconsistent by sub-proof #600.
% 136.14/20.26 | |
% 136.14/20.26 | Case 2:
% 136.14/20.26 | |
% 136.14/20.26 | | (10) all_57_5 = e3 & op(e2, e1) = e3
% 136.14/20.26 | |
% 136.14/20.26 | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #547.
% 136.14/20.26 | |
% 136.14/20.26 | End of split
% 136.14/20.26 |
% 136.14/20.26 End of proof
% 136.14/20.26
% 136.14/20.26 Sub-proof #421 shows that the following formulas are inconsistent:
% 136.14/20.26 ----------------------------------------------------------------
% 136.14/20.26 (1) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0)
% 136.14/20.26 (2) ~ (all_52_4 = e0)
% 136.14/20.26 (3) op(e3, e3) = e2
% 136.14/20.26 (4) ~ (e2 = e0)
% 136.14/20.26 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.26 (6) op(e3, e2) = all_52_4
% 136.14/20.26
% 136.14/20.26 Begin of proof
% 136.14/20.26 |
% 136.14/20.26 | BETA: splitting (1) gives:
% 136.14/20.26 |
% 136.14/20.26 | Case 1:
% 136.14/20.26 | |
% 136.14/20.26 | | (7) all_57_0 = e0 & op(e3, e3) = e0
% 136.14/20.26 | |
% 136.14/20.26 | | ALPHA: (7) implies:
% 136.14/20.26 | | (8) op(e3, e3) = e0
% 136.14/20.26 | |
% 136.14/20.26 | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #495.
% 136.14/20.26 | |
% 136.14/20.26 | Case 2:
% 136.14/20.26 | |
% 136.14/20.26 | | (9) all_57_1 = e0 & op(e3, e2) = e0
% 136.14/20.26 | |
% 136.14/20.26 | | REF_CLOSE: (2), (5), (6), (9) are inconsistent by sub-proof #693.
% 136.14/20.26 | |
% 136.14/20.26 | End of split
% 136.14/20.26 |
% 136.14/20.26 End of proof
% 136.14/20.26
% 136.14/20.26 Sub-proof #422 shows that the following formulas are inconsistent:
% 136.14/20.26 ----------------------------------------------------------------
% 136.14/20.26 (1) all_54_12 = all_52_3
% 136.14/20.26 (2) ~ (all_52_2 = all_52_3)
% 136.14/20.26 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.26 (4) ~ (all_52_3 = e3)
% 136.14/20.26 (5) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 136.14/20.26 (6) all_57_6 = e1 & op(e1, e3) = e1
% 136.14/20.26 (7) ~ (all_52_3 = e2)
% 136.14/20.26 (8) op(e1, e3) = all_52_2
% 136.14/20.26 (9) ~ (all_52_3 = e0)
% 136.14/20.26
% 136.14/20.26 Begin of proof
% 136.14/20.26 |
% 136.14/20.26 | ALPHA: (6) implies:
% 136.14/20.26 | (10) op(e1, e3) = e1
% 136.14/20.26 |
% 136.14/20.26 | BETA: splitting (5) gives:
% 136.14/20.26 |
% 136.14/20.26 | Case 1:
% 136.14/20.26 | |
% 136.14/20.26 | | (11) all_54_12 = e3
% 136.14/20.26 | |
% 136.14/20.26 | | REF_CLOSE: (1), (4), (11) are inconsistent by sub-proof #424.
% 136.14/20.26 | |
% 136.14/20.26 | Case 2:
% 136.14/20.26 | |
% 136.14/20.26 | | (12) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 136.14/20.26 | |
% 136.14/20.26 | | BETA: splitting (12) gives:
% 136.14/20.26 | |
% 136.14/20.26 | | Case 1:
% 136.14/20.26 | | |
% 136.14/20.26 | | | (13) all_54_12 = e2
% 136.14/20.26 | | |
% 136.14/20.26 | | | REF_CLOSE: (1), (7), (13) are inconsistent by sub-proof #423.
% 136.14/20.26 | | |
% 136.14/20.26 | | Case 2:
% 136.14/20.26 | | |
% 136.14/20.26 | | | (14) all_54_12 = e1 | all_54_12 = e0
% 136.14/20.26 | | |
% 136.14/20.26 | | | BETA: splitting (14) gives:
% 136.14/20.26 | | |
% 136.14/20.26 | | | Case 1:
% 136.14/20.26 | | | |
% 136.14/20.26 | | | | (15) all_54_12 = e1
% 136.14/20.26 | | | |
% 136.14/20.26 | | | | COMBINE_EQS: (1), (15) imply:
% 136.14/20.26 | | | | (16) all_52_3 = e1
% 136.14/20.26 | | | |
% 136.14/20.26 | | | | SIMP: (16) implies:
% 136.14/20.26 | | | | (17) all_52_3 = e1
% 136.14/20.26 | | | |
% 136.14/20.26 | | | | REDUCE: (2), (17) imply:
% 136.14/20.26 | | | | (18) ~ (all_52_2 = e1)
% 136.14/20.26 | | | |
% 136.14/20.26 | | | | REF_CLOSE: (3), (8), (10), (18) are inconsistent by sub-proof #725.
% 136.14/20.26 | | | |
% 136.14/20.26 | | | Case 2:
% 136.14/20.26 | | | |
% 136.14/20.26 | | | | (19) all_54_12 = e0
% 136.14/20.26 | | | |
% 136.14/20.26 | | | | COMBINE_EQS: (1), (19) imply:
% 136.14/20.26 | | | | (20) all_52_3 = e0
% 136.14/20.26 | | | |
% 136.14/20.26 | | | | SIMP: (20) implies:
% 136.14/20.26 | | | | (21) all_52_3 = e0
% 136.14/20.26 | | | |
% 136.14/20.26 | | | | REDUCE: (9), (21) imply:
% 136.14/20.26 | | | | (22) $false
% 136.14/20.26 | | | |
% 136.14/20.26 | | | | CLOSE: (22) is inconsistent.
% 136.14/20.26 | | | |
% 136.14/20.26 | | | End of split
% 136.14/20.26 | | |
% 136.14/20.26 | | End of split
% 136.14/20.26 | |
% 136.14/20.26 | End of split
% 136.14/20.26 |
% 136.14/20.26 End of proof
% 136.14/20.26
% 136.14/20.26 Sub-proof #423 shows that the following formulas are inconsistent:
% 136.14/20.26 ----------------------------------------------------------------
% 136.14/20.26 (1) all_54_12 = all_52_3
% 136.14/20.26 (2) all_54_12 = e2
% 136.14/20.26 (3) ~ (all_52_3 = e2)
% 136.14/20.26
% 136.14/20.26 Begin of proof
% 136.14/20.26 |
% 136.14/20.26 | COMBINE_EQS: (1), (2) imply:
% 136.14/20.26 | (4) all_52_3 = e2
% 136.14/20.26 |
% 136.14/20.26 | SIMP: (4) implies:
% 136.14/20.26 | (5) all_52_3 = e2
% 136.14/20.26 |
% 136.14/20.26 | REDUCE: (3), (5) imply:
% 136.14/20.26 | (6) $false
% 136.14/20.26 |
% 136.14/20.26 | CLOSE: (6) is inconsistent.
% 136.14/20.26 |
% 136.14/20.26 End of proof
% 136.14/20.26
% 136.14/20.26 Sub-proof #424 shows that the following formulas are inconsistent:
% 136.14/20.26 ----------------------------------------------------------------
% 136.14/20.26 (1) all_54_12 = all_52_3
% 136.14/20.26 (2) all_54_12 = e3
% 136.14/20.26 (3) ~ (all_52_3 = e3)
% 136.14/20.26
% 136.14/20.26 Begin of proof
% 136.14/20.26 |
% 136.14/20.26 | COMBINE_EQS: (1), (2) imply:
% 136.14/20.26 | (4) all_52_3 = e3
% 136.14/20.26 |
% 136.14/20.26 | SIMP: (4) implies:
% 136.14/20.26 | (5) all_52_3 = e3
% 136.14/20.26 |
% 136.14/20.26 | REDUCE: (3), (5) imply:
% 136.14/20.26 | (6) $false
% 136.14/20.26 |
% 136.14/20.26 | CLOSE: (6) is inconsistent.
% 136.14/20.26 |
% 136.14/20.26 End of proof
% 136.14/20.26
% 136.14/20.26 Sub-proof #425 shows that the following formulas are inconsistent:
% 136.14/20.26 ----------------------------------------------------------------
% 136.14/20.26 (1) all_57_2 = e1 & op(e2, e3) = e1
% 136.14/20.26 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.26 (3) op(e2, e3) = all_16_0
% 136.14/20.26 (4) ~ (all_16_0 = e1)
% 136.14/20.26
% 136.14/20.26 Begin of proof
% 136.14/20.26 |
% 136.14/20.26 | ALPHA: (1) implies:
% 136.14/20.26 | (5) op(e2, e3) = e1
% 136.14/20.26 |
% 136.14/20.26 | GROUND_INST: instantiating (2) with e1, all_16_0, e3, e2, simplifying with
% 136.14/20.26 | (3), (5) gives:
% 136.14/20.26 | (6) all_16_0 = e1
% 136.14/20.26 |
% 136.14/20.26 | REDUCE: (4), (6) imply:
% 136.14/20.26 | (7) $false
% 136.14/20.26 |
% 136.14/20.26 | CLOSE: (7) is inconsistent.
% 136.14/20.26 |
% 136.14/20.26 End of proof
% 136.14/20.26
% 136.14/20.26 Sub-proof #426 shows that the following formulas are inconsistent:
% 136.14/20.26 ----------------------------------------------------------------
% 136.14/20.26 (1) op(e3, e3) = e2
% 136.14/20.26 (2) ~ (e2 = e0)
% 136.14/20.26 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.26 (4) ~ (e3 = e0)
% 136.14/20.26 (5) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0)
% 136.14/20.26 (6) all_57_2 = e3
% 136.14/20.26
% 136.14/20.26 Begin of proof
% 136.14/20.26 |
% 136.14/20.26 | BETA: splitting (5) gives:
% 136.14/20.26 |
% 136.14/20.26 | Case 1:
% 136.14/20.26 | |
% 136.14/20.26 | | (7) all_57_0 = e0 & op(e3, e3) = e0
% 136.14/20.26 | |
% 136.14/20.26 | | ALPHA: (7) implies:
% 136.14/20.26 | | (8) op(e3, e3) = e0
% 136.14/20.26 | |
% 136.14/20.26 | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #495.
% 136.14/20.26 | |
% 136.14/20.26 | Case 2:
% 136.14/20.26 | |
% 136.14/20.26 | | (9) all_57_2 = e0 & op(e2, e3) = e0
% 136.14/20.26 | |
% 136.14/20.26 | | REF_CLOSE: (4), (6), (9) are inconsistent by sub-proof #521.
% 136.14/20.26 | |
% 136.14/20.26 | End of split
% 136.14/20.26 |
% 136.14/20.26 End of proof
% 136.14/20.26
% 136.14/20.26 Sub-proof #427 shows that the following formulas are inconsistent:
% 136.14/20.26 ----------------------------------------------------------------
% 136.14/20.26 (1) op(e0, e0) = all_4_2
% 136.14/20.26 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.26 (3) ~ (all_4_2 = e2)
% 136.14/20.26 (4) op(e0, e0) = e2
% 136.14/20.26 (5) op(e0, e0) = all_56_31
% 136.14/20.26
% 136.14/20.26 Begin of proof
% 136.14/20.26 |
% 136.14/20.26 | GROUND_INST: instantiating (2) with all_4_2, all_56_31, e0, e0, simplifying
% 136.14/20.26 | with (1), (5) gives:
% 136.14/20.26 | (6) all_56_31 = all_4_2
% 136.14/20.26 |
% 136.14/20.26 | GROUND_INST: instantiating (2) with e2, all_56_31, e0, e0, simplifying with
% 136.14/20.26 | (4), (5) gives:
% 136.14/20.26 | (7) all_56_31 = e2
% 136.14/20.26 |
% 136.14/20.26 | COMBINE_EQS: (6), (7) imply:
% 136.14/20.26 | (8) all_4_2 = e2
% 136.14/20.26 |
% 136.14/20.26 | REDUCE: (3), (8) imply:
% 136.14/20.26 | (9) $false
% 136.14/20.26 |
% 136.14/20.26 | CLOSE: (9) is inconsistent.
% 136.14/20.26 |
% 136.14/20.26 End of proof
% 136.14/20.26
% 136.14/20.26 Sub-proof #428 shows that the following formulas are inconsistent:
% 136.14/20.26 ----------------------------------------------------------------
% 136.14/20.26 (1) op(e1, e0) = e2
% 136.14/20.26 (2) op(e0, e1) = e2
% 136.14/20.26 (3) ~ (e2 = e0)
% 136.14/20.26 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.26 (5) ~ (e2 = e1)
% 136.14/20.26 (6) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.14/20.26 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 136.14/20.26 op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.14/20.26 op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 136.14/20.26 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 136.14/20.26 e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 136.14/20.26 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 136.14/20.26 = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 136.14/20.26 $i(all_56_21) & $i(all_56_29))
% 136.14/20.26
% 136.14/20.26 Begin of proof
% 136.14/20.26 |
% 136.14/20.26 | BETA: splitting (6) gives:
% 136.14/20.26 |
% 136.14/20.26 | Case 1:
% 136.14/20.26 | |
% 136.14/20.26 | | (7) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15
% 136.14/20.26 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0
% 136.14/20.26 | | & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.14/20.26 | | op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)
% 136.14/20.26 | |
% 136.14/20.26 | | ALPHA: (7) implies:
% 136.14/20.26 | | (8) op(e1, e0) = e1
% 136.14/20.26 | |
% 136.14/20.26 | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #720.
% 136.14/20.26 | |
% 136.14/20.26 | Case 2:
% 136.14/20.26 | |
% 136.14/20.26 | | (9) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13
% 136.14/20.26 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 136.14/20.26 | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1,
% 136.14/20.26 | | e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 136.14/20.26 | | $i(all_56_21) & $i(all_56_29)
% 136.14/20.26 | |
% 136.14/20.26 | | ALPHA: (9) implies:
% 136.14/20.26 | | (10) op(e0, e1) = e0
% 136.14/20.26 | |
% 136.14/20.26 | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #660.
% 136.14/20.26 | |
% 136.14/20.26 | End of split
% 136.14/20.26 |
% 136.14/20.26 End of proof
% 136.14/20.26
% 136.14/20.26 Sub-proof #429 shows that the following formulas are inconsistent:
% 136.14/20.26 ----------------------------------------------------------------
% 136.14/20.26 (1) ~ (all_52_2 = e2)
% 136.14/20.26 (2) ~ (all_52_2 = e1)
% 136.14/20.26 (3) ~ (all_52_2 = e0)
% 136.14/20.26 (4) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 136.14/20.26 (5) all_54_8 = all_52_2
% 136.14/20.26
% 136.14/20.26 Begin of proof
% 136.14/20.26 |
% 136.14/20.26 | BETA: splitting (4) gives:
% 136.14/20.26 |
% 136.14/20.26 | Case 1:
% 136.14/20.26 | |
% 136.14/20.26 | | (6) all_54_8 = e2
% 136.14/20.26 | |
% 136.14/20.26 | | REF_CLOSE: (1), (5), (6) are inconsistent by sub-proof #430.
% 136.14/20.26 | |
% 136.14/20.26 | Case 2:
% 136.14/20.26 | |
% 136.14/20.26 | | (7) all_54_8 = e1 | all_54_8 = e0
% 136.14/20.26 | |
% 136.14/20.26 | | REF_CLOSE: (2), (3), (5), (7) are inconsistent by sub-proof #474.
% 136.14/20.26 | |
% 136.14/20.26 | End of split
% 136.14/20.26 |
% 136.14/20.26 End of proof
% 136.14/20.26
% 136.14/20.26 Sub-proof #430 shows that the following formulas are inconsistent:
% 136.14/20.26 ----------------------------------------------------------------
% 136.14/20.26 (1) all_54_8 = all_52_2
% 136.14/20.26 (2) all_54_8 = e2
% 136.14/20.26 (3) ~ (all_52_2 = e2)
% 136.14/20.26
% 136.14/20.26 Begin of proof
% 136.14/20.26 |
% 136.14/20.26 | COMBINE_EQS: (1), (2) imply:
% 136.14/20.26 | (4) all_52_2 = e2
% 136.14/20.26 |
% 136.14/20.26 | SIMP: (4) implies:
% 136.14/20.26 | (5) all_52_2 = e2
% 136.14/20.26 |
% 136.14/20.26 | REDUCE: (3), (5) imply:
% 136.14/20.26 | (6) $false
% 136.14/20.26 |
% 136.14/20.26 | CLOSE: (6) is inconsistent.
% 136.14/20.26 |
% 136.14/20.26 End of proof
% 136.14/20.26
% 136.14/20.26 Sub-proof #431 shows that the following formulas are inconsistent:
% 136.14/20.26 ----------------------------------------------------------------
% 136.14/20.26 (1) ~ (all_44_1 = e2) & op(e3, e3) = all_44_1 & $i(all_44_1)
% 136.14/20.26 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.26 (3) op(e3, e3) = e2
% 136.14/20.26
% 136.14/20.26 Begin of proof
% 136.14/20.26 |
% 136.14/20.26 | ALPHA: (1) implies:
% 136.14/20.26 | (4) ~ (all_44_1 = e2)
% 136.14/20.26 | (5) op(e3, e3) = all_44_1
% 136.14/20.26 |
% 136.14/20.26 | GROUND_INST: instantiating (2) with e2, all_44_1, e3, e3, simplifying with
% 136.14/20.26 | (3), (5) gives:
% 136.14/20.26 | (6) all_44_1 = e2
% 136.14/20.26 |
% 136.14/20.26 | REDUCE: (4), (6) imply:
% 136.14/20.26 | (7) $false
% 136.14/20.26 |
% 136.14/20.26 | CLOSE: (7) is inconsistent.
% 136.14/20.26 |
% 136.14/20.26 End of proof
% 136.14/20.26
% 136.14/20.26 Sub-proof #432 shows that the following formulas are inconsistent:
% 136.14/20.26 ----------------------------------------------------------------
% 136.14/20.26 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.26 (2) op(e3, e0) = all_44_0
% 136.14/20.26 (3) op(e3, e0) = e1
% 136.14/20.26 (4) ~ (all_44_0 = e1)
% 136.14/20.26
% 136.14/20.26 Begin of proof
% 136.14/20.26 |
% 136.14/20.26 | GROUND_INST: instantiating (1) with e1, all_44_0, e0, e3, simplifying with
% 136.14/20.26 | (2), (3) gives:
% 136.14/20.26 | (5) all_44_0 = e1
% 136.14/20.26 |
% 136.14/20.26 | REDUCE: (4), (5) imply:
% 136.14/20.26 | (6) $false
% 136.14/20.26 |
% 136.14/20.26 | CLOSE: (6) is inconsistent.
% 136.14/20.26 |
% 136.14/20.26 End of proof
% 136.14/20.26
% 136.14/20.26 Sub-proof #433 shows that the following formulas are inconsistent:
% 136.14/20.26 ----------------------------------------------------------------
% 136.14/20.26 (1) ~ (e2 = e0)
% 136.14/20.26 (2) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 136.14/20.26 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 136.14/20.26 (3) ~ (all_52_7 = e3)
% 136.14/20.26 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.26 (5) ~ (e2 = e1)
% 136.14/20.26 (6) ~ (e3 = e0)
% 136.14/20.26 (7) ~ (e3 = e2)
% 136.14/20.26 (8) op(e0, e2) = all_52_7
% 136.14/20.26 (9) all_57_15 = e2
% 136.14/20.26 (10) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 136.14/20.26 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 136.14/20.26 e1)
% 136.14/20.26 (11) all_57_14 = e2
% 136.14/20.26 (12) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 136.14/20.26 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 136.14/20.26 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 136.14/20.26 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 136.14/20.26 (13) ~ (e3 = e1)
% 136.14/20.26 (14) ~ (e1 = e0)
% 136.14/20.26
% 136.14/20.26 Begin of proof
% 136.14/20.26 |
% 136.14/20.26 | BETA: splitting (2) gives:
% 136.14/20.26 |
% 136.14/20.26 | Case 1:
% 136.14/20.26 | |
% 136.14/20.26 | | (15) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 136.14/20.26 | | e3)
% 136.14/20.26 | |
% 136.14/20.26 | | BETA: splitting (15) gives:
% 136.14/20.26 | |
% 136.14/20.26 | | Case 1:
% 136.14/20.26 | | |
% 136.14/20.26 | | | (16) all_57_12 = e3 & op(e0, e3) = e3
% 136.14/20.26 | | |
% 136.14/20.26 | | | ALPHA: (16) implies:
% 136.14/20.26 | | | (17) all_57_12 = e3
% 136.14/20.26 | | |
% 136.14/20.26 | | | REF_CLOSE: (1), (5), (6), (9), (10), (11), (12), (13), (14), (17) are
% 136.14/20.26 | | | inconsistent by sub-proof #434.
% 136.14/20.26 | | |
% 136.14/20.26 | | Case 2:
% 136.14/20.26 | | |
% 136.14/20.26 | | | (18) all_57_13 = e3 & op(e0, e2) = e3
% 136.14/20.26 | | |
% 136.14/20.26 | | | REF_CLOSE: (3), (4), (8), (18) are inconsistent by sub-proof #556.
% 136.14/20.26 | | |
% 136.14/20.26 | | End of split
% 136.14/20.26 | |
% 136.14/20.26 | Case 2:
% 136.14/20.26 | |
% 136.14/20.26 | | (19) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 136.14/20.26 | | e3)
% 136.14/20.26 | |
% 136.14/20.26 | | BETA: splitting (19) gives:
% 136.14/20.26 | |
% 136.14/20.26 | | Case 1:
% 136.14/20.26 | | |
% 136.14/20.26 | | | (20) all_57_14 = e3 & op(e0, e1) = e3
% 136.14/20.26 | | |
% 136.14/20.26 | | | ALPHA: (20) implies:
% 136.14/20.26 | | | (21) all_57_14 = e3
% 136.14/20.26 | | |
% 136.14/20.26 | | | COMBINE_EQS: (11), (21) imply:
% 136.14/20.26 | | | (22) e3 = e2
% 136.14/20.26 | | |
% 136.14/20.26 | | | REDUCE: (7), (22) imply:
% 136.14/20.26 | | | (23) $false
% 136.14/20.26 | | |
% 136.14/20.26 | | | CLOSE: (23) is inconsistent.
% 136.14/20.26 | | |
% 136.14/20.26 | | Case 2:
% 136.14/20.26 | | |
% 136.14/20.26 | | | (24) all_57_15 = e3 & op(e0, e0) = e3
% 136.14/20.26 | | |
% 136.14/20.26 | | | ALPHA: (24) implies:
% 136.14/20.26 | | | (25) all_57_15 = e3
% 136.14/20.26 | | |
% 136.14/20.26 | | | COMBINE_EQS: (9), (25) imply:
% 136.14/20.26 | | | (26) e3 = e2
% 136.14/20.26 | | |
% 136.14/20.26 | | | REDUCE: (7), (26) imply:
% 136.14/20.26 | | | (27) $false
% 136.14/20.26 | | |
% 136.14/20.26 | | | CLOSE: (27) is inconsistent.
% 136.14/20.26 | | |
% 136.14/20.26 | | End of split
% 136.14/20.26 | |
% 136.14/20.26 | End of split
% 136.14/20.26 |
% 136.14/20.26 End of proof
% 136.14/20.26
% 136.14/20.26 Sub-proof #434 shows that the following formulas are inconsistent:
% 136.14/20.26 ----------------------------------------------------------------
% 136.14/20.26 (1) ~ (e2 = e0)
% 136.14/20.26 (2) ~ (e2 = e1)
% 136.14/20.26 (3) ~ (e3 = e0)
% 136.14/20.26 (4) all_57_15 = e2
% 136.14/20.26 (5) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 136.14/20.26 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 136.14/20.26 (6) all_57_12 = e3
% 136.14/20.26 (7) all_57_14 = e2
% 136.14/20.26 (8) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 136.14/20.26 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 136.14/20.26 e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 136.14/20.26 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 136.14/20.26 (9) ~ (e3 = e1)
% 136.14/20.26 (10) ~ (e1 = e0)
% 136.14/20.26
% 136.14/20.26 Begin of proof
% 136.14/20.26 |
% 136.14/20.26 | BETA: splitting (8) gives:
% 136.14/20.26 |
% 136.14/20.26 | Case 1:
% 136.14/20.26 | |
% 136.14/20.26 | | (11) all_57_15 = e0 & op(e0, e0) = e0
% 136.14/20.26 | |
% 136.14/20.26 | | REF_CLOSE: (1), (4), (11) are inconsistent by sub-proof #437.
% 136.14/20.26 | |
% 136.14/20.26 | Case 2:
% 136.14/20.26 | |
% 136.14/20.26 | | (12) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 136.14/20.26 | | e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 136.14/20.26 | | op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 136.14/20.26 | | (all_57_14 = e0 & op(e0, e1) = e0))
% 136.14/20.26 | |
% 136.14/20.26 | | ALPHA: (12) implies:
% 136.14/20.26 | | (13) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 136.14/20.26 | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 136.14/20.26 | |
% 136.14/20.26 | | BETA: splitting (13) gives:
% 136.14/20.26 | |
% 136.14/20.26 | | Case 1:
% 136.14/20.26 | | |
% 136.14/20.26 | | | (14) all_57_12 = e0 & op(e0, e3) = e0
% 136.14/20.26 | | |
% 136.14/20.26 | | | REF_CLOSE: (3), (6), (14) are inconsistent by sub-proof #436.
% 136.14/20.26 | | |
% 136.14/20.26 | | Case 2:
% 136.14/20.26 | | |
% 136.14/20.26 | | | (15) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1)
% 136.14/20.26 | | | = e0)
% 136.14/20.26 | | |
% 136.14/20.26 | | | BETA: splitting (15) gives:
% 136.14/20.26 | | |
% 136.14/20.26 | | | Case 1:
% 136.14/20.26 | | | |
% 136.14/20.26 | | | | (16) all_57_13 = e0 & op(e0, e2) = e0
% 136.14/20.26 | | | |
% 136.14/20.26 | | | | ALPHA: (16) implies:
% 136.14/20.26 | | | | (17) all_57_13 = e0
% 136.14/20.26 | | | |
% 136.14/20.26 | | | | BETA: splitting (5) gives:
% 136.14/20.26 | | | |
% 136.14/20.26 | | | | Case 1:
% 136.14/20.26 | | | | |
% 136.14/20.26 | | | | | (18) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0,
% 136.14/20.26 | | | | | e2) = e1)
% 136.14/20.26 | | | | |
% 136.14/20.26 | | | | | BETA: splitting (18) gives:
% 136.14/20.26 | | | | |
% 136.14/20.26 | | | | | Case 1:
% 136.14/20.26 | | | | | |
% 136.14/20.26 | | | | | | (19) all_57_12 = e1 & op(e0, e3) = e1
% 136.14/20.26 | | | | | |
% 136.14/20.26 | | | | | | REF_CLOSE: (6), (9), (19) are inconsistent by sub-proof #490.
% 136.14/20.26 | | | | | |
% 136.14/20.26 | | | | | Case 2:
% 136.14/20.26 | | | | | |
% 136.14/20.26 | | | | | | (20) all_57_13 = e1 & op(e0, e2) = e1
% 136.14/20.26 | | | | | |
% 136.14/20.26 | | | | | | ALPHA: (20) implies:
% 136.14/20.26 | | | | | | (21) all_57_13 = e1
% 136.14/20.26 | | | | | |
% 136.14/20.26 | | | | | | REF_CLOSE: (10), (17), (21) are inconsistent by sub-proof #681.
% 136.14/20.26 | | | | | |
% 136.14/20.26 | | | | | End of split
% 136.14/20.26 | | | | |
% 136.14/20.26 | | | | Case 2:
% 136.14/20.26 | | | | |
% 136.14/20.26 | | | | | (22) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0,
% 136.14/20.26 | | | | | e0) = e1)
% 136.14/20.26 | | | | |
% 136.14/20.26 | | | | | BETA: splitting (22) gives:
% 136.14/20.26 | | | | |
% 136.14/20.26 | | | | | Case 1:
% 136.14/20.26 | | | | | |
% 136.14/20.26 | | | | | | (23) all_57_14 = e1 & op(e0, e1) = e1
% 136.14/20.26 | | | | | |
% 136.14/20.26 | | | | | | ALPHA: (23) implies:
% 136.14/20.26 | | | | | | (24) all_57_14 = e1
% 136.14/20.26 | | | | | |
% 136.14/20.26 | | | | | | REF_CLOSE: (2), (7), (24) are inconsistent by sub-proof #560.
% 136.14/20.26 | | | | | |
% 136.14/20.26 | | | | | Case 2:
% 136.14/20.26 | | | | | |
% 136.14/20.26 | | | | | | (25) all_57_15 = e1 & op(e0, e0) = e1
% 136.14/20.26 | | | | | |
% 136.14/20.26 | | | | | | REF_CLOSE: (2), (4), (25) are inconsistent by sub-proof #435.
% 136.14/20.26 | | | | | |
% 136.14/20.26 | | | | | End of split
% 136.14/20.26 | | | | |
% 136.14/20.26 | | | | End of split
% 136.14/20.26 | | | |
% 136.14/20.26 | | | Case 2:
% 136.14/20.26 | | | |
% 136.14/20.26 | | | | (26) all_57_14 = e0 & op(e0, e1) = e0
% 136.14/20.26 | | | |
% 136.14/20.26 | | | | REF_CLOSE: (1), (7), (26) are inconsistent by sub-proof #580.
% 136.14/20.26 | | | |
% 136.14/20.26 | | | End of split
% 136.14/20.26 | | |
% 136.14/20.26 | | End of split
% 136.14/20.26 | |
% 136.14/20.26 | End of split
% 136.14/20.26 |
% 136.14/20.26 End of proof
% 136.14/20.26
% 136.14/20.26 Sub-proof #435 shows that the following formulas are inconsistent:
% 136.14/20.26 ----------------------------------------------------------------
% 136.14/20.26 (1) all_57_15 = e1 & op(e0, e0) = e1
% 136.14/20.26 (2) all_57_15 = e2
% 136.14/20.26 (3) ~ (e2 = e1)
% 136.14/20.26
% 136.14/20.26 Begin of proof
% 136.14/20.26 |
% 136.14/20.26 | ALPHA: (1) implies:
% 136.14/20.26 | (4) all_57_15 = e1
% 136.14/20.26 |
% 136.14/20.26 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.26 | (5) e2 = e1
% 136.14/20.26 |
% 136.14/20.26 | SIMP: (5) implies:
% 136.14/20.26 | (6) e2 = e1
% 136.14/20.26 |
% 136.14/20.26 | REDUCE: (3), (6) imply:
% 136.14/20.26 | (7) $false
% 136.14/20.26 |
% 136.14/20.26 | CLOSE: (7) is inconsistent.
% 136.14/20.26 |
% 136.14/20.26 End of proof
% 136.14/20.26
% 136.14/20.26 Sub-proof #436 shows that the following formulas are inconsistent:
% 136.14/20.26 ----------------------------------------------------------------
% 136.14/20.26 (1) all_57_12 = e0 & op(e0, e3) = e0
% 136.14/20.26 (2) all_57_12 = e3
% 136.14/20.26 (3) ~ (e3 = e0)
% 136.14/20.26
% 136.14/20.26 Begin of proof
% 136.14/20.26 |
% 136.14/20.26 | ALPHA: (1) implies:
% 136.14/20.26 | (4) all_57_12 = e0
% 136.14/20.26 |
% 136.14/20.26 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.26 | (5) e3 = e0
% 136.14/20.26 |
% 136.14/20.26 | REDUCE: (3), (5) imply:
% 136.14/20.26 | (6) $false
% 136.14/20.26 |
% 136.14/20.26 | CLOSE: (6) is inconsistent.
% 136.14/20.26 |
% 136.14/20.26 End of proof
% 136.14/20.26
% 136.14/20.26 Sub-proof #437 shows that the following formulas are inconsistent:
% 136.14/20.26 ----------------------------------------------------------------
% 136.14/20.26 (1) all_57_15 = e0 & op(e0, e0) = e0
% 136.14/20.26 (2) all_57_15 = e2
% 136.14/20.26 (3) ~ (e2 = e0)
% 136.14/20.26
% 136.14/20.26 Begin of proof
% 136.14/20.26 |
% 136.14/20.26 | ALPHA: (1) implies:
% 136.14/20.26 | (4) all_57_15 = e0
% 136.14/20.26 |
% 136.14/20.26 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.26 | (5) e2 = e0
% 136.14/20.26 |
% 136.14/20.26 | SIMP: (5) implies:
% 136.14/20.26 | (6) e2 = e0
% 136.14/20.26 |
% 136.14/20.26 | REDUCE: (3), (6) imply:
% 136.14/20.26 | (7) $false
% 136.14/20.26 |
% 136.14/20.26 | CLOSE: (7) is inconsistent.
% 136.14/20.26 |
% 136.14/20.26 End of proof
% 136.14/20.26
% 136.14/20.26 Sub-proof #438 shows that the following formulas are inconsistent:
% 136.14/20.26 ----------------------------------------------------------------
% 136.14/20.26 (1) all_57_4 = e3 & op(e3, e1) = e3
% 136.14/20.26 (2) all_57_4 = e1
% 136.14/20.26 (3) ~ (e3 = e1)
% 136.14/20.26
% 136.14/20.26 Begin of proof
% 136.14/20.26 |
% 136.14/20.26 | ALPHA: (1) implies:
% 136.14/20.26 | (4) all_57_4 = e3
% 136.14/20.26 |
% 136.14/20.26 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.26 | (5) e3 = e1
% 136.14/20.26 |
% 136.14/20.26 | REDUCE: (3), (5) imply:
% 136.14/20.26 | (6) $false
% 136.14/20.26 |
% 136.14/20.26 | CLOSE: (6) is inconsistent.
% 136.14/20.26 |
% 136.14/20.26 End of proof
% 136.14/20.26
% 136.14/20.26 Sub-proof #439 shows that the following formulas are inconsistent:
% 136.14/20.26 ----------------------------------------------------------------
% 136.14/20.26 (1) op(e1, e0) = e2
% 136.14/20.26 (2) op(e0, e0) = e3
% 136.14/20.26 (3) ~ (e2 = e0)
% 136.14/20.26 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.26 (5) ~ (e2 = e1)
% 136.14/20.26 (6) ~ (e3 = e0)
% 136.14/20.27 (7) all_57_9 = e3
% 136.14/20.27 (8) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 136.14/20.27 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 136.14/20.27 e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 136.14/20.27 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 136.14/20.27 (9) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2)
% 136.14/20.27 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 136.14/20.27 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25
% 136.14/20.27 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 136.14/20.27 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3)
% 136.14/20.27 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.14/20.27 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 136.14/20.27 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) &
% 136.14/20.27 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 &
% 136.14/20.27 all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~
% 136.14/20.27 (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) =
% 136.14/20.27 e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) =
% 136.14/20.27 all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23
% 136.14/20.27 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.14/20.27 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1,
% 136.14/20.27 e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 136.14/20.27 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.14/20.27 $i(all_56_29))
% 136.14/20.27 (10) all_57_11 = e2
% 136.14/20.27 (11) ~ (e3 = e1)
% 136.14/20.27 (12) ~ (e1 = e0)
% 136.14/20.27 (13) op(e0, e0) = all_56_31
% 136.14/20.27 (14) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 136.14/20.27 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 136.14/20.27
% 136.14/20.27 Begin of proof
% 136.14/20.27 |
% 136.14/20.27 | BETA: splitting (14) gives:
% 136.14/20.27 |
% 136.14/20.27 | Case 1:
% 136.14/20.27 | |
% 136.14/20.27 | | (15) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 136.14/20.27 | | e1)
% 136.14/20.27 | |
% 136.14/20.27 | | BETA: splitting (15) gives:
% 136.14/20.27 | |
% 136.14/20.27 | | Case 1:
% 136.14/20.27 | | |
% 136.14/20.27 | | | (16) all_57_9 = e1 & op(e3, e0) = e1
% 136.14/20.27 | | |
% 136.14/20.27 | | | ALPHA: (16) implies:
% 136.14/20.27 | | | (17) all_57_9 = e1
% 136.14/20.27 | | |
% 136.14/20.27 | | | REF_CLOSE: (7), (11), (17) are inconsistent by sub-proof #690.
% 136.14/20.27 | | |
% 136.14/20.27 | | Case 2:
% 136.14/20.27 | | |
% 136.14/20.27 | | | (18) all_57_10 = e1 & op(e2, e0) = e1
% 136.14/20.27 | | |
% 136.14/20.27 | | | ALPHA: (18) implies:
% 136.14/20.27 | | | (19) all_57_10 = e1
% 136.14/20.27 | | |
% 136.14/20.27 | | | BETA: splitting (8) gives:
% 136.14/20.27 | | |
% 136.14/20.27 | | | Case 1:
% 136.14/20.27 | | | |
% 136.14/20.27 | | | | (20) all_57_15 = e0 & op(e0, e0) = e0
% 136.14/20.27 | | | |
% 136.14/20.27 | | | | ALPHA: (20) implies:
% 136.14/20.27 | | | | (21) op(e0, e0) = e0
% 136.14/20.27 | | | |
% 136.14/20.27 | | | | REF_CLOSE: (3), (4), (6), (9), (12), (13), (21) are inconsistent by
% 136.14/20.27 | | | | sub-proof #710.
% 136.14/20.27 | | | |
% 136.14/20.27 | | | Case 2:
% 136.14/20.27 | | | |
% 136.14/20.27 | | | | (22) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 136.14/20.27 | | | | e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 136.14/20.27 | | | | ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 136.14/20.27 | | | | e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 136.14/20.27 | | | |
% 136.14/20.27 | | | | REF_CLOSE: (3), (6), (7), (10), (12), (19), (22) are inconsistent by
% 136.14/20.27 | | | | sub-proof #637.
% 136.14/20.27 | | | |
% 136.14/20.27 | | | End of split
% 136.14/20.27 | | |
% 136.14/20.27 | | End of split
% 136.14/20.27 | |
% 136.14/20.27 | Case 2:
% 136.14/20.27 | |
% 136.14/20.27 | | (23) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 136.14/20.27 | | e1)
% 136.14/20.27 | |
% 136.14/20.27 | | REF_CLOSE: (1), (2), (4), (5), (11), (23) are inconsistent by sub-proof
% 136.14/20.27 | | #557.
% 136.14/20.27 | |
% 136.14/20.27 | End of split
% 136.14/20.27 |
% 136.14/20.27 End of proof
% 136.14/20.27
% 136.14/20.27 Sub-proof #440 shows that the following formulas are inconsistent:
% 136.14/20.27 ----------------------------------------------------------------
% 136.14/20.27 (1) op(e2, e0) = all_52_13
% 136.14/20.27 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.27 (3) ~ (all_52_13 = e2)
% 136.14/20.27 (4) op(e3, e0) = all_52_12
% 136.14/20.27 (5) ~ (all_52_12 = e2)
% 136.14/20.27 (6) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 136.14/20.27
% 136.14/20.27 Begin of proof
% 136.14/20.27 |
% 136.14/20.27 | BETA: splitting (6) gives:
% 136.14/20.27 |
% 136.14/20.27 | Case 1:
% 136.14/20.27 | |
% 136.14/20.27 | | (7) all_57_9 = e2 & op(e3, e0) = e2
% 136.14/20.27 | |
% 136.14/20.27 | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #460.
% 136.14/20.27 | |
% 136.14/20.27 | Case 2:
% 136.14/20.27 | |
% 136.14/20.27 | | (8) all_57_10 = e2 & op(e2, e0) = e2
% 136.14/20.27 | |
% 136.14/20.27 | | ALPHA: (8) implies:
% 136.14/20.27 | | (9) op(e2, e0) = e2
% 136.14/20.27 | |
% 136.14/20.27 | | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #768.
% 136.14/20.27 | |
% 136.14/20.27 | End of split
% 136.14/20.27 |
% 136.14/20.27 End of proof
% 136.14/20.27
% 136.14/20.27 Sub-proof #441 shows that the following formulas are inconsistent:
% 136.14/20.27 ----------------------------------------------------------------
% 136.14/20.27 (1) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2)
% 136.14/20.27 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.27 (3) ~ (all_52_9 = e2)
% 136.14/20.27 (4) op(e2, e1) = all_52_9
% 136.14/20.27 (5) ~ (all_52_8 = e2)
% 136.14/20.27 (6) op(e3, e1) = all_52_8
% 136.14/20.27
% 136.14/20.27 Begin of proof
% 136.14/20.27 |
% 136.14/20.27 | BETA: splitting (1) gives:
% 136.14/20.27 |
% 136.14/20.27 | Case 1:
% 136.14/20.27 | |
% 136.14/20.27 | | (7) all_57_4 = e2 & op(e3, e1) = e2
% 136.14/20.27 | |
% 136.14/20.27 | | REF_CLOSE: (2), (5), (6), (7) are inconsistent by sub-proof #442.
% 136.14/20.27 | |
% 136.14/20.27 | Case 2:
% 136.14/20.27 | |
% 136.14/20.27 | | (8) all_57_5 = e2 & op(e2, e1) = e2
% 136.14/20.27 | |
% 136.14/20.27 | | ALPHA: (8) implies:
% 136.14/20.27 | | (9) op(e2, e1) = e2
% 136.14/20.27 | |
% 136.14/20.27 | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #770.
% 136.14/20.27 | |
% 136.14/20.27 | End of split
% 136.14/20.27 |
% 136.14/20.27 End of proof
% 136.14/20.27
% 136.14/20.27 Sub-proof #442 shows that the following formulas are inconsistent:
% 136.14/20.27 ----------------------------------------------------------------
% 136.14/20.27 (1) all_57_4 = e2 & op(e3, e1) = e2
% 136.14/20.27 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.27 (3) op(e3, e1) = all_52_8
% 136.14/20.27 (4) ~ (all_52_8 = e2)
% 136.14/20.27
% 136.14/20.27 Begin of proof
% 136.14/20.27 |
% 136.14/20.27 | ALPHA: (1) implies:
% 136.14/20.27 | (5) op(e3, e1) = e2
% 136.14/20.27 |
% 136.14/20.27 | GROUND_INST: instantiating (2) with all_52_8, e2, e1, e3, simplifying with
% 136.14/20.27 | (3), (5) gives:
% 136.14/20.27 | (6) all_52_8 = e2
% 136.14/20.27 |
% 136.14/20.27 | REDUCE: (4), (6) imply:
% 136.14/20.27 | (7) $false
% 136.14/20.27 |
% 136.14/20.27 | CLOSE: (7) is inconsistent.
% 136.14/20.27 |
% 136.14/20.27 End of proof
% 136.14/20.27
% 136.14/20.27 Sub-proof #443 shows that the following formulas are inconsistent:
% 136.14/20.27 ----------------------------------------------------------------
% 136.14/20.27 (1) op(e3, e3) = e2
% 136.14/20.27 (2) ~ (e2 = e0)
% 136.14/20.27 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.27 (4) ~ (all_52_1 = e2)
% 136.14/20.27 (5) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.14/20.27 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 136.14/20.27 op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.14/20.27 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.14/20.27 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 &
% 136.14/20.27 all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~
% 136.14/20.27 (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3,
% 136.14/20.27 e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 136.14/20.27 op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 136.14/20.27 $i(all_56_17) & $i(all_56_25))
% 136.14/20.27 (6) op(e2, e3) = all_52_1
% 136.14/20.27
% 136.14/20.27 Begin of proof
% 136.14/20.27 |
% 136.14/20.27 | BETA: splitting (5) gives:
% 136.14/20.27 |
% 136.14/20.27 | Case 1:
% 136.14/20.27 | |
% 136.14/20.27 | | (7) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.14/20.27 | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 136.14/20.27 | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.14/20.27 | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.14/20.27 | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)
% 136.14/20.27 | |
% 136.14/20.27 | | ALPHA: (7) implies:
% 136.14/20.27 | | (8) op(e3, e3) = e0
% 136.14/20.27 | |
% 136.14/20.27 | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #495.
% 136.14/20.27 | |
% 136.14/20.27 | Case 2:
% 136.14/20.27 | |
% 136.14/20.27 | | (9) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.14/20.27 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.14/20.27 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.14/20.27 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1)
% 136.14/20.27 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)
% 136.14/20.27 | |
% 136.14/20.27 | | ALPHA: (9) implies:
% 136.14/20.27 | | (10) op(e2, e3) = e2
% 136.14/20.27 | |
% 136.14/20.27 | | REF_CLOSE: (3), (4), (6), (10) are inconsistent by sub-proof #779.
% 136.14/20.27 | |
% 136.14/20.27 | End of split
% 136.14/20.27 |
% 136.14/20.27 End of proof
% 136.14/20.27
% 136.14/20.27 Sub-proof #444 shows that the following formulas are inconsistent:
% 136.14/20.27 ----------------------------------------------------------------
% 136.14/20.27 (1) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2)
% 136.14/20.27 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3,
% 136.14/20.27 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 136.14/20.27 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 136.14/20.27 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 136.14/20.27 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.14/20.27 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) =
% 136.14/20.27 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.14/20.27 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 136.14/20.27 $i(all_56_21) & $i(all_56_29))
% 136.14/20.27 (2) op(e3, e3) = e2
% 136.14/20.27 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.27 (4) ~ (e2 = e1)
% 136.14/20.27 (5) op(e2, e2) = e2
% 136.14/20.27
% 136.14/20.27 Begin of proof
% 136.14/20.27 |
% 136.14/20.27 | BETA: splitting (1) gives:
% 136.14/20.27 |
% 136.14/20.27 | Case 1:
% 136.14/20.27 | |
% 136.14/20.27 | | (6) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 136.14/20.27 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 136.14/20.27 | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 136.14/20.27 | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 136.14/20.27 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)
% 136.14/20.27 | |
% 136.14/20.27 | | ALPHA: (6) implies:
% 136.14/20.27 | | (7) ~ (all_56_11 = e2)
% 136.14/20.27 | | (8) op(e2, e2) = all_56_11
% 136.14/20.27 | |
% 136.14/20.27 | | REF_CLOSE: (3), (5), (7), (8) are inconsistent by sub-proof #531.
% 136.14/20.27 | |
% 136.14/20.27 | Case 2:
% 136.14/20.27 | |
% 136.14/20.27 | | (9) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 136.14/20.27 | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 136.14/20.27 | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 136.14/20.27 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 136.14/20.27 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 136.14/20.27 | |
% 136.14/20.27 | | ALPHA: (9) implies:
% 136.14/20.27 | | (10) op(e3, e3) = e1
% 136.14/20.27 | |
% 136.14/20.27 | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #743.
% 136.14/20.27 | |
% 136.14/20.27 | End of split
% 136.14/20.27 |
% 136.14/20.27 End of proof
% 136.14/20.27
% 136.14/20.27 Sub-proof #445 shows that the following formulas are inconsistent:
% 136.14/20.27 ----------------------------------------------------------------
% 136.14/20.27 (1) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 136.14/20.27 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 136.14/20.27 (2) ~ (all_52_4 = e0)
% 136.14/20.27 (3) ~ (e2 = e0)
% 136.14/20.27 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.27 (5) ~ (e2 = e1)
% 136.14/20.27 (6) ~ (e3 = e0)
% 136.14/20.27 (7) ~ (e3 = e2)
% 136.14/20.27 (8) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 136.14/20.27 (9) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 136.14/20.27 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 136.14/20.27 (10) op(e2, e0) = e0
% 136.14/20.27 (11) op(e3, e2) = all_52_4
% 136.14/20.27 (12) all_57_10 = e0
% 136.14/20.27 (13) ~ (e3 = e1)
% 136.14/20.27 (14) ~ (e1 = e0)
% 136.14/20.27 (15) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 136.14/20.27 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 136.14/20.27
% 136.14/20.27 Begin of proof
% 136.14/20.27 |
% 136.14/20.27 | BETA: splitting (8) gives:
% 136.14/20.27 |
% 136.14/20.27 | Case 1:
% 136.14/20.27 | |
% 136.14/20.27 | | (16) all_57_1 = e0 & op(e3, e2) = e0
% 136.14/20.27 | |
% 136.14/20.27 | | REF_CLOSE: (2), (4), (11), (16) are inconsistent by sub-proof #693.
% 136.14/20.27 | |
% 136.14/20.27 | Case 2:
% 136.14/20.27 | |
% 136.14/20.27 | | (17) all_57_3 = e0 & op(e2, e2) = e0
% 136.14/20.27 | |
% 136.14/20.27 | | ALPHA: (17) implies:
% 136.14/20.27 | | (18) all_57_3 = e0
% 136.14/20.27 | | (19) op(e2, e2) = e0
% 136.14/20.27 | |
% 136.14/20.27 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (12), (13), (14), (15),
% 136.14/20.27 | | (18), (19) are inconsistent by sub-proof #446.
% 136.14/20.27 | |
% 136.14/20.27 | End of split
% 136.14/20.27 |
% 136.14/20.27 End of proof
% 136.14/20.27
% 136.14/20.27 Sub-proof #446 shows that the following formulas are inconsistent:
% 136.14/20.27 ----------------------------------------------------------------
% 136.14/20.27 (1) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 136.14/20.27 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 136.14/20.27 (2) op(e2, e2) = e0
% 136.14/20.27 (3) ~ (e2 = e0)
% 136.14/20.27 (4) all_57_3 = e0
% 136.14/20.27 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.27 (6) ~ (e2 = e1)
% 136.14/20.27 (7) ~ (e3 = e0)
% 136.14/20.27 (8) ~ (e3 = e2)
% 136.14/20.27 (9) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 136.14/20.27 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 136.14/20.27 (10) op(e2, e0) = e0
% 136.14/20.27 (11) all_57_10 = e0
% 136.14/20.27 (12) ~ (e3 = e1)
% 136.14/20.27 (13) ~ (e1 = e0)
% 136.14/20.27 (14) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 136.14/20.27 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 136.14/20.27
% 136.14/20.27 Begin of proof
% 136.14/20.27 |
% 136.14/20.27 | BETA: splitting (9) gives:
% 136.14/20.27 |
% 136.14/20.27 | Case 1:
% 136.14/20.27 | |
% 136.14/20.27 | | (15) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 136.14/20.27 | | e3)
% 136.14/20.27 | |
% 136.14/20.27 | | BETA: splitting (15) gives:
% 136.14/20.27 | |
% 136.14/20.27 | | Case 1:
% 136.14/20.27 | | |
% 136.14/20.27 | | | (16) all_57_2 = e3 & op(e2, e3) = e3
% 136.14/20.27 | | |
% 136.14/20.27 | | | ALPHA: (16) implies:
% 136.14/20.27 | | | (17) all_57_2 = e3
% 136.14/20.27 | | |
% 136.14/20.27 | | | BETA: splitting (1) gives:
% 136.14/20.27 | | |
% 136.14/20.27 | | | Case 1:
% 136.14/20.27 | | | |
% 136.14/20.27 | | | | (18) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2)
% 136.14/20.27 | | | | = e2)
% 136.14/20.27 | | | |
% 136.14/20.27 | | | | BETA: splitting (18) gives:
% 136.14/20.27 | | | |
% 136.14/20.27 | | | | Case 1:
% 136.14/20.27 | | | | |
% 136.14/20.27 | | | | | (19) all_57_2 = e2 & op(e2, e3) = e2
% 136.14/20.27 | | | | |
% 136.14/20.27 | | | | | REF_CLOSE: (8), (17), (19) are inconsistent by sub-proof #454.
% 136.14/20.27 | | | | |
% 136.14/20.27 | | | | Case 2:
% 136.14/20.27 | | | | |
% 136.14/20.27 | | | | | (20) all_57_3 = e2 & op(e2, e2) = e2
% 136.14/20.27 | | | | |
% 136.14/20.27 | | | | | ALPHA: (20) implies:
% 136.14/20.27 | | | | | (21) all_57_3 = e2
% 136.14/20.27 | | | | |
% 136.14/20.27 | | | | | REF_CLOSE: (3), (4), (21) are inconsistent by sub-proof #679.
% 136.14/20.27 | | | | |
% 136.14/20.27 | | | | End of split
% 136.14/20.27 | | | |
% 136.14/20.27 | | | Case 2:
% 136.14/20.27 | | | |
% 136.14/20.27 | | | | (22) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0)
% 136.14/20.27 | | | | = e2)
% 136.14/20.27 | | | |
% 136.14/20.27 | | | | BETA: splitting (22) gives:
% 136.14/20.27 | | | |
% 136.14/20.27 | | | | Case 1:
% 136.14/20.27 | | | | |
% 136.14/20.27 | | | | | (23) all_57_5 = e2 & op(e2, e1) = e2
% 136.14/20.27 | | | | |
% 136.14/20.27 | | | | | ALPHA: (23) implies:
% 136.14/20.27 | | | | | (24) all_57_5 = e2
% 136.14/20.27 | | | | |
% 136.14/20.27 | | | | | REF_CLOSE: (2), (5), (6), (10), (12), (13), (14), (17), (24) are
% 136.14/20.27 | | | | | inconsistent by sub-proof #452.
% 136.14/20.27 | | | | |
% 136.14/20.27 | | | | Case 2:
% 136.14/20.27 | | | | |
% 136.14/20.27 | | | | | (25) all_57_10 = e2 & op(e2, e0) = e2
% 136.14/20.27 | | | | |
% 136.14/20.27 | | | | | ALPHA: (25) implies:
% 136.14/20.27 | | | | | (26) op(e2, e0) = e2
% 136.14/20.27 | | | | |
% 136.14/20.27 | | | | | REF_CLOSE: (3), (5), (10), (26) are inconsistent by sub-proof #451.
% 136.14/20.27 | | | | |
% 136.14/20.27 | | | | End of split
% 136.14/20.27 | | | |
% 136.14/20.27 | | | End of split
% 136.14/20.27 | | |
% 136.14/20.27 | | Case 2:
% 136.14/20.27 | | |
% 136.14/20.27 | | | (27) all_57_3 = e3 & op(e2, e2) = e3
% 136.14/20.27 | | |
% 136.14/20.27 | | | ALPHA: (27) implies:
% 136.14/20.27 | | | (28) op(e2, e2) = e3
% 136.14/20.27 | | |
% 136.14/20.27 | | | REF_CLOSE: (2), (5), (7), (28) are inconsistent by sub-proof #641.
% 136.14/20.27 | | |
% 136.14/20.27 | | End of split
% 136.14/20.27 | |
% 136.14/20.27 | Case 2:
% 136.14/20.27 | |
% 136.14/20.27 | | (29) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 136.14/20.27 | | e3)
% 136.14/20.27 | |
% 136.14/20.27 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13), (14),
% 136.14/20.27 | | (29) are inconsistent by sub-proof #447.
% 136.14/20.27 | |
% 136.14/20.27 | End of split
% 136.14/20.27 |
% 136.14/20.27 End of proof
% 136.14/20.27
% 136.14/20.27 Sub-proof #447 shows that the following formulas are inconsistent:
% 136.14/20.27 ----------------------------------------------------------------
% 136.14/20.27 (1) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 136.14/20.27 (2) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 136.14/20.27 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 136.14/20.27 (3) ~ (e2 = e0)
% 136.14/20.27 (4) all_57_3 = e0
% 136.14/20.27 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.27 (6) ~ (e2 = e1)
% 136.14/20.27 (7) ~ (e3 = e0)
% 136.14/20.27 (8) ~ (e3 = e2)
% 136.14/20.27 (9) op(e2, e0) = e0
% 136.14/20.27 (10) all_57_10 = e0
% 136.14/20.27 (11) ~ (e3 = e1)
% 136.14/20.27 (12) ~ (e1 = e0)
% 136.14/20.27 (13) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 136.14/20.27 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 136.14/20.27
% 136.14/20.27 Begin of proof
% 136.14/20.27 |
% 136.14/20.27 | BETA: splitting (1) gives:
% 136.14/20.27 |
% 136.14/20.27 | Case 1:
% 136.14/20.27 | |
% 136.14/20.27 | | (14) all_57_5 = e3 & op(e2, e1) = e3
% 136.14/20.27 | |
% 136.14/20.27 | | ALPHA: (14) implies:
% 136.14/20.27 | | (15) all_57_5 = e3
% 136.14/20.27 | |
% 136.14/20.27 | | BETA: splitting (13) gives:
% 136.14/20.27 | |
% 136.14/20.27 | | Case 1:
% 136.14/20.27 | | |
% 136.14/20.27 | | | (16) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 136.14/20.27 | | | e1)
% 136.14/20.27 | | |
% 136.14/20.27 | | | BETA: splitting (16) gives:
% 136.14/20.27 | | |
% 136.14/20.27 | | | Case 1:
% 136.14/20.27 | | | |
% 136.14/20.27 | | | | (17) all_57_2 = e1 & op(e2, e3) = e1
% 136.14/20.27 | | | |
% 136.14/20.27 | | | | ALPHA: (17) implies:
% 136.14/20.27 | | | | (18) op(e2, e3) = e1
% 136.14/20.27 | | | |
% 136.14/20.27 | | | | BETA: splitting (2) gives:
% 136.14/20.27 | | | |
% 136.14/20.27 | | | | Case 1:
% 136.14/20.27 | | | | |
% 136.14/20.27 | | | | | (19) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2,
% 136.14/20.27 | | | | | e2) = e2)
% 136.14/20.27 | | | | |
% 136.14/20.27 | | | | | BETA: splitting (19) gives:
% 136.14/20.27 | | | | |
% 136.14/20.27 | | | | | Case 1:
% 136.14/20.27 | | | | | |
% 136.14/20.27 | | | | | | (20) all_57_2 = e2 & op(e2, e3) = e2
% 136.14/20.27 | | | | | |
% 136.14/20.27 | | | | | | ALPHA: (20) implies:
% 136.14/20.27 | | | | | | (21) op(e2, e3) = e2
% 136.14/20.27 | | | | | |
% 136.14/20.27 | | | | | | REF_CLOSE: (5), (6), (18), (21) are inconsistent by sub-proof #450.
% 136.14/20.27 | | | | | |
% 136.14/20.27 | | | | | Case 2:
% 136.14/20.27 | | | | | |
% 136.14/20.27 | | | | | | (22) all_57_3 = e2 & op(e2, e2) = e2
% 136.14/20.27 | | | | | |
% 136.14/20.27 | | | | | | ALPHA: (22) implies:
% 136.14/20.27 | | | | | | (23) all_57_3 = e2
% 136.14/20.27 | | | | | |
% 136.14/20.27 | | | | | | REF_CLOSE: (3), (4), (23) are inconsistent by sub-proof #679.
% 136.14/20.27 | | | | | |
% 136.14/20.27 | | | | | End of split
% 136.14/20.27 | | | | |
% 136.14/20.27 | | | | Case 2:
% 136.14/20.27 | | | | |
% 136.14/20.27 | | | | | (24) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2,
% 136.14/20.27 | | | | | e0) = e2)
% 136.14/20.27 | | | | |
% 136.14/20.27 | | | | | BETA: splitting (24) gives:
% 136.14/20.27 | | | | |
% 136.14/20.27 | | | | | Case 1:
% 136.14/20.27 | | | | | |
% 136.14/20.27 | | | | | | (25) all_57_5 = e2 & op(e2, e1) = e2
% 136.14/20.27 | | | | | |
% 136.14/20.27 | | | | | | ALPHA: (25) implies:
% 136.14/20.27 | | | | | | (26) all_57_5 = e2
% 136.14/20.27 | | | | | |
% 136.14/20.27 | | | | | | REF_CLOSE: (8), (15), (26) are inconsistent by sub-proof #501.
% 136.14/20.27 | | | | | |
% 136.14/20.27 | | | | | Case 2:
% 136.14/20.27 | | | | | |
% 136.14/20.27 | | | | | | (27) all_57_10 = e2 & op(e2, e0) = e2
% 136.14/20.27 | | | | | |
% 136.14/20.27 | | | | | | ALPHA: (27) implies:
% 136.14/20.27 | | | | | | (28) op(e2, e0) = e2
% 136.14/20.27 | | | | | |
% 136.14/20.27 | | | | | | REF_CLOSE: (3), (5), (9), (28) are inconsistent by sub-proof #451.
% 136.14/20.27 | | | | | |
% 136.14/20.27 | | | | | End of split
% 136.14/20.27 | | | | |
% 136.14/20.27 | | | | End of split
% 136.14/20.27 | | | |
% 136.14/20.27 | | | Case 2:
% 136.14/20.27 | | | |
% 136.14/20.27 | | | | (29) all_57_3 = e1 & op(e2, e2) = e1
% 136.14/20.27 | | | |
% 136.14/20.27 | | | | REF_CLOSE: (4), (12), (29) are inconsistent by sub-proof #449.
% 136.14/20.27 | | | |
% 136.14/20.27 | | | End of split
% 136.14/20.27 | | |
% 136.14/20.27 | | Case 2:
% 136.14/20.27 | | |
% 136.14/20.27 | | | (30) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 136.14/20.27 | | | e1)
% 136.14/20.27 | | |
% 136.14/20.27 | | | BETA: splitting (30) gives:
% 136.14/20.27 | | |
% 136.14/20.27 | | | Case 1:
% 136.14/20.27 | | | |
% 136.14/20.27 | | | | (31) all_57_5 = e1 & op(e2, e1) = e1
% 136.14/20.27 | | | |
% 136.14/20.27 | | | | REF_CLOSE: (11), (15), (31) are inconsistent by sub-proof #673.
% 136.14/20.27 | | | |
% 136.14/20.27 | | | Case 2:
% 136.14/20.27 | | | |
% 136.14/20.27 | | | | (32) all_57_10 = e1 & op(e2, e0) = e1
% 136.14/20.27 | | | |
% 136.14/20.27 | | | | ALPHA: (32) implies:
% 136.14/20.27 | | | | (33) op(e2, e0) = e1
% 136.14/20.27 | | | |
% 136.14/20.27 | | | | REF_CLOSE: (5), (9), (12), (33) are inconsistent by sub-proof #695.
% 136.14/20.27 | | | |
% 136.14/20.27 | | | End of split
% 136.14/20.27 | | |
% 136.14/20.27 | | End of split
% 136.14/20.27 | |
% 136.14/20.27 | Case 2:
% 136.14/20.27 | |
% 136.14/20.27 | | (34) all_57_10 = e3 & op(e2, e0) = e3
% 136.14/20.27 | |
% 136.14/20.27 | | ALPHA: (34) implies:
% 136.14/20.27 | | (35) all_57_10 = e3
% 136.14/20.27 | |
% 136.14/20.27 | | REF_CLOSE: (7), (10), (35) are inconsistent by sub-proof #448.
% 136.14/20.27 | |
% 136.14/20.27 | End of split
% 136.14/20.27 |
% 136.14/20.27 End of proof
% 136.14/20.27
% 136.14/20.27 Sub-proof #448 shows that the following formulas are inconsistent:
% 136.14/20.27 ----------------------------------------------------------------
% 136.14/20.27 (1) all_57_10 = e3
% 136.14/20.27 (2) all_57_10 = e0
% 136.14/20.27 (3) ~ (e3 = e0)
% 136.14/20.27
% 136.14/20.27 Begin of proof
% 136.14/20.27 |
% 136.14/20.27 | COMBINE_EQS: (1), (2) imply:
% 136.14/20.27 | (4) e3 = e0
% 136.14/20.27 |
% 136.14/20.27 | SIMP: (4) implies:
% 136.14/20.27 | (5) e3 = e0
% 136.14/20.27 |
% 136.14/20.27 | REDUCE: (3), (5) imply:
% 136.14/20.27 | (6) $false
% 136.14/20.27 |
% 136.14/20.27 | CLOSE: (6) is inconsistent.
% 136.14/20.27 |
% 136.14/20.27 End of proof
% 136.14/20.27
% 136.14/20.27 Sub-proof #449 shows that the following formulas are inconsistent:
% 136.14/20.27 ----------------------------------------------------------------
% 136.14/20.27 (1) all_57_3 = e1 & op(e2, e2) = e1
% 136.14/20.27 (2) all_57_3 = e0
% 136.14/20.27 (3) ~ (e1 = e0)
% 136.14/20.27
% 136.14/20.27 Begin of proof
% 136.14/20.27 |
% 136.14/20.27 | ALPHA: (1) implies:
% 136.14/20.27 | (4) all_57_3 = e1
% 136.14/20.27 |
% 136.14/20.27 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.27 | (5) e1 = e0
% 136.14/20.27 |
% 136.14/20.27 | REDUCE: (3), (5) imply:
% 136.14/20.27 | (6) $false
% 136.14/20.27 |
% 136.14/20.27 | CLOSE: (6) is inconsistent.
% 136.14/20.27 |
% 136.14/20.27 End of proof
% 136.14/20.27
% 136.14/20.27 Sub-proof #450 shows that the following formulas are inconsistent:
% 136.14/20.27 ----------------------------------------------------------------
% 136.14/20.27 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.27 (2) op(e2, e3) = e2
% 136.14/20.27 (3) op(e2, e3) = e1
% 136.14/20.27 (4) ~ (e2 = e1)
% 136.14/20.27
% 136.14/20.27 Begin of proof
% 136.14/20.27 |
% 136.14/20.27 | GROUND_INST: instantiating (1) with e1, e2, e3, e2, simplifying with (2), (3)
% 136.14/20.27 | gives:
% 136.14/20.27 | (5) e2 = e1
% 136.14/20.27 |
% 136.14/20.27 | REDUCE: (4), (5) imply:
% 136.14/20.27 | (6) $false
% 136.14/20.27 |
% 136.14/20.27 | CLOSE: (6) is inconsistent.
% 136.14/20.27 |
% 136.14/20.27 End of proof
% 136.14/20.27
% 136.14/20.27 Sub-proof #451 shows that the following formulas are inconsistent:
% 136.14/20.27 ----------------------------------------------------------------
% 136.14/20.27 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.27 (2) op(e2, e0) = e2
% 136.14/20.27 (3) op(e2, e0) = e0
% 136.14/20.27 (4) ~ (e2 = e0)
% 136.14/20.27
% 136.14/20.27 Begin of proof
% 136.14/20.27 |
% 136.14/20.27 | GROUND_INST: instantiating (1) with e0, e2, e0, e2, simplifying with (2), (3)
% 136.14/20.27 | gives:
% 136.14/20.27 | (5) e2 = e0
% 136.14/20.27 |
% 136.14/20.27 | REDUCE: (4), (5) imply:
% 136.14/20.27 | (6) $false
% 136.14/20.27 |
% 136.14/20.27 | CLOSE: (6) is inconsistent.
% 136.14/20.27 |
% 136.14/20.27 End of proof
% 136.14/20.27
% 136.14/20.27 Sub-proof #452 shows that the following formulas are inconsistent:
% 136.14/20.27 ----------------------------------------------------------------
% 136.14/20.27 (1) op(e2, e2) = e0
% 136.14/20.27 (2) all_57_5 = e2
% 136.14/20.27 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.27 (4) ~ (e2 = e1)
% 136.14/20.27 (5) op(e2, e0) = e0
% 136.14/20.27 (6) all_57_2 = e3
% 136.14/20.27 (7) ~ (e3 = e1)
% 136.14/20.27 (8) ~ (e1 = e0)
% 136.14/20.27 (9) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 136.14/20.27 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 136.14/20.27
% 136.14/20.27 Begin of proof
% 136.14/20.27 |
% 136.14/20.27 | BETA: splitting (9) gives:
% 136.14/20.27 |
% 136.14/20.27 | Case 1:
% 136.14/20.27 | |
% 136.14/20.27 | | (10) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 136.14/20.27 | | e1)
% 136.14/20.27 | |
% 136.14/20.27 | | BETA: splitting (10) gives:
% 136.14/20.27 | |
% 136.14/20.27 | | Case 1:
% 136.14/20.27 | | |
% 136.14/20.27 | | | (11) all_57_2 = e1 & op(e2, e3) = e1
% 136.14/20.27 | | |
% 136.14/20.27 | | | REF_CLOSE: (6), (7), (11) are inconsistent by sub-proof #453.
% 136.14/20.27 | | |
% 136.14/20.27 | | Case 2:
% 136.14/20.27 | | |
% 136.14/20.28 | | | (12) all_57_3 = e1 & op(e2, e2) = e1
% 136.14/20.28 | | |
% 136.14/20.28 | | | ALPHA: (12) implies:
% 136.14/20.28 | | | (13) op(e2, e2) = e1
% 136.14/20.28 | | |
% 136.14/20.28 | | | REF_CLOSE: (1), (3), (8), (13) are inconsistent by sub-proof #675.
% 136.14/20.28 | | |
% 136.14/20.28 | | End of split
% 136.14/20.28 | |
% 136.14/20.28 | Case 2:
% 136.14/20.28 | |
% 136.14/20.28 | | (14) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 136.14/20.28 | | e1)
% 136.14/20.28 | |
% 136.14/20.28 | | BETA: splitting (14) gives:
% 136.14/20.28 | |
% 136.14/20.28 | | Case 1:
% 136.14/20.28 | | |
% 136.14/20.28 | | | (15) all_57_5 = e1 & op(e2, e1) = e1
% 136.14/20.28 | | |
% 136.14/20.28 | | | REF_CLOSE: (2), (4), (15) are inconsistent by sub-proof #500.
% 136.14/20.28 | | |
% 136.14/20.28 | | Case 2:
% 136.14/20.28 | | |
% 136.14/20.28 | | | (16) all_57_10 = e1 & op(e2, e0) = e1
% 136.14/20.28 | | |
% 136.14/20.28 | | | ALPHA: (16) implies:
% 136.14/20.28 | | | (17) op(e2, e0) = e1
% 136.14/20.28 | | |
% 136.14/20.28 | | | REF_CLOSE: (3), (5), (8), (17) are inconsistent by sub-proof #695.
% 136.14/20.28 | | |
% 136.14/20.28 | | End of split
% 136.14/20.28 | |
% 136.14/20.28 | End of split
% 136.14/20.28 |
% 136.14/20.28 End of proof
% 136.14/20.28
% 136.14/20.28 Sub-proof #453 shows that the following formulas are inconsistent:
% 136.14/20.28 ----------------------------------------------------------------
% 136.14/20.28 (1) all_57_2 = e1 & op(e2, e3) = e1
% 136.14/20.28 (2) all_57_2 = e3
% 136.14/20.28 (3) ~ (e3 = e1)
% 136.14/20.28
% 136.14/20.28 Begin of proof
% 136.14/20.28 |
% 136.14/20.28 | ALPHA: (1) implies:
% 136.14/20.28 | (4) all_57_2 = e1
% 136.14/20.28 |
% 136.14/20.28 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.28 | (5) e3 = e1
% 136.14/20.28 |
% 136.14/20.28 | REDUCE: (3), (5) imply:
% 136.14/20.28 | (6) $false
% 136.14/20.28 |
% 136.14/20.28 | CLOSE: (6) is inconsistent.
% 136.14/20.28 |
% 136.14/20.28 End of proof
% 136.14/20.28
% 136.14/20.28 Sub-proof #454 shows that the following formulas are inconsistent:
% 136.14/20.28 ----------------------------------------------------------------
% 136.14/20.28 (1) all_57_2 = e2 & op(e2, e3) = e2
% 136.14/20.28 (2) all_57_2 = e3
% 136.14/20.28 (3) ~ (e3 = e2)
% 136.14/20.28
% 136.14/20.28 Begin of proof
% 136.14/20.28 |
% 136.14/20.28 | ALPHA: (1) implies:
% 136.14/20.28 | (4) all_57_2 = e2
% 136.14/20.28 |
% 136.14/20.28 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.28 | (5) e3 = e2
% 136.14/20.28 |
% 136.14/20.28 | REDUCE: (3), (5) imply:
% 136.14/20.28 | (6) $false
% 136.14/20.28 |
% 136.14/20.28 | CLOSE: (6) is inconsistent.
% 136.14/20.28 |
% 136.14/20.28 End of proof
% 136.14/20.28
% 136.14/20.28 Sub-proof #455 shows that the following formulas are inconsistent:
% 136.14/20.28 ----------------------------------------------------------------
% 136.14/20.28 (1) all_57_5 = e0 & op(e2, e1) = e0
% 136.14/20.28 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.28 (3) op(e2, e1) = all_52_9
% 136.14/20.28 (4) ~ (all_52_9 = e0)
% 136.14/20.28
% 136.14/20.28 Begin of proof
% 136.14/20.28 |
% 136.14/20.28 | ALPHA: (1) implies:
% 136.14/20.28 | (5) op(e2, e1) = e0
% 136.14/20.28 |
% 136.14/20.28 | GROUND_INST: instantiating (2) with all_52_9, e0, e1, e2, simplifying with
% 136.14/20.28 | (3), (5) gives:
% 136.14/20.28 | (6) all_52_9 = e0
% 136.14/20.28 |
% 136.14/20.28 | REDUCE: (4), (6) imply:
% 136.14/20.28 | (7) $false
% 136.14/20.28 |
% 136.14/20.28 | CLOSE: (7) is inconsistent.
% 136.14/20.28 |
% 136.14/20.28 End of proof
% 136.14/20.28
% 136.14/20.28 Sub-proof #456 shows that the following formulas are inconsistent:
% 136.14/20.28 ----------------------------------------------------------------
% 136.14/20.28 (1) all_57_2 = e0
% 136.14/20.28 (2) op(e2, e2) = e0
% 136.14/20.28 (3) all_57_5 = e2
% 136.14/20.28 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.28 (5) ~ (e2 = e1)
% 136.14/20.28 (6) ~ (e3 = e0)
% 136.14/20.28 (7) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 136.14/20.28 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 136.14/20.28 (8) ~ (all_52_9 = e3)
% 136.14/20.28 (9) op(e2, e1) = all_52_9
% 136.14/20.28 (10) ~ (e3 = e1)
% 136.14/20.28 (11) ~ (e1 = e0)
% 136.14/20.28 (12) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 136.14/20.28 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 136.14/20.28
% 136.14/20.28 Begin of proof
% 136.14/20.28 |
% 136.14/20.28 | BETA: splitting (7) gives:
% 136.14/20.28 |
% 136.14/20.28 | Case 1:
% 136.14/20.28 | |
% 136.14/20.28 | | (13) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 136.14/20.28 | | e3)
% 136.14/20.28 | |
% 136.14/20.28 | | REF_CLOSE: (1), (2), (4), (6), (13) are inconsistent by sub-proof #502.
% 136.14/20.28 | |
% 136.14/20.28 | Case 2:
% 136.14/20.28 | |
% 136.14/20.28 | | (14) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 136.14/20.28 | | e3)
% 136.14/20.28 | |
% 136.14/20.28 | | BETA: splitting (14) gives:
% 136.14/20.28 | |
% 136.14/20.28 | | Case 1:
% 136.14/20.28 | | |
% 136.14/20.28 | | | (15) all_57_5 = e3 & op(e2, e1) = e3
% 136.14/20.28 | | |
% 136.14/20.28 | | | REF_CLOSE: (4), (8), (9), (15) are inconsistent by sub-proof #547.
% 136.14/20.28 | | |
% 136.14/20.28 | | Case 2:
% 136.14/20.28 | | |
% 136.14/20.28 | | | (16) all_57_10 = e3 & op(e2, e0) = e3
% 136.14/20.28 | | |
% 136.14/20.28 | | | ALPHA: (16) implies:
% 136.14/20.28 | | | (17) all_57_10 = e3
% 136.14/20.28 | | |
% 136.14/20.28 | | | REF_CLOSE: (1), (2), (3), (4), (5), (10), (11), (12), (17) are
% 136.14/20.28 | | | inconsistent by sub-proof #499.
% 136.14/20.28 | | |
% 136.14/20.28 | | End of split
% 136.14/20.28 | |
% 136.14/20.28 | End of split
% 136.14/20.28 |
% 136.14/20.28 End of proof
% 136.14/20.28
% 136.14/20.28 Sub-proof #457 shows that the following formulas are inconsistent:
% 136.14/20.28 ----------------------------------------------------------------
% 136.14/20.28 (1) op(e2, e2) = e0
% 136.14/20.28 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.28 (3) ~ (e3 = e0)
% 136.14/20.28 (4) ~ (all_10_2 = e0)
% 136.14/20.28 (5) op(e3, e3) = all_10_2
% 136.14/20.28 (6) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.14/20.28 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 136.14/20.28 op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.14/20.28 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.14/20.28 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 &
% 136.14/20.28 all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~
% 136.14/20.28 (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3,
% 136.14/20.28 e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 136.14/20.28 op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 136.14/20.28 $i(all_56_17) & $i(all_56_25))
% 136.14/20.28
% 136.14/20.28 Begin of proof
% 136.14/20.28 |
% 136.14/20.28 | BETA: splitting (6) gives:
% 136.14/20.28 |
% 136.14/20.28 | Case 1:
% 136.14/20.28 | |
% 136.14/20.28 | | (7) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.14/20.28 | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 136.14/20.28 | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.14/20.28 | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.14/20.28 | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)
% 136.14/20.28 | |
% 136.14/20.28 | | ALPHA: (7) implies:
% 136.14/20.28 | | (8) op(e3, e3) = e0
% 136.14/20.28 | |
% 136.14/20.28 | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #534.
% 136.14/20.28 | |
% 136.14/20.28 | Case 2:
% 136.14/20.28 | |
% 136.14/20.28 | | (9) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.14/20.28 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.14/20.28 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.14/20.28 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1)
% 136.14/20.28 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)
% 136.14/20.28 | |
% 136.14/20.28 | | ALPHA: (9) implies:
% 136.14/20.28 | | (10) op(e2, e2) = e3
% 136.14/20.28 | |
% 136.14/20.28 | | REF_CLOSE: (1), (2), (3), (10) are inconsistent by sub-proof #641.
% 136.14/20.28 | |
% 136.14/20.28 | End of split
% 136.14/20.28 |
% 136.14/20.28 End of proof
% 136.14/20.28
% 136.14/20.28 Sub-proof #458 shows that the following formulas are inconsistent:
% 136.14/20.28 ----------------------------------------------------------------
% 136.14/20.28 (1) ~ (e2 = e0)
% 136.14/20.28 (2) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 136.14/20.28 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 136.14/20.28 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.28 (4) ~ (e2 = e1)
% 136.14/20.28 (5) ~ (e3 = e0)
% 136.14/20.28 (6) ~ (e3 = e2)
% 136.14/20.28 (7) op(e0, e1) = all_52_11
% 136.14/20.28 (8) ~ (all_52_11 = e3)
% 136.14/20.28 (9) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 136.14/20.28 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 136.14/20.28 (10) op(e0, e0) = e2
% 136.14/20.28 (11) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 136.14/20.28 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 136.14/20.28 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 136.14/20.28 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 136.14/20.28 (12) ~ (e3 = e1)
% 136.14/20.28 (13) ~ (e1 = e0)
% 136.14/20.28 (14) all_57_12 = e2
% 136.14/20.28
% 136.14/20.28 Begin of proof
% 136.14/20.28 |
% 136.14/20.28 | BETA: splitting (2) gives:
% 136.14/20.28 |
% 136.14/20.28 | Case 1:
% 136.14/20.28 | |
% 136.14/20.28 | | (15) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 136.14/20.28 | | e3)
% 136.14/20.28 | |
% 136.14/20.28 | | BETA: splitting (15) gives:
% 136.14/20.28 | |
% 136.14/20.28 | | Case 1:
% 136.14/20.28 | | |
% 136.14/20.28 | | | (16) all_57_12 = e3 & op(e0, e3) = e3
% 136.14/20.28 | | |
% 136.14/20.28 | | | ALPHA: (16) implies:
% 136.14/20.28 | | | (17) all_57_12 = e3
% 136.14/20.28 | | |
% 136.14/20.28 | | | REF_CLOSE: (6), (14), (17) are inconsistent by sub-proof #518.
% 136.14/20.28 | | |
% 136.14/20.28 | | Case 2:
% 136.14/20.28 | | |
% 136.14/20.28 | | | (18) all_57_13 = e3 & op(e0, e2) = e3
% 136.14/20.28 | | |
% 136.14/20.28 | | | ALPHA: (18) implies:
% 136.14/20.28 | | | (19) all_57_13 = e3
% 136.14/20.28 | | |
% 136.14/20.28 | | | REF_CLOSE: (1), (3), (4), (5), (9), (10), (11), (12), (13), (14), (19) are
% 136.14/20.28 | | | inconsistent by sub-proof #482.
% 136.14/20.28 | | |
% 136.14/20.28 | | End of split
% 136.14/20.28 | |
% 136.14/20.28 | Case 2:
% 136.14/20.28 | |
% 136.14/20.28 | | (20) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 136.14/20.28 | | e3)
% 136.14/20.28 | |
% 136.14/20.28 | | REF_CLOSE: (3), (6), (7), (8), (10), (20) are inconsistent by sub-proof
% 136.14/20.28 | | #459.
% 136.14/20.28 | |
% 136.14/20.28 | End of split
% 136.14/20.28 |
% 136.14/20.28 End of proof
% 136.14/20.28
% 136.14/20.28 Sub-proof #459 shows that the following formulas are inconsistent:
% 136.14/20.28 ----------------------------------------------------------------
% 136.14/20.28 (1) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 136.14/20.28 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.28 (3) ~ (e3 = e2)
% 136.14/20.28 (4) op(e0, e1) = all_52_11
% 136.14/20.28 (5) ~ (all_52_11 = e3)
% 136.14/20.28 (6) op(e0, e0) = e2
% 136.14/20.28
% 136.14/20.28 Begin of proof
% 136.14/20.28 |
% 136.14/20.28 | BETA: splitting (1) gives:
% 136.14/20.28 |
% 136.14/20.28 | Case 1:
% 136.14/20.28 | |
% 136.14/20.28 | | (7) all_57_14 = e3 & op(e0, e1) = e3
% 136.14/20.28 | |
% 136.14/20.28 | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #652.
% 136.14/20.28 | |
% 136.14/20.28 | Case 2:
% 136.14/20.28 | |
% 136.14/20.28 | | (8) all_57_15 = e3 & op(e0, e0) = e3
% 136.14/20.28 | |
% 136.14/20.28 | | ALPHA: (8) implies:
% 136.14/20.28 | | (9) op(e0, e0) = e3
% 136.14/20.28 | |
% 136.14/20.28 | | REF_CLOSE: (2), (3), (6), (9) are inconsistent by sub-proof #634.
% 136.14/20.28 | |
% 136.14/20.28 | End of split
% 136.14/20.28 |
% 136.14/20.28 End of proof
% 136.14/20.28
% 136.14/20.28 Sub-proof #460 shows that the following formulas are inconsistent:
% 136.14/20.28 ----------------------------------------------------------------
% 136.14/20.28 (1) all_57_9 = e2 & op(e3, e0) = e2
% 136.14/20.28 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.28 (3) op(e3, e0) = all_52_12
% 136.14/20.28 (4) ~ (all_52_12 = e2)
% 136.14/20.28
% 136.14/20.28 Begin of proof
% 136.14/20.28 |
% 136.14/20.28 | ALPHA: (1) implies:
% 136.14/20.28 | (5) op(e3, e0) = e2
% 136.14/20.28 |
% 136.14/20.28 | GROUND_INST: instantiating (2) with all_52_12, e2, e0, e3, simplifying with
% 136.14/20.28 | (3), (5) gives:
% 136.14/20.28 | (6) all_52_12 = e2
% 136.14/20.28 |
% 136.14/20.28 | REDUCE: (4), (6) imply:
% 136.14/20.28 | (7) $false
% 136.14/20.28 |
% 136.14/20.28 | CLOSE: (7) is inconsistent.
% 136.14/20.28 |
% 136.14/20.28 End of proof
% 136.14/20.28
% 136.14/20.28 Sub-proof #461 shows that the following formulas are inconsistent:
% 136.14/20.28 ----------------------------------------------------------------
% 136.14/20.28 (1) all_57_5 = e0 & op(e2, e1) = e0
% 136.14/20.28 (2) all_57_5 = e1
% 136.14/20.28 (3) ~ (e1 = e0)
% 136.14/20.28
% 136.14/20.28 Begin of proof
% 136.14/20.28 |
% 136.14/20.28 | ALPHA: (1) implies:
% 136.14/20.28 | (4) all_57_5 = e0
% 136.14/20.28 |
% 136.14/20.28 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.28 | (5) e1 = e0
% 136.14/20.28 |
% 136.14/20.28 | REDUCE: (3), (5) imply:
% 136.14/20.28 | (6) $false
% 136.14/20.28 |
% 136.14/20.28 | CLOSE: (6) is inconsistent.
% 136.14/20.28 |
% 136.14/20.28 End of proof
% 136.14/20.28
% 136.14/20.28 Sub-proof #462 shows that the following formulas are inconsistent:
% 136.14/20.28 ----------------------------------------------------------------
% 136.14/20.28 (1) all_57_4 = e1 & op(e3, e1) = e1
% 136.14/20.28 (2) all_57_4 = e2
% 136.14/20.28 (3) ~ (e2 = e1)
% 136.14/20.28
% 136.14/20.28 Begin of proof
% 136.14/20.28 |
% 136.14/20.28 | ALPHA: (1) implies:
% 136.14/20.28 | (4) all_57_4 = e1
% 136.14/20.28 |
% 136.14/20.28 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.28 | (5) e2 = e1
% 136.14/20.28 |
% 136.14/20.28 | REDUCE: (3), (5) imply:
% 136.14/20.28 | (6) $false
% 136.14/20.28 |
% 136.14/20.28 | CLOSE: (6) is inconsistent.
% 136.14/20.28 |
% 136.14/20.28 End of proof
% 136.14/20.28
% 136.14/20.28 Sub-proof #463 shows that the following formulas are inconsistent:
% 136.14/20.28 ----------------------------------------------------------------
% 136.14/20.28 (1) ~ (all_52_6 = e3)
% 136.14/20.28 (2) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 136.14/20.28 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 136.14/20.28 (3) ~ (e2 = e0)
% 136.14/20.28 (4) all_57_1 = e2
% 136.14/20.28 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.28 (6) ~ (e2 = e1)
% 136.14/20.28 (7) ~ (e3 = e0)
% 136.14/20.28 (8) ~ (e3 = e2)
% 136.14/20.28 (9) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 136.14/20.28 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 136.14/20.28 (10) op(e1, e2) = all_52_6
% 136.14/20.28 (11) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 136.14/20.28 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 136.14/20.28 (12) ~ (e3 = e1)
% 136.14/20.28 (13) ~ (e1 = e0)
% 136.14/20.28 (14) all_57_3 = e2
% 136.14/20.28
% 136.14/20.28 Begin of proof
% 136.14/20.28 |
% 136.14/20.28 | BETA: splitting (9) gives:
% 136.14/20.28 |
% 136.14/20.28 | Case 1:
% 136.14/20.28 | |
% 136.14/20.28 | | (15) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 136.14/20.28 | | e3)
% 136.14/20.28 | |
% 136.14/20.28 | | BETA: splitting (15) gives:
% 136.14/20.28 | |
% 136.14/20.28 | | Case 1:
% 136.14/20.28 | | |
% 136.14/20.28 | | | (16) all_57_1 = e3 & op(e3, e2) = e3
% 136.14/20.28 | | |
% 136.14/20.28 | | | REF_CLOSE: (4), (8), (16) are inconsistent by sub-proof #704.
% 136.14/20.28 | | |
% 136.14/20.28 | | Case 2:
% 136.14/20.28 | | |
% 136.14/20.28 | | | (17) all_57_3 = e3 & op(e2, e2) = e3
% 136.14/20.28 | | |
% 136.14/20.28 | | | ALPHA: (17) implies:
% 136.14/20.28 | | | (18) all_57_3 = e3
% 136.14/20.28 | | |
% 136.14/20.28 | | | REF_CLOSE: (8), (14), (18) are inconsistent by sub-proof #762.
% 136.14/20.28 | | |
% 136.14/20.28 | | End of split
% 136.14/20.28 | |
% 136.14/20.28 | Case 2:
% 136.14/20.28 | |
% 136.14/20.28 | | (19) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 136.14/20.28 | | e3)
% 136.14/20.28 | |
% 136.14/20.28 | | BETA: splitting (19) gives:
% 136.14/20.28 | |
% 136.14/20.28 | | Case 1:
% 136.14/20.28 | | |
% 136.14/20.28 | | | (20) all_57_7 = e3 & op(e1, e2) = e3
% 136.14/20.28 | | |
% 136.14/20.28 | | | ALPHA: (20) implies:
% 136.14/20.28 | | | (21) op(e1, e2) = e3
% 136.14/20.28 | | |
% 136.14/20.28 | | | REF_CLOSE: (1), (5), (10), (21) are inconsistent by sub-proof #654.
% 136.14/20.28 | | |
% 136.14/20.28 | | Case 2:
% 136.14/20.28 | | |
% 136.14/20.28 | | | (22) all_57_13 = e3 & op(e0, e2) = e3
% 136.14/20.28 | | |
% 136.14/20.28 | | | ALPHA: (22) implies:
% 136.14/20.28 | | | (23) all_57_13 = e3
% 136.14/20.28 | | |
% 136.14/20.28 | | | BETA: splitting (2) gives:
% 136.14/20.28 | | |
% 136.14/20.28 | | | Case 1:
% 136.14/20.28 | | | |
% 136.14/20.28 | | | | (24) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2)
% 136.14/20.28 | | | | = e0)
% 136.14/20.28 | | | |
% 136.14/20.28 | | | | BETA: splitting (24) gives:
% 136.14/20.28 | | | |
% 136.14/20.28 | | | | Case 1:
% 136.14/20.28 | | | | |
% 136.14/20.28 | | | | | (25) all_57_1 = e0 & op(e3, e2) = e0
% 136.14/20.28 | | | | |
% 136.14/20.28 | | | | | REF_CLOSE: (3), (4), (25) are inconsistent by sub-proof #466.
% 136.14/20.28 | | | | |
% 136.14/20.28 | | | | Case 2:
% 136.14/20.28 | | | | |
% 136.14/20.28 | | | | | (26) all_57_3 = e0 & op(e2, e2) = e0
% 136.14/20.28 | | | | |
% 136.14/20.28 | | | | | REF_CLOSE: (3), (14), (26) are inconsistent by sub-proof #627.
% 136.14/20.28 | | | | |
% 136.14/20.28 | | | | End of split
% 136.14/20.28 | | | |
% 136.14/20.28 | | | Case 2:
% 136.14/20.28 | | | |
% 136.14/20.28 | | | | (27) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2)
% 136.14/20.28 | | | | = e0)
% 136.14/20.28 | | | |
% 136.14/20.28 | | | | BETA: splitting (27) gives:
% 136.14/20.28 | | | |
% 136.14/20.28 | | | | Case 1:
% 136.14/20.28 | | | | |
% 136.14/20.28 | | | | | (28) all_57_7 = e0 & op(e1, e2) = e0
% 136.14/20.28 | | | | |
% 136.14/20.28 | | | | | ALPHA: (28) implies:
% 136.14/20.28 | | | | | (29) all_57_7 = e0
% 136.14/20.28 | | | | |
% 136.14/20.28 | | | | | BETA: splitting (11) gives:
% 136.14/20.28 | | | | |
% 136.14/20.28 | | | | | Case 1:
% 136.14/20.28 | | | | | |
% 136.14/20.28 | | | | | | (30) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2,
% 136.14/20.28 | | | | | | e2) = e1)
% 136.14/20.28 | | | | | |
% 136.14/20.28 | | | | | | BETA: splitting (30) gives:
% 136.14/20.28 | | | | | |
% 136.14/20.28 | | | | | | Case 1:
% 136.14/20.28 | | | | | | |
% 136.14/20.28 | | | | | | | (31) all_57_1 = e1 & op(e3, e2) = e1
% 136.14/20.28 | | | | | | |
% 136.14/20.28 | | | | | | | REF_CLOSE: (4), (6), (31) are inconsistent by sub-proof #465.
% 136.14/20.28 | | | | | | |
% 136.14/20.28 | | | | | | Case 2:
% 136.14/20.28 | | | | | | |
% 136.14/20.28 | | | | | | | (32) all_57_3 = e1 & op(e2, e2) = e1
% 136.14/20.28 | | | | | | |
% 136.14/20.28 | | | | | | | ALPHA: (32) implies:
% 136.14/20.28 | | | | | | | (33) all_57_3 = e1
% 136.14/20.28 | | | | | | |
% 136.14/20.28 | | | | | | | COMBINE_EQS: (14), (33) imply:
% 136.14/20.28 | | | | | | | (34) e2 = e1
% 136.14/20.28 | | | | | | |
% 136.14/20.28 | | | | | | | REDUCE: (6), (34) imply:
% 136.14/20.28 | | | | | | | (35) $false
% 136.14/20.28 | | | | | | |
% 136.14/20.28 | | | | | | | CLOSE: (35) is inconsistent.
% 136.14/20.28 | | | | | | |
% 136.14/20.28 | | | | | | End of split
% 136.14/20.28 | | | | | |
% 136.14/20.28 | | | | | Case 2:
% 136.14/20.28 | | | | | |
% 136.14/20.28 | | | | | | (36) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0,
% 136.14/20.28 | | | | | | e2) = e1)
% 136.14/20.28 | | | | | |
% 136.14/20.28 | | | | | | BETA: splitting (36) gives:
% 136.14/20.28 | | | | | |
% 136.14/20.28 | | | | | | Case 1:
% 136.14/20.28 | | | | | | |
% 136.14/20.28 | | | | | | | (37) all_57_7 = e1 & op(e1, e2) = e1
% 136.14/20.28 | | | | | | |
% 136.14/20.28 | | | | | | | ALPHA: (37) implies:
% 136.14/20.28 | | | | | | | (38) all_57_7 = e1
% 136.14/20.28 | | | | | | |
% 136.14/20.28 | | | | | | | REF_CLOSE: (13), (29), (38) are inconsistent by sub-proof #464.
% 136.14/20.28 | | | | | | |
% 136.14/20.28 | | | | | | Case 2:
% 136.14/20.28 | | | | | | |
% 136.14/20.28 | | | | | | | (39) all_57_13 = e1 & op(e0, e2) = e1
% 136.14/20.28 | | | | | | |
% 136.14/20.28 | | | | | | | REF_CLOSE: (12), (23), (39) are inconsistent by sub-proof #726.
% 136.14/20.28 | | | | | | |
% 136.14/20.28 | | | | | | End of split
% 136.14/20.28 | | | | | |
% 136.14/20.28 | | | | | End of split
% 136.14/20.28 | | | | |
% 136.14/20.28 | | | | Case 2:
% 136.14/20.28 | | | | |
% 136.14/20.28 | | | | | (40) all_57_13 = e0 & op(e0, e2) = e0
% 136.14/20.28 | | | | |
% 136.14/20.28 | | | | | ALPHA: (40) implies:
% 136.14/20.28 | | | | | (41) all_57_13 = e0
% 136.14/20.28 | | | | |
% 136.14/20.28 | | | | | COMBINE_EQS: (23), (41) imply:
% 136.14/20.28 | | | | | (42) e3 = e0
% 136.14/20.28 | | | | |
% 136.14/20.28 | | | | | REDUCE: (7), (42) imply:
% 136.14/20.28 | | | | | (43) $false
% 136.14/20.28 | | | | |
% 136.14/20.28 | | | | | CLOSE: (43) is inconsistent.
% 136.14/20.28 | | | | |
% 136.14/20.28 | | | | End of split
% 136.14/20.28 | | | |
% 136.14/20.28 | | | End of split
% 136.14/20.28 | | |
% 136.14/20.28 | | End of split
% 136.14/20.28 | |
% 136.14/20.28 | End of split
% 136.14/20.28 |
% 136.14/20.28 End of proof
% 136.14/20.28
% 136.14/20.28 Sub-proof #464 shows that the following formulas are inconsistent:
% 136.14/20.28 ----------------------------------------------------------------
% 136.14/20.28 (1) all_57_7 = e1
% 136.14/20.28 (2) all_57_7 = e0
% 136.14/20.28 (3) ~ (e1 = e0)
% 136.14/20.28
% 136.14/20.28 Begin of proof
% 136.14/20.28 |
% 136.14/20.28 | COMBINE_EQS: (1), (2) imply:
% 136.14/20.28 | (4) e1 = e0
% 136.14/20.28 |
% 136.14/20.28 | SIMP: (4) implies:
% 136.14/20.28 | (5) e1 = e0
% 136.14/20.28 |
% 136.14/20.28 | REDUCE: (3), (5) imply:
% 136.14/20.28 | (6) $false
% 136.14/20.28 |
% 136.14/20.28 | CLOSE: (6) is inconsistent.
% 136.14/20.28 |
% 136.14/20.28 End of proof
% 136.14/20.28
% 136.14/20.28 Sub-proof #465 shows that the following formulas are inconsistent:
% 136.14/20.28 ----------------------------------------------------------------
% 136.14/20.28 (1) all_57_1 = e1 & op(e3, e2) = e1
% 136.14/20.28 (2) all_57_1 = e2
% 136.14/20.28 (3) ~ (e2 = e1)
% 136.14/20.28
% 136.14/20.28 Begin of proof
% 136.14/20.28 |
% 136.14/20.28 | ALPHA: (1) implies:
% 136.14/20.28 | (4) all_57_1 = e1
% 136.14/20.28 |
% 136.14/20.28 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.28 | (5) e2 = e1
% 136.14/20.28 |
% 136.14/20.28 | REDUCE: (3), (5) imply:
% 136.14/20.28 | (6) $false
% 136.14/20.28 |
% 136.14/20.28 | CLOSE: (6) is inconsistent.
% 136.14/20.28 |
% 136.14/20.28 End of proof
% 136.14/20.28
% 136.14/20.28 Sub-proof #466 shows that the following formulas are inconsistent:
% 136.14/20.28 ----------------------------------------------------------------
% 136.14/20.28 (1) all_57_1 = e0 & op(e3, e2) = e0
% 136.14/20.28 (2) all_57_1 = e2
% 136.14/20.28 (3) ~ (e2 = e0)
% 136.14/20.28
% 136.14/20.28 Begin of proof
% 136.14/20.28 |
% 136.14/20.28 | ALPHA: (1) implies:
% 136.14/20.28 | (4) all_57_1 = e0
% 136.14/20.28 |
% 136.14/20.28 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.28 | (5) e2 = e0
% 136.14/20.28 |
% 136.14/20.28 | REDUCE: (3), (5) imply:
% 136.14/20.28 | (6) $false
% 136.14/20.28 |
% 136.14/20.28 | CLOSE: (6) is inconsistent.
% 136.14/20.28 |
% 136.14/20.28 End of proof
% 136.14/20.28
% 136.14/20.28 Sub-proof #467 shows that the following formulas are inconsistent:
% 136.14/20.28 ----------------------------------------------------------------
% 136.14/20.28 (1) all_56_31 = e2
% 136.14/20.28 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.28 (3) ~ (e2 = e1)
% 136.14/20.28 (4) ~ (e3 = e0)
% 136.14/20.28 (5) op(e1, e1) = e3
% 136.14/20.28 (6) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.14/20.28 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 136.14/20.28 op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.14/20.28 op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 136.14/20.28 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 136.14/20.28 e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 136.14/20.28 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 136.14/20.28 = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 136.14/20.28 $i(all_56_21) & $i(all_56_29))
% 136.14/20.28
% 136.14/20.28 Begin of proof
% 136.14/20.28 |
% 136.14/20.28 | BETA: splitting (6) gives:
% 136.14/20.28 |
% 136.14/20.28 | Case 1:
% 136.14/20.28 | |
% 136.14/20.28 | | (7) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15
% 136.14/20.28 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0
% 136.14/20.28 | | & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.14/20.28 | | op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)
% 136.14/20.28 | |
% 136.14/20.28 | | ALPHA: (7) implies:
% 136.14/20.28 | | (8) op(e1, e1) = e0
% 136.14/20.28 | |
% 136.14/20.28 | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #753.
% 136.14/20.28 | |
% 136.14/20.28 | Case 2:
% 136.14/20.28 | |
% 136.14/20.28 | | (9) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13
% 136.14/20.28 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 136.14/20.28 | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1,
% 136.14/20.28 | | e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 136.14/20.28 | | $i(all_56_21) & $i(all_56_29)
% 136.14/20.28 | |
% 136.14/20.28 | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #525.
% 136.14/20.28 | |
% 136.14/20.28 | End of split
% 136.14/20.28 |
% 136.14/20.28 End of proof
% 136.14/20.28
% 136.14/20.28 Sub-proof #468 shows that the following formulas are inconsistent:
% 136.14/20.28 ----------------------------------------------------------------
% 136.14/20.28 (1) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2)
% 136.14/20.28 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 136.14/20.28 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25
% 136.14/20.28 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 136.14/20.28 $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~
% 136.14/20.28 (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 136.14/20.28 (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 136.14/20.28 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 136.14/20.28 = all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.14/20.28 $i(all_56_29))
% 136.14/20.28 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.28 (3) ~ (e2 = e1)
% 136.14/20.28 (4) op(e1, e3) = e2
% 136.14/20.28 (5) ~ (all_52_9 = e2)
% 136.14/20.28 (6) op(e2, e1) = all_52_9
% 136.14/20.28 (7) op(e1, e3) = all_52_2
% 136.14/20.28
% 136.14/20.28 Begin of proof
% 136.14/20.28 |
% 136.14/20.28 | BETA: splitting (1) gives:
% 136.14/20.28 |
% 136.14/20.28 | Case 1:
% 136.14/20.28 | |
% 136.14/20.28 | | (8) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.14/20.28 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.14/20.28 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.14/20.28 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1)
% 136.14/20.28 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)
% 136.14/20.28 | |
% 136.14/20.28 | | ALPHA: (8) implies:
% 136.14/20.28 | | (9) op(e1, e3) = e1
% 136.14/20.28 | |
% 136.14/20.28 | | REF_CLOSE: (2), (3), (4), (7), (9) are inconsistent by sub-proof #517.
% 136.14/20.28 | |
% 136.14/20.28 | Case 2:
% 136.14/20.28 | |
% 136.14/20.28 | | (10) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13
% 136.14/20.28 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) =
% 136.14/20.28 | | e1 & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 136.14/20.28 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 136.14/20.28 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 136.14/20.28 | |
% 136.14/20.28 | | ALPHA: (10) implies:
% 136.14/20.28 | | (11) op(e2, e1) = e2
% 136.14/20.28 | |
% 136.14/20.28 | | REF_CLOSE: (2), (5), (6), (11) are inconsistent by sub-proof #770.
% 136.14/20.28 | |
% 136.14/20.28 | End of split
% 136.14/20.28 |
% 136.14/20.28 End of proof
% 136.14/20.28
% 136.14/20.28 Sub-proof #469 shows that the following formulas are inconsistent:
% 136.14/20.28 ----------------------------------------------------------------
% 136.14/20.28 (1) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2)
% 136.14/20.28 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3,
% 136.14/20.28 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 136.14/20.28 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 136.14/20.28 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 136.14/20.28 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.14/20.28 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) =
% 136.14/20.28 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.14/20.28 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 136.14/20.28 $i(all_56_21) & $i(all_56_29))
% 136.14/20.28 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.28 (3) op(e3, e3) = all_10_2
% 136.14/20.28 (4) ~ (all_10_2 = e2)
% 136.14/20.28 (5) op(e3, e1) = all_52_8
% 136.14/20.28 (6) ~ (all_52_8 = e3)
% 136.14/20.28
% 136.14/20.28 Begin of proof
% 136.14/20.28 |
% 136.14/20.28 | BETA: splitting (1) gives:
% 136.14/20.28 |
% 136.14/20.28 | Case 1:
% 136.14/20.28 | |
% 136.14/20.28 | | (7) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 136.14/20.28 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 136.14/20.28 | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 136.14/20.28 | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 136.14/20.28 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)
% 136.14/20.28 | |
% 136.14/20.28 | | ALPHA: (7) implies:
% 136.14/20.28 | | (8) op(e3, e3) = e2
% 136.14/20.28 | |
% 136.14/20.28 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #536.
% 136.14/20.28 | |
% 136.14/20.28 | Case 2:
% 136.14/20.28 | |
% 136.14/20.28 | | (9) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 136.14/20.28 | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 136.14/20.28 | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 136.14/20.28 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 136.14/20.28 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 136.14/20.28 | |
% 136.14/20.28 | | ALPHA: (9) implies:
% 136.14/20.28 | | (10) op(e3, e1) = e3
% 136.14/20.28 | |
% 136.14/20.28 | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #705.
% 136.14/20.28 | |
% 136.14/20.28 | End of split
% 136.14/20.28 |
% 136.14/20.28 End of proof
% 136.14/20.28
% 136.14/20.28 Sub-proof #470 shows that the following formulas are inconsistent:
% 136.14/20.28 ----------------------------------------------------------------
% 136.14/20.29 (1) all_54_13 = e1 | all_54_13 = e0
% 136.14/20.29 (2) all_54_13 = all_52_7
% 136.14/20.29 (3) ~ (all_52_7 = e1)
% 136.14/20.29 (4) ~ (all_52_7 = e0)
% 136.14/20.29
% 136.14/20.29 Begin of proof
% 136.14/20.29 |
% 136.14/20.29 | BETA: splitting (1) gives:
% 136.14/20.29 |
% 136.14/20.29 | Case 1:
% 136.14/20.29 | |
% 136.14/20.29 | | (5) all_54_13 = e1
% 136.14/20.29 | |
% 136.14/20.29 | | COMBINE_EQS: (2), (5) imply:
% 136.14/20.29 | | (6) all_52_7 = e1
% 136.14/20.29 | |
% 136.14/20.29 | | SIMP: (6) implies:
% 136.14/20.29 | | (7) all_52_7 = e1
% 136.14/20.29 | |
% 136.14/20.29 | | REDUCE: (3), (7) imply:
% 136.14/20.29 | | (8) $false
% 136.14/20.29 | |
% 136.14/20.29 | | CLOSE: (8) is inconsistent.
% 136.14/20.29 | |
% 136.14/20.29 | Case 2:
% 136.14/20.29 | |
% 136.14/20.29 | | (9) all_54_13 = e0
% 136.14/20.29 | |
% 136.14/20.29 | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #471.
% 136.14/20.29 | |
% 136.14/20.29 | End of split
% 136.14/20.29 |
% 136.14/20.29 End of proof
% 136.14/20.29
% 136.14/20.29 Sub-proof #471 shows that the following formulas are inconsistent:
% 136.14/20.29 ----------------------------------------------------------------
% 136.14/20.29 (1) all_54_13 = all_52_7
% 136.14/20.29 (2) all_54_13 = e0
% 136.14/20.29 (3) ~ (all_52_7 = e0)
% 136.14/20.29
% 136.14/20.29 Begin of proof
% 136.14/20.29 |
% 136.14/20.29 | COMBINE_EQS: (1), (2) imply:
% 136.14/20.29 | (4) all_52_7 = e0
% 136.14/20.29 |
% 136.14/20.29 | SIMP: (4) implies:
% 136.14/20.29 | (5) all_52_7 = e0
% 136.14/20.29 |
% 136.14/20.29 | REDUCE: (3), (5) imply:
% 136.14/20.29 | (6) $false
% 136.14/20.29 |
% 136.14/20.29 | CLOSE: (6) is inconsistent.
% 136.14/20.29 |
% 136.14/20.29 End of proof
% 136.14/20.29
% 136.14/20.29 Sub-proof #472 shows that the following formulas are inconsistent:
% 136.14/20.29 ----------------------------------------------------------------
% 136.14/20.29 (1) all_54_13 = all_52_7
% 136.14/20.29 (2) all_54_13 = e2
% 136.14/20.29 (3) ~ (all_52_7 = e2)
% 136.14/20.29
% 136.14/20.29 Begin of proof
% 136.14/20.29 |
% 136.14/20.29 | COMBINE_EQS: (1), (2) imply:
% 136.14/20.29 | (4) all_52_7 = e2
% 136.14/20.29 |
% 136.14/20.29 | SIMP: (4) implies:
% 136.14/20.29 | (5) all_52_7 = e2
% 136.14/20.29 |
% 136.14/20.29 | REDUCE: (3), (5) imply:
% 136.14/20.29 | (6) $false
% 136.14/20.29 |
% 136.14/20.29 | CLOSE: (6) is inconsistent.
% 136.14/20.29 |
% 136.14/20.29 End of proof
% 136.14/20.29
% 136.14/20.29 Sub-proof #473 shows that the following formulas are inconsistent:
% 136.14/20.29 ----------------------------------------------------------------
% 136.14/20.29 (1) ~ (all_52_2 = e1)
% 136.14/20.29 (2) all_54_8 = all_50_0
% 136.14/20.29 (3) ~ (all_52_2 = e0)
% 136.14/20.29 (4) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 136.14/20.29 (5) ~ (all_50_0 = e2)
% 136.14/20.29 (6) all_54_8 = all_52_2
% 136.14/20.29
% 136.14/20.29 Begin of proof
% 136.14/20.29 |
% 136.14/20.29 | BETA: splitting (4) gives:
% 136.14/20.29 |
% 136.14/20.29 | Case 1:
% 136.14/20.29 | |
% 136.14/20.29 | | (7) all_54_8 = e2
% 136.14/20.29 | |
% 136.14/20.29 | | COMBINE_EQS: (2), (7) imply:
% 136.14/20.29 | | (8) all_50_0 = e2
% 136.14/20.29 | |
% 136.14/20.29 | | SIMP: (8) implies:
% 136.14/20.29 | | (9) all_50_0 = e2
% 136.14/20.29 | |
% 136.14/20.29 | | REDUCE: (5), (9) imply:
% 136.14/20.29 | | (10) $false
% 136.14/20.29 | |
% 136.14/20.29 | | CLOSE: (10) is inconsistent.
% 136.14/20.29 | |
% 136.14/20.29 | Case 2:
% 136.14/20.29 | |
% 136.14/20.29 | | (11) all_54_8 = e1 | all_54_8 = e0
% 136.14/20.29 | |
% 136.14/20.29 | | REF_CLOSE: (1), (3), (6), (11) are inconsistent by sub-proof #474.
% 136.14/20.29 | |
% 136.14/20.29 | End of split
% 136.14/20.29 |
% 136.14/20.29 End of proof
% 136.14/20.29
% 136.14/20.29 Sub-proof #474 shows that the following formulas are inconsistent:
% 136.14/20.29 ----------------------------------------------------------------
% 136.14/20.29 (1) all_54_8 = e1 | all_54_8 = e0
% 136.14/20.29 (2) all_54_8 = all_52_2
% 136.14/20.29 (3) ~ (all_52_2 = e1)
% 136.14/20.29 (4) ~ (all_52_2 = e0)
% 136.14/20.29
% 136.14/20.29 Begin of proof
% 136.14/20.29 |
% 136.14/20.29 | BETA: splitting (1) gives:
% 136.14/20.29 |
% 136.14/20.29 | Case 1:
% 136.14/20.29 | |
% 136.14/20.29 | | (5) all_54_8 = e1
% 136.14/20.29 | |
% 136.14/20.29 | | COMBINE_EQS: (2), (5) imply:
% 136.14/20.29 | | (6) all_52_2 = e1
% 136.14/20.29 | |
% 136.14/20.29 | | SIMP: (6) implies:
% 136.14/20.29 | | (7) all_52_2 = e1
% 136.14/20.29 | |
% 136.14/20.29 | | REDUCE: (3), (7) imply:
% 136.14/20.29 | | (8) $false
% 136.14/20.29 | |
% 136.14/20.29 | | CLOSE: (8) is inconsistent.
% 136.14/20.29 | |
% 136.14/20.29 | Case 2:
% 136.14/20.29 | |
% 136.14/20.29 | | (9) all_54_8 = e0
% 136.14/20.29 | |
% 136.14/20.29 | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #475.
% 136.14/20.29 | |
% 136.14/20.29 | End of split
% 136.14/20.29 |
% 136.14/20.29 End of proof
% 136.14/20.29
% 136.14/20.29 Sub-proof #475 shows that the following formulas are inconsistent:
% 136.14/20.29 ----------------------------------------------------------------
% 136.14/20.29 (1) all_54_8 = all_52_2
% 136.14/20.29 (2) all_54_8 = e0
% 136.14/20.29 (3) ~ (all_52_2 = e0)
% 136.14/20.29
% 136.14/20.29 Begin of proof
% 136.14/20.29 |
% 136.14/20.29 | COMBINE_EQS: (1), (2) imply:
% 136.14/20.29 | (4) all_52_2 = e0
% 136.14/20.29 |
% 136.14/20.29 | SIMP: (4) implies:
% 136.14/20.29 | (5) all_52_2 = e0
% 136.14/20.29 |
% 136.14/20.29 | REDUCE: (3), (5) imply:
% 136.14/20.29 | (6) $false
% 136.14/20.29 |
% 136.14/20.29 | CLOSE: (6) is inconsistent.
% 136.14/20.29 |
% 136.14/20.29 End of proof
% 136.14/20.29
% 136.14/20.29 Sub-proof #476 shows that the following formulas are inconsistent:
% 136.14/20.29 ----------------------------------------------------------------
% 136.14/20.29 (1) op(e1, e1) = all_6_2
% 136.14/20.29 (2) ~ (all_6_2 = e3)
% 136.14/20.29 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.29 (4) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 136.14/20.29 (5) all_54_2 = all_52_8
% 136.14/20.29 (6) all_54_10 = all_6_2
% 136.14/20.29 (7) op(e1, e1) = e0
% 136.14/20.29 (8) ~ (all_6_2 = e2)
% 136.14/20.29 (9) ~ (all_52_8 = all_6_2)
% 136.14/20.29 (10) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 136.14/20.29 (11) ~ (all_52_8 = e2)
% 136.14/20.29 (12) ~ (all_52_8 = e1)
% 136.14/20.29
% 136.14/20.29 Begin of proof
% 136.14/20.29 |
% 136.14/20.29 | BETA: splitting (4) gives:
% 136.14/20.29 |
% 136.14/20.29 | Case 1:
% 136.14/20.29 | |
% 136.14/20.29 | | (13) all_54_2 = e2
% 136.14/20.29 | |
% 136.14/20.29 | | COMBINE_EQS: (5), (13) imply:
% 136.14/20.29 | | (14) all_52_8 = e2
% 136.14/20.29 | |
% 136.14/20.29 | | REDUCE: (11), (14) imply:
% 136.14/20.29 | | (15) $false
% 136.14/20.29 | |
% 136.14/20.29 | | CLOSE: (15) is inconsistent.
% 136.14/20.29 | |
% 136.14/20.29 | Case 2:
% 136.14/20.29 | |
% 136.14/20.29 | | (16) all_54_2 = e1 | all_54_2 = e0
% 136.14/20.29 | |
% 136.14/20.29 | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (12), (16) are
% 136.14/20.29 | | inconsistent by sub-proof #477.
% 136.14/20.29 | |
% 136.14/20.29 | End of split
% 136.14/20.29 |
% 136.14/20.29 End of proof
% 136.14/20.29
% 136.14/20.29 Sub-proof #477 shows that the following formulas are inconsistent:
% 136.14/20.29 ----------------------------------------------------------------
% 136.14/20.29 (1) op(e1, e1) = all_6_2
% 136.14/20.29 (2) ~ (all_6_2 = e3)
% 136.14/20.29 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.29 (4) all_54_2 = all_52_8
% 136.14/20.29 (5) all_54_10 = all_6_2
% 136.14/20.29 (6) op(e1, e1) = e0
% 136.14/20.29 (7) ~ (all_6_2 = e2)
% 136.14/20.29 (8) ~ (all_52_8 = all_6_2)
% 136.14/20.29 (9) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 136.14/20.29 (10) ~ (all_52_8 = e1)
% 136.14/20.29 (11) all_54_2 = e1 | all_54_2 = e0
% 136.14/20.29
% 136.14/20.29 Begin of proof
% 136.14/20.29 |
% 136.14/20.29 | BETA: splitting (11) gives:
% 136.14/20.29 |
% 136.14/20.29 | Case 1:
% 136.14/20.29 | |
% 136.14/20.29 | | (12) all_54_2 = e1
% 136.14/20.29 | |
% 136.14/20.29 | | COMBINE_EQS: (4), (12) imply:
% 136.14/20.29 | | (13) all_52_8 = e1
% 136.14/20.29 | |
% 136.14/20.29 | | REDUCE: (10), (13) imply:
% 136.14/20.29 | | (14) $false
% 136.14/20.29 | |
% 136.14/20.29 | | CLOSE: (14) is inconsistent.
% 136.14/20.29 | |
% 136.14/20.29 | Case 2:
% 136.14/20.29 | |
% 136.14/20.29 | | (15) all_54_2 = e0
% 136.14/20.29 | |
% 136.14/20.29 | | COMBINE_EQS: (4), (15) imply:
% 136.14/20.29 | | (16) all_52_8 = e0
% 136.14/20.29 | |
% 136.14/20.29 | | REDUCE: (8), (16) imply:
% 136.14/20.29 | | (17) ~ (all_6_2 = e0)
% 136.14/20.29 | |
% 136.14/20.29 | | SIMP: (17) implies:
% 136.14/20.29 | | (18) ~ (all_6_2 = e0)
% 136.14/20.29 | |
% 136.14/20.29 | | BETA: splitting (9) gives:
% 136.14/20.29 | |
% 136.14/20.29 | | Case 1:
% 136.14/20.29 | | |
% 136.14/20.29 | | | (19) all_54_10 = e3
% 136.14/20.29 | | |
% 136.14/20.29 | | | REF_CLOSE: (2), (5), (19) are inconsistent by sub-proof #742.
% 136.14/20.29 | | |
% 136.14/20.29 | | Case 2:
% 136.14/20.29 | | |
% 136.14/20.29 | | | (20) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 136.14/20.29 | | |
% 136.14/20.29 | | | BETA: splitting (20) gives:
% 136.14/20.29 | | |
% 136.14/20.29 | | | Case 1:
% 136.14/20.29 | | | |
% 136.14/20.29 | | | | (21) all_54_10 = e2
% 136.14/20.29 | | | |
% 136.14/20.29 | | | | REF_CLOSE: (5), (7), (21) are inconsistent by sub-proof #741.
% 136.14/20.29 | | | |
% 136.14/20.29 | | | Case 2:
% 136.14/20.29 | | | |
% 136.14/20.29 | | | | (22) all_54_10 = e1 | all_54_10 = e0
% 136.14/20.29 | | | |
% 136.14/20.29 | | | | BETA: splitting (22) gives:
% 136.14/20.29 | | | |
% 136.14/20.29 | | | | Case 1:
% 136.14/20.29 | | | | |
% 136.14/20.29 | | | | | (23) all_54_10 = e1
% 136.14/20.29 | | | | |
% 136.14/20.29 | | | | | COMBINE_EQS: (5), (23) imply:
% 136.14/20.29 | | | | | (24) all_6_2 = e1
% 136.14/20.29 | | | | |
% 136.14/20.29 | | | | | SIMP: (24) implies:
% 136.14/20.29 | | | | | (25) all_6_2 = e1
% 136.14/20.29 | | | | |
% 136.14/20.29 | | | | | REDUCE: (18), (25) imply:
% 136.14/20.29 | | | | | (26) ~ (e1 = e0)
% 136.14/20.29 | | | | |
% 136.14/20.29 | | | | | REDUCE: (1), (25) imply:
% 136.14/20.29 | | | | | (27) op(e1, e1) = e1
% 136.14/20.29 | | | | |
% 136.14/20.29 | | | | | REF_CLOSE: (3), (6), (26), (27) are inconsistent by sub-proof #721.
% 136.14/20.29 | | | | |
% 136.14/20.29 | | | | Case 2:
% 136.14/20.29 | | | | |
% 136.14/20.29 | | | | | (28) all_54_10 = e0
% 136.14/20.29 | | | | |
% 136.14/20.29 | | | | | REF_CLOSE: (5), (18), (28) are inconsistent by sub-proof #506.
% 136.14/20.29 | | | | |
% 136.14/20.29 | | | | End of split
% 136.14/20.29 | | | |
% 136.14/20.29 | | | End of split
% 136.14/20.29 | | |
% 136.14/20.29 | | End of split
% 136.14/20.29 | |
% 136.14/20.29 | End of split
% 136.14/20.29 |
% 136.14/20.29 End of proof
% 136.14/20.29
% 136.14/20.29 Sub-proof #478 shows that the following formulas are inconsistent:
% 136.14/20.29 ----------------------------------------------------------------
% 136.14/20.29 (1) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 136.14/20.29 (2) ~ (all_52_9 = e2)
% 136.14/20.29 (3) all_54_6 = all_52_9
% 136.14/20.29 (4) ~ (all_52_9 = e0)
% 136.14/20.29 (5) ~ (all_52_9 = e1)
% 136.14/20.29
% 136.14/20.29 Begin of proof
% 136.14/20.29 |
% 136.14/20.29 | BETA: splitting (1) gives:
% 136.14/20.29 |
% 136.14/20.29 | Case 1:
% 136.14/20.29 | |
% 136.14/20.29 | | (6) all_54_6 = e2
% 136.14/20.29 | |
% 136.14/20.29 | | COMBINE_EQS: (3), (6) imply:
% 136.14/20.29 | | (7) all_52_9 = e2
% 136.14/20.29 | |
% 136.14/20.29 | | REDUCE: (2), (7) imply:
% 136.14/20.29 | | (8) $false
% 136.14/20.29 | |
% 136.14/20.29 | | CLOSE: (8) is inconsistent.
% 136.14/20.29 | |
% 136.14/20.29 | Case 2:
% 136.14/20.29 | |
% 136.14/20.29 | | (9) all_54_6 = e1 | all_54_6 = e0
% 136.14/20.29 | |
% 136.14/20.29 | | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #479.
% 136.14/20.29 | |
% 136.14/20.29 | End of split
% 136.14/20.29 |
% 136.14/20.29 End of proof
% 136.14/20.29
% 136.14/20.29 Sub-proof #479 shows that the following formulas are inconsistent:
% 136.14/20.29 ----------------------------------------------------------------
% 136.14/20.29 (1) all_54_6 = e1 | all_54_6 = e0
% 136.14/20.29 (2) all_54_6 = all_52_9
% 136.14/20.29 (3) ~ (all_52_9 = e1)
% 136.14/20.29 (4) ~ (all_52_9 = e0)
% 136.14/20.29
% 136.14/20.29 Begin of proof
% 136.14/20.29 |
% 136.14/20.29 | BETA: splitting (1) gives:
% 136.14/20.29 |
% 136.14/20.29 | Case 1:
% 136.14/20.29 | |
% 136.14/20.29 | | (5) all_54_6 = e1
% 136.14/20.29 | |
% 136.14/20.29 | | COMBINE_EQS: (2), (5) imply:
% 136.14/20.29 | | (6) all_52_9 = e1
% 136.14/20.29 | |
% 136.14/20.29 | | SIMP: (6) implies:
% 136.14/20.29 | | (7) all_52_9 = e1
% 136.14/20.29 | |
% 136.14/20.29 | | REDUCE: (3), (7) imply:
% 136.14/20.29 | | (8) $false
% 136.14/20.29 | |
% 136.14/20.29 | | CLOSE: (8) is inconsistent.
% 136.14/20.29 | |
% 136.14/20.29 | Case 2:
% 136.14/20.29 | |
% 136.14/20.29 | | (9) all_54_6 = e0
% 136.14/20.29 | |
% 136.14/20.29 | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #480.
% 136.14/20.29 | |
% 136.14/20.29 | End of split
% 136.14/20.29 |
% 136.14/20.29 End of proof
% 136.14/20.29
% 136.14/20.29 Sub-proof #480 shows that the following formulas are inconsistent:
% 136.14/20.29 ----------------------------------------------------------------
% 136.14/20.29 (1) all_54_6 = all_52_9
% 136.14/20.29 (2) all_54_6 = e0
% 136.14/20.29 (3) ~ (all_52_9 = e0)
% 136.14/20.29
% 136.14/20.29 Begin of proof
% 136.14/20.29 |
% 136.14/20.29 | COMBINE_EQS: (1), (2) imply:
% 136.14/20.29 | (4) all_52_9 = e0
% 136.14/20.29 |
% 136.14/20.29 | SIMP: (4) implies:
% 136.14/20.29 | (5) all_52_9 = e0
% 136.14/20.29 |
% 136.14/20.29 | REDUCE: (3), (5) imply:
% 136.14/20.29 | (6) $false
% 136.14/20.29 |
% 136.14/20.29 | CLOSE: (6) is inconsistent.
% 136.14/20.29 |
% 136.14/20.29 End of proof
% 136.14/20.29
% 136.14/20.29 Sub-proof #481 shows that the following formulas are inconsistent:
% 136.14/20.29 ----------------------------------------------------------------
% 136.14/20.29 (1) all_54_4 = all_52_1
% 136.14/20.29 (2) all_54_4 = e3
% 136.14/20.29 (3) ~ (all_52_1 = e3)
% 136.14/20.29
% 136.14/20.29 Begin of proof
% 136.14/20.29 |
% 136.14/20.29 | COMBINE_EQS: (1), (2) imply:
% 136.14/20.29 | (4) all_52_1 = e3
% 136.14/20.29 |
% 136.14/20.29 | SIMP: (4) implies:
% 136.14/20.29 | (5) all_52_1 = e3
% 136.14/20.29 |
% 136.14/20.29 | REDUCE: (3), (5) imply:
% 136.14/20.29 | (6) $false
% 136.14/20.29 |
% 136.14/20.29 | CLOSE: (6) is inconsistent.
% 136.14/20.29 |
% 136.14/20.29 End of proof
% 136.14/20.29
% 136.14/20.29 Sub-proof #482 shows that the following formulas are inconsistent:
% 136.14/20.29 ----------------------------------------------------------------
% 136.14/20.29 (1) ~ (e2 = e0)
% 136.14/20.29 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.29 (3) ~ (e2 = e1)
% 136.14/20.29 (4) all_57_13 = e3
% 136.14/20.29 (5) ~ (e3 = e0)
% 136.14/20.29 (6) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 136.14/20.29 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 136.14/20.29 (7) op(e0, e0) = e2
% 136.14/20.29 (8) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 136.14/20.29 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 136.14/20.29 e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 136.14/20.29 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 136.14/20.29 (9) ~ (e3 = e1)
% 136.14/20.29 (10) ~ (e1 = e0)
% 136.14/20.29 (11) all_57_12 = e2
% 136.14/20.29
% 136.14/20.29 Begin of proof
% 136.14/20.29 |
% 136.14/20.29 | BETA: splitting (8) gives:
% 136.14/20.29 |
% 136.14/20.29 | Case 1:
% 136.14/20.29 | |
% 136.14/20.29 | | (12) all_57_15 = e0 & op(e0, e0) = e0
% 136.14/20.29 | |
% 136.14/20.29 | | ALPHA: (12) implies:
% 136.14/20.29 | | (13) op(e0, e0) = e0
% 136.14/20.29 | |
% 136.14/20.29 | | REF_CLOSE: (1), (2), (7), (13) are inconsistent by sub-proof #714.
% 136.14/20.29 | |
% 136.14/20.29 | Case 2:
% 136.14/20.29 | |
% 136.14/20.29 | | (14) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 136.14/20.29 | | e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 136.14/20.29 | | op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 136.14/20.29 | | (all_57_14 = e0 & op(e0, e1) = e0))
% 136.14/20.29 | |
% 136.14/20.29 | | ALPHA: (14) implies:
% 136.14/20.29 | | (15) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 136.14/20.29 | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 136.14/20.29 | |
% 136.14/20.29 | | BETA: splitting (6) gives:
% 136.14/20.29 | |
% 136.14/20.29 | | Case 1:
% 136.14/20.29 | | |
% 136.14/20.29 | | | (16) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2)
% 136.14/20.29 | | | = e1)
% 136.14/20.29 | | |
% 136.14/20.29 | | | BETA: splitting (16) gives:
% 136.14/20.29 | | |
% 136.14/20.29 | | | Case 1:
% 136.14/20.29 | | | |
% 136.14/20.29 | | | | (17) all_57_12 = e1 & op(e0, e3) = e1
% 136.14/20.29 | | | |
% 136.14/20.29 | | | | REF_CLOSE: (3), (11), (17) are inconsistent by sub-proof #516.
% 136.14/20.29 | | | |
% 136.14/20.29 | | | Case 2:
% 136.14/20.29 | | | |
% 136.14/20.29 | | | | (18) all_57_13 = e1 & op(e0, e2) = e1
% 136.14/20.29 | | | |
% 136.14/20.29 | | | | REF_CLOSE: (4), (9), (18) are inconsistent by sub-proof #726.
% 136.14/20.29 | | | |
% 136.14/20.29 | | | End of split
% 136.14/20.29 | | |
% 136.14/20.29 | | Case 2:
% 136.14/20.29 | | |
% 136.14/20.29 | | | (19) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0)
% 136.14/20.29 | | | = e1)
% 136.14/20.29 | | |
% 136.14/20.29 | | | BETA: splitting (19) gives:
% 136.14/20.29 | | |
% 136.14/20.29 | | | Case 1:
% 136.14/20.29 | | | |
% 136.14/20.29 | | | | (20) all_57_14 = e1 & op(e0, e1) = e1
% 136.14/20.29 | | | |
% 136.14/20.29 | | | | ALPHA: (20) implies:
% 136.14/20.29 | | | | (21) all_57_14 = e1
% 136.14/20.29 | | | |
% 136.14/20.29 | | | | BETA: splitting (15) gives:
% 136.14/20.29 | | | |
% 136.14/20.29 | | | | Case 1:
% 136.14/20.29 | | | | |
% 136.14/20.29 | | | | | (22) all_57_12 = e0 & op(e0, e3) = e0
% 136.14/20.29 | | | | |
% 136.14/20.29 | | | | | ALPHA: (22) implies:
% 136.14/20.29 | | | | | (23) all_57_12 = e0
% 136.14/20.29 | | | | |
% 136.14/20.29 | | | | | REF_CLOSE: (1), (11), (23) are inconsistent by sub-proof #682.
% 136.14/20.29 | | | | |
% 136.14/20.29 | | | | Case 2:
% 136.14/20.29 | | | | |
% 136.14/20.29 | | | | | (24) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 136.14/20.29 | | | | | e1) = e0)
% 136.14/20.29 | | | | |
% 136.14/20.29 | | | | | BETA: splitting (24) gives:
% 136.14/20.29 | | | | |
% 136.14/20.29 | | | | | Case 1:
% 136.14/20.29 | | | | | |
% 136.14/20.29 | | | | | | (25) all_57_13 = e0 & op(e0, e2) = e0
% 136.14/20.29 | | | | | |
% 136.14/20.29 | | | | | | ALPHA: (25) implies:
% 136.14/20.29 | | | | | | (26) all_57_13 = e0
% 136.14/20.29 | | | | | |
% 136.14/20.29 | | | | | | REF_CLOSE: (4), (5), (26) are inconsistent by sub-proof #484.
% 136.14/20.29 | | | | | |
% 136.14/20.29 | | | | | Case 2:
% 136.14/20.29 | | | | | |
% 136.14/20.29 | | | | | | (27) all_57_14 = e0 & op(e0, e1) = e0
% 136.14/20.29 | | | | | |
% 136.14/20.29 | | | | | | REF_CLOSE: (10), (21), (27) are inconsistent by sub-proof #483.
% 136.14/20.29 | | | | | |
% 136.14/20.29 | | | | | End of split
% 136.14/20.29 | | | | |
% 136.14/20.29 | | | | End of split
% 136.14/20.29 | | | |
% 136.14/20.29 | | | Case 2:
% 136.14/20.29 | | | |
% 136.14/20.29 | | | | (28) all_57_15 = e1 & op(e0, e0) = e1
% 136.14/20.29 | | | |
% 136.14/20.29 | | | | ALPHA: (28) implies:
% 136.14/20.29 | | | | (29) op(e0, e0) = e1
% 136.14/20.29 | | | |
% 136.14/20.29 | | | | REF_CLOSE: (2), (3), (7), (29) are inconsistent by sub-proof #636.
% 136.14/20.29 | | | |
% 136.14/20.29 | | | End of split
% 136.14/20.29 | | |
% 136.14/20.29 | | End of split
% 136.14/20.29 | |
% 136.14/20.29 | End of split
% 136.14/20.29 |
% 136.14/20.29 End of proof
% 136.14/20.29
% 136.14/20.29 Sub-proof #483 shows that the following formulas are inconsistent:
% 136.14/20.29 ----------------------------------------------------------------
% 136.14/20.29 (1) all_57_14 = e0 & op(e0, e1) = e0
% 136.14/20.29 (2) all_57_14 = e1
% 136.14/20.29 (3) ~ (e1 = e0)
% 136.14/20.29
% 136.14/20.29 Begin of proof
% 136.14/20.29 |
% 136.14/20.29 | ALPHA: (1) implies:
% 136.14/20.29 | (4) all_57_14 = e0
% 136.14/20.29 |
% 136.14/20.29 | COMBINE_EQS: (2), (4) imply:
% 136.14/20.29 | (5) e1 = e0
% 136.14/20.29 |
% 136.14/20.29 | REDUCE: (3), (5) imply:
% 136.14/20.29 | (6) $false
% 136.14/20.29 |
% 136.14/20.29 | CLOSE: (6) is inconsistent.
% 136.14/20.29 |
% 136.14/20.29 End of proof
% 136.14/20.29
% 136.14/20.29 Sub-proof #484 shows that the following formulas are inconsistent:
% 136.14/20.29 ----------------------------------------------------------------
% 136.14/20.29 (1) all_57_13 = e3
% 136.14/20.29 (2) all_57_13 = e0
% 136.14/20.29 (3) ~ (e3 = e0)
% 136.14/20.29
% 136.14/20.29 Begin of proof
% 136.14/20.29 |
% 136.14/20.29 | COMBINE_EQS: (1), (2) imply:
% 136.14/20.29 | (4) e3 = e0
% 136.14/20.29 |
% 136.14/20.29 | SIMP: (4) implies:
% 136.14/20.29 | (5) e3 = e0
% 136.14/20.29 |
% 136.14/20.29 | REDUCE: (3), (5) imply:
% 136.14/20.29 | (6) $false
% 136.14/20.29 |
% 136.14/20.29 | CLOSE: (6) is inconsistent.
% 136.14/20.29 |
% 136.14/20.29 End of proof
% 136.14/20.29
% 136.14/20.29 Sub-proof #485 shows that the following formulas are inconsistent:
% 136.14/20.29 ----------------------------------------------------------------
% 136.14/20.29 (1) op(e1, e1) = all_6_2
% 136.14/20.29 (2) all_57_6 = e0
% 136.14/20.29 (3) ~ (all_52_4 = e0)
% 136.14/20.29 (4) op(e2, e2) = e0
% 136.14/20.29 (5) ~ (e2 = e0)
% 136.14/20.29 (6) op(e3, e3) = e1
% 136.14/20.29 (7) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 136.14/20.29 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 136.14/20.29 (8) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 136.14/20.29 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 136.14/20.29 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.14/20.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.14/20.29 (10) ~ (e2 = e1)
% 136.14/20.29 (11) ~ (e3 = e0)
% 136.14/20.29 (12) ~ (all_52_2 = e1)
% 136.14/20.29 (13) ~ (e3 = e2)
% 136.14/20.29 (14) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 136.14/20.29 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 136.14/20.29 (15) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 136.14/20.29 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 136.14/20.29 (16) ~ (all_52_1 = e1)
% 136.14/20.29 (17) all_57_2 = e2
% 136.14/20.29 (18) op(e1, e1) = e0
% 136.14/20.29 (19) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 136.14/20.29 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 136.47/20.29 (20) ~ (all_52_8 = all_6_2)
% 136.47/20.29 (21) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 136.47/20.29 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 136.47/20.29 (22) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 136.47/20.29 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 136.47/20.29 (23) all_57_12 = e3
% 136.47/20.29 (24) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 136.47/20.29 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 136.47/20.29 (25) op(e1, e3) = all_52_2
% 136.47/20.29 (26) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 136.47/20.29 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 136.47/20.29 (27) op(e3, e2) = all_52_4
% 136.47/20.29 (28) ~ (all_40_0 = e3)
% 136.47/20.29 (29) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 136.47/20.29 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 136.47/20.29 (30) op(e0, e0) = e2
% 136.47/20.29 (31) op(e2, e3) = all_52_1
% 136.47/20.29 (32) op(e3, e1) = all_52_8
% 136.47/20.29 (33) ~ (e3 = e1)
% 136.47/20.29 (34) ~ (e1 = e0)
% 136.47/20.29 (35) all_57_7 = e2
% 136.47/20.29 (36) ~ (all_52_4 = e1)
% 136.47/20.29 (37) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 136.47/20.29 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 136.47/20.29 (38) op(e0, e1) = all_40_0
% 136.47/20.29 (39) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 136.47/20.29 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 136.47/20.29 (40) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 136.47/20.29 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 136.47/20.29
% 136.47/20.29 Begin of proof
% 136.47/20.29 |
% 136.47/20.29 | BETA: splitting (22) gives:
% 136.47/20.29 |
% 136.47/20.29 | Case 1:
% 136.47/20.29 | |
% 136.47/20.29 | | (41) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 136.47/20.29 | | e1)
% 136.47/20.29 | |
% 136.47/20.29 | | REF_CLOSE: (4), (9), (27), (34), (36), (41) are inconsistent by sub-proof
% 136.47/20.29 | | #564.
% 136.47/20.29 | |
% 136.47/20.29 | Case 2:
% 136.47/20.29 | |
% 136.47/20.29 | | (42) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 136.47/20.29 | | e1)
% 136.47/20.29 | |
% 136.47/20.29 | | BETA: splitting (42) gives:
% 136.47/20.29 | |
% 136.47/20.29 | | Case 1:
% 136.47/20.29 | | |
% 136.47/20.29 | | | (43) all_57_7 = e1 & op(e1, e2) = e1
% 136.47/20.29 | | |
% 136.47/20.29 | | | REF_CLOSE: (10), (35), (43) are inconsistent by sub-proof #727.
% 136.47/20.29 | | |
% 136.47/20.29 | | Case 2:
% 136.47/20.29 | | |
% 136.47/20.29 | | | (44) all_57_13 = e1 & op(e0, e2) = e1
% 136.47/20.29 | | |
% 136.47/20.29 | | | ALPHA: (44) implies:
% 136.47/20.29 | | | (45) all_57_13 = e1
% 136.47/20.29 | | |
% 136.47/20.29 | | | BETA: splitting (29) gives:
% 136.47/20.29 | | |
% 136.47/20.29 | | | Case 1:
% 136.47/20.29 | | | |
% 136.47/20.29 | | | | (46) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2)
% 136.47/20.29 | | | | = e1)
% 136.47/20.29 | | | |
% 136.47/20.29 | | | | BETA: splitting (46) gives:
% 136.47/20.29 | | | |
% 136.47/20.29 | | | | Case 1:
% 136.47/20.29 | | | | |
% 136.47/20.29 | | | | | (47) all_57_6 = e1 & op(e1, e3) = e1
% 136.47/20.29 | | | | |
% 136.47/20.29 | | | | | ALPHA: (47) implies:
% 136.47/20.29 | | | | | (48) op(e1, e3) = e1
% 136.47/20.29 | | | | |
% 136.47/20.29 | | | | | REF_CLOSE: (9), (12), (25), (48) are inconsistent by sub-proof #725.
% 136.47/20.29 | | | | |
% 136.47/20.29 | | | | Case 2:
% 136.47/20.29 | | | | |
% 136.47/20.29 | | | | | (49) all_57_7 = e1 & op(e1, e2) = e1
% 136.47/20.29 | | | | |
% 136.47/20.29 | | | | | REF_CLOSE: (10), (35), (49) are inconsistent by sub-proof #727.
% 136.47/20.29 | | | | |
% 136.47/20.29 | | | | End of split
% 136.47/20.29 | | | |
% 136.47/20.29 | | | Case 2:
% 136.47/20.29 | | | |
% 136.47/20.29 | | | | (50) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0)
% 136.47/20.29 | | | | = e1)
% 136.47/20.29 | | | |
% 136.47/20.29 | | | | BETA: splitting (50) gives:
% 136.47/20.29 | | | |
% 136.47/20.29 | | | | Case 1:
% 136.47/20.29 | | | | |
% 136.47/20.29 | | | | | (51) all_57_8 = e1 & op(e1, e1) = e1
% 136.47/20.29 | | | | |
% 136.47/20.29 | | | | | ALPHA: (51) implies:
% 136.47/20.29 | | | | | (52) op(e1, e1) = e1
% 136.47/20.29 | | | | |
% 136.47/20.29 | | | | | REF_CLOSE: (9), (18), (34), (52) are inconsistent by sub-proof #721.
% 136.47/20.29 | | | | |
% 136.47/20.29 | | | | Case 2:
% 136.47/20.29 | | | | |
% 136.47/20.29 | | | | | (53) all_57_11 = e1 & op(e1, e0) = e1
% 136.47/20.29 | | | | |
% 136.47/20.29 | | | | | ALPHA: (53) implies:
% 136.47/20.29 | | | | | (54) all_57_11 = e1
% 136.47/20.29 | | | | |
% 136.47/20.29 | | | | | BETA: splitting (14) gives:
% 136.47/20.29 | | | | |
% 136.47/20.29 | | | | | Case 1:
% 136.47/20.29 | | | | | |
% 136.47/20.29 | | | | | | (55) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2,
% 136.47/20.29 | | | | | | e2) = e3)
% 136.47/20.29 | | | | | |
% 136.47/20.29 | | | | | | BETA: splitting (55) gives:
% 136.47/20.29 | | | | | |
% 136.47/20.29 | | | | | | Case 1:
% 136.47/20.29 | | | | | | |
% 136.47/20.29 | | | | | | | (56) all_57_1 = e3 & op(e3, e2) = e3
% 136.47/20.29 | | | | | | |
% 136.47/20.29 | | | | | | | ALPHA: (56) implies:
% 136.47/20.29 | | | | | | | (57) all_57_1 = e3
% 136.47/20.29 | | | | | | |
% 136.47/20.29 | | | | | | | BETA: splitting (19) gives:
% 136.47/20.29 | | | | | | |
% 136.47/20.29 | | | | | | | Case 1:
% 136.47/20.29 | | | | | | | |
% 136.47/20.29 | | | | | | | | (58) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 &
% 136.47/20.29 | | | | | | | | op(e3, e2) = e2)
% 136.47/20.29 | | | | | | | |
% 136.47/20.29 | | | | | | | | BETA: splitting (58) gives:
% 136.47/20.29 | | | | | | | |
% 136.47/20.29 | | | | | | | | Case 1:
% 136.47/20.29 | | | | | | | | |
% 136.47/20.29 | | | | | | | | | (59) all_57_0 = e2 & op(e3, e3) = e2
% 136.47/20.29 | | | | | | | | |
% 136.47/20.29 | | | | | | | | | ALPHA: (59) implies:
% 136.47/20.29 | | | | | | | | | (60) op(e3, e3) = e2
% 136.47/20.29 | | | | | | | | |
% 136.47/20.29 | | | | | | | | | REF_CLOSE: (5), (8), (9), (10), (11), (17), (23), (24), (33),
% 136.47/20.29 | | | | | | | | | (34), (60) are inconsistent by sub-proof #489.
% 136.47/20.29 | | | | | | | | |
% 136.47/20.29 | | | | | | | | Case 2:
% 136.47/20.29 | | | | | | | | |
% 136.47/20.29 | | | | | | | | | (61) all_57_1 = e2 & op(e3, e2) = e2
% 136.47/20.29 | | | | | | | | |
% 136.47/20.29 | | | | | | | | | REF_CLOSE: (13), (57), (61) are inconsistent by sub-proof
% 136.47/20.29 | | | | | | | | | #563.
% 136.47/20.29 | | | | | | | | |
% 136.47/20.29 | | | | | | | | End of split
% 136.47/20.29 | | | | | | | |
% 136.47/20.29 | | | | | | | Case 2:
% 136.47/20.29 | | | | | | | |
% 136.47/20.29 | | | | | | | | (62) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 &
% 136.47/20.29 | | | | | | | | op(e3, e0) = e2)
% 136.47/20.29 | | | | | | | |
% 136.47/20.29 | | | | | | | | BETA: splitting (62) gives:
% 136.47/20.29 | | | | | | | |
% 136.47/20.29 | | | | | | | | Case 1:
% 136.47/20.29 | | | | | | | | |
% 136.47/20.29 | | | | | | | | | (63) all_57_4 = e2 & op(e3, e1) = e2
% 136.47/20.29 | | | | | | | | |
% 136.47/20.29 | | | | | | | | | ALPHA: (63) implies:
% 136.47/20.29 | | | | | | | | | (64) all_57_4 = e2
% 136.47/20.29 | | | | | | | | |
% 136.47/20.29 | | | | | | | | | BETA: splitting (7) gives:
% 136.47/20.29 | | | | | | | | |
% 136.47/20.29 | | | | | | | | | Case 1:
% 136.47/20.29 | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | (65) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 &
% 136.47/20.29 | | | | | | | | | | op(e3, e2) = e0)
% 136.47/20.29 | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | REF_CLOSE: (3), (6), (9), (27), (34), (65) are inconsistent
% 136.47/20.29 | | | | | | | | | | by sub-proof #692.
% 136.47/20.29 | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | Case 2:
% 136.47/20.29 | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | (66) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 &
% 136.47/20.29 | | | | | | | | | | op(e3, e0) = e0)
% 136.47/20.29 | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | BETA: splitting (66) gives:
% 136.47/20.29 | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | Case 1:
% 136.47/20.29 | | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | | (67) all_57_4 = e0 & op(e3, e1) = e0
% 136.47/20.29 | | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | | ALPHA: (67) implies:
% 136.47/20.29 | | | | | | | | | | | (68) op(e3, e1) = e0
% 136.47/20.29 | | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | | REF_CLOSE: (1), (9), (18), (20), (32), (68) are inconsistent
% 136.47/20.29 | | | | | | | | | | | by sub-proof #619.
% 136.47/20.29 | | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | Case 2:
% 136.47/20.29 | | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | | (69) all_57_9 = e0 & op(e3, e0) = e0
% 136.47/20.29 | | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | | ALPHA: (69) implies:
% 136.47/20.29 | | | | | | | | | | | (70) all_57_9 = e0
% 136.47/20.29 | | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | | BETA: splitting (21) gives:
% 136.47/20.29 | | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | | Case 1:
% 136.47/20.29 | | | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | | | (71) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 136.47/20.29 | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 136.47/20.29 | | | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | | | BETA: splitting (71) gives:
% 136.47/20.29 | | | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | | | Case 1:
% 136.47/20.29 | | | | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | | | | (72) all_57_9 = e3 & op(e3, e0) = e3
% 136.47/20.29 | | | | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | | | | REF_CLOSE: (11), (70), (72) are inconsistent by sub-proof
% 136.47/20.29 | | | | | | | | | | | | | #614.
% 136.47/20.29 | | | | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | | | Case 2:
% 136.47/20.29 | | | | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | | | | (73) all_57_10 = e3 & op(e2, e0) = e3
% 136.47/20.29 | | | | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | | | | ALPHA: (73) implies:
% 136.47/20.29 | | | | | | | | | | | | | (74) all_57_10 = e3
% 136.47/20.29 | | | | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | | | | BETA: splitting (37) gives:
% 136.47/20.29 | | | | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | | | | Case 1:
% 136.47/20.29 | | | | | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | | | | | (75) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 136.47/20.29 | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 136.47/20.29 | | | | | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | | | | | BETA: splitting (75) gives:
% 136.47/20.29 | | | | | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | | | | | Case 1:
% 136.47/20.29 | | | | | | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | | | | | | (76) all_57_4 = e3 & op(e3, e1) = e3
% 136.47/20.29 | | | | | | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | | | | | | REF_CLOSE: (13), (64), (76) are inconsistent by sub-proof
% 136.47/20.29 | | | | | | | | | | | | | | | #734.
% 136.47/20.29 | | | | | | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | | | | | Case 2:
% 136.47/20.29 | | | | | | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | | | | | | (77) all_57_5 = e3 & op(e2, e1) = e3
% 136.47/20.29 | | | | | | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | | | | | | ALPHA: (77) implies:
% 136.47/20.29 | | | | | | | | | | | | | | | (78) all_57_5 = e3
% 136.47/20.29 | | | | | | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | | | | | | BETA: splitting (26) gives:
% 136.47/20.29 | | | | | | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | | | | | | Case 1:
% 136.47/20.29 | | | | | | | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | | | | | | | (79) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 136.47/20.29 | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 136.47/20.29 | | | | | | | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 136.47/20.29 | | | | | | | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | | | | | | | Case 1:
% 136.47/20.29 | | | | | | | | | | | | | | | | |
% 136.47/20.29 | | | | | | | | | | | | | | | | | (80) all_57_6 = e3 & op(e1, e3) = e3
% 136.47/20.30 | | | | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | | | | ALPHA: (80) implies:
% 136.47/20.30 | | | | | | | | | | | | | | | | | (81) all_57_6 = e3
% 136.47/20.30 | | | | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (81) imply:
% 136.47/20.30 | | | | | | | | | | | | | | | | | (82) e3 = e0
% 136.47/20.30 | | | | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | | | | REDUCE: (11), (82) imply:
% 136.47/20.30 | | | | | | | | | | | | | | | | | (83) $false
% 136.47/20.30 | | | | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | | | | CLOSE: (83) is inconsistent.
% 136.47/20.30 | | | | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | | | Case 2:
% 136.47/20.30 | | | | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | | | | (84) all_57_7 = e3 & op(e1, e2) = e3
% 136.47/20.30 | | | | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | | | | ALPHA: (84) implies:
% 136.47/20.30 | | | | | | | | | | | | | | | | | (85) all_57_7 = e3
% 136.47/20.30 | | | | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | | | | COMBINE_EQS: (35), (85) imply:
% 136.47/20.30 | | | | | | | | | | | | | | | | | (86) e3 = e2
% 136.47/20.30 | | | | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | | | | SIMP: (86) implies:
% 136.47/20.30 | | | | | | | | | | | | | | | | | (87) e3 = e2
% 136.47/20.30 | | | | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (87) imply:
% 136.47/20.30 | | | | | | | | | | | | | | | | | (88) all_57_10 = e2
% 136.47/20.30 | | | | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (9), (10), (11), (13),
% 136.47/20.30 | | | | | | | | | | | | | | | | | (16), (19), (27), (31), (33), (34), (39), (40),
% 136.47/20.30 | | | | | | | | | | | | | | | | | (64), (78), (88) are inconsistent by sub-proof
% 136.47/20.30 | | | | | | | | | | | | | | | | | #666.
% 136.47/20.30 | | | | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | | | End of split
% 136.47/20.30 | | | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | | Case 2:
% 136.47/20.30 | | | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | | | (89) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 136.47/20.30 | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 136.47/20.30 | | | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | | | BETA: splitting (89) gives:
% 136.47/20.30 | | | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | | | Case 1:
% 136.47/20.30 | | | | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | | | | (90) all_57_8 = e3 & op(e1, e1) = e3
% 136.47/20.30 | | | | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | | | | ALPHA: (90) implies:
% 136.47/20.30 | | | | | | | | | | | | | | | | | (91) op(e1, e1) = e3
% 136.47/20.30 | | | | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (18), (91) are inconsistent by
% 136.47/20.30 | | | | | | | | | | | | | | | | | sub-proof #753.
% 136.47/20.30 | | | | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | | | Case 2:
% 136.47/20.30 | | | | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | | | | (92) all_57_11 = e3 & op(e1, e0) = e3
% 136.47/20.30 | | | | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (9), (11), (13), (15), (17), (23), (33),
% 136.47/20.30 | | | | | | | | | | | | | | | | | (54), (92) are inconsistent by sub-proof #488.
% 136.47/20.30 | | | | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | | | End of split
% 136.47/20.30 | | | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | | End of split
% 136.47/20.30 | | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | End of split
% 136.47/20.30 | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | Case 2:
% 136.47/20.30 | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | (93) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 136.47/20.30 | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 136.47/20.30 | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 136.47/20.30 | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | Case 1:
% 136.47/20.30 | | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | | (94) all_57_8 = e3 & op(e1, e1) = e3
% 136.47/20.30 | | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | | ALPHA: (94) implies:
% 136.47/20.30 | | | | | | | | | | | | | | | (95) op(e1, e1) = e3
% 136.47/20.30 | | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (18), (95) are inconsistent by
% 136.47/20.30 | | | | | | | | | | | | | | | sub-proof #753.
% 136.47/20.30 | | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | Case 2:
% 136.47/20.30 | | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | | (96) all_57_14 = e3 & op(e0, e1) = e3
% 136.47/20.30 | | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | | ALPHA: (96) implies:
% 136.47/20.30 | | | | | | | | | | | | | | | (97) op(e0, e1) = e3
% 136.47/20.30 | | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | | REF_CLOSE: (9), (28), (38), (97) are inconsistent by
% 136.47/20.30 | | | | | | | | | | | | | | | sub-proof #529.
% 136.47/20.30 | | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | | End of split
% 136.47/20.30 | | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | End of split
% 136.47/20.30 | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | End of split
% 136.47/20.30 | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | Case 2:
% 136.47/20.30 | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | (98) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 136.47/20.30 | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 136.47/20.30 | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | BETA: splitting (98) gives:
% 136.47/20.30 | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | Case 1:
% 136.47/20.30 | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | (99) all_57_11 = e3 & op(e1, e0) = e3
% 136.47/20.30 | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | REF_CLOSE: (2), (6), (9), (11), (13), (15), (17), (23), (33),
% 136.47/20.30 | | | | | | | | | | | | | (54), (99) are inconsistent by sub-proof #488.
% 136.47/20.30 | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | Case 2:
% 136.47/20.30 | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | (100) all_57_15 = e3 & op(e0, e0) = e3
% 136.47/20.30 | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | ALPHA: (100) implies:
% 136.47/20.30 | | | | | | | | | | | | | (101) op(e0, e0) = e3
% 136.47/20.30 | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | | REF_CLOSE: (9), (13), (30), (101) are inconsistent by
% 136.47/20.30 | | | | | | | | | | | | | sub-proof #634.
% 136.47/20.30 | | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | | End of split
% 136.47/20.30 | | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | | End of split
% 136.47/20.30 | | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | | End of split
% 136.47/20.30 | | | | | | | | | |
% 136.47/20.30 | | | | | | | | | End of split
% 136.47/20.30 | | | | | | | | |
% 136.47/20.30 | | | | | | | | Case 2:
% 136.47/20.30 | | | | | | | | |
% 136.47/20.30 | | | | | | | | | (102) all_57_9 = e2 & op(e3, e0) = e2
% 136.47/20.30 | | | | | | | | |
% 136.47/20.30 | | | | | | | | | ALPHA: (102) implies:
% 136.47/20.30 | | | | | | | | | (103) all_57_9 = e2
% 136.47/20.30 | | | | | | | | |
% 136.47/20.30 | | | | | | | | | REF_CLOSE: (1), (3), (5), (6), (7), (9), (18), (20), (27),
% 136.47/20.30 | | | | | | | | | (32), (34), (103) are inconsistent by sub-proof
% 136.47/20.30 | | | | | | | | | #487.
% 136.47/20.30 | | | | | | | | |
% 136.47/20.30 | | | | | | | | End of split
% 136.47/20.30 | | | | | | | |
% 136.47/20.30 | | | | | | | End of split
% 136.47/20.30 | | | | | | |
% 136.47/20.30 | | | | | | Case 2:
% 136.47/20.30 | | | | | | |
% 136.47/20.30 | | | | | | | (104) all_57_3 = e3 & op(e2, e2) = e3
% 136.47/20.30 | | | | | | |
% 136.47/20.30 | | | | | | | ALPHA: (104) implies:
% 136.47/20.30 | | | | | | | (105) op(e2, e2) = e3
% 136.47/20.30 | | | | | | |
% 136.47/20.30 | | | | | | | REF_CLOSE: (4), (9), (11), (105) are inconsistent by sub-proof
% 136.47/20.30 | | | | | | | #641.
% 136.47/20.30 | | | | | | |
% 136.47/20.30 | | | | | | End of split
% 136.47/20.30 | | | | | |
% 136.47/20.30 | | | | | Case 2:
% 136.47/20.30 | | | | | |
% 136.47/20.30 | | | | | | (106) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 &
% 136.47/20.30 | | | | | | op(e0, e2) = e3)
% 136.47/20.30 | | | | | |
% 136.47/20.30 | | | | | | BETA: splitting (106) gives:
% 136.47/20.30 | | | | | |
% 136.47/20.30 | | | | | | Case 1:
% 136.47/20.30 | | | | | | |
% 136.47/20.30 | | | | | | | (107) all_57_7 = e3 & op(e1, e2) = e3
% 136.47/20.30 | | | | | | |
% 136.47/20.30 | | | | | | | ALPHA: (107) implies:
% 136.47/20.30 | | | | | | | (108) all_57_7 = e3
% 136.47/20.30 | | | | | | |
% 136.47/20.30 | | | | | | | REF_CLOSE: (13), (35), (108) are inconsistent by sub-proof #486.
% 136.47/20.30 | | | | | | |
% 136.47/20.30 | | | | | | Case 2:
% 136.47/20.30 | | | | | | |
% 136.47/20.30 | | | | | | | (109) all_57_13 = e3 & op(e0, e2) = e3
% 136.47/20.30 | | | | | | |
% 136.47/20.30 | | | | | | | ALPHA: (109) implies:
% 136.47/20.30 | | | | | | | (110) all_57_13 = e3
% 136.47/20.30 | | | | | | |
% 136.47/20.30 | | | | | | | COMBINE_EQS: (45), (110) imply:
% 136.47/20.30 | | | | | | | (111) e3 = e1
% 136.47/20.30 | | | | | | |
% 136.47/20.30 | | | | | | | SIMP: (111) implies:
% 136.47/20.30 | | | | | | | (112) e3 = e1
% 136.47/20.30 | | | | | | |
% 136.47/20.30 | | | | | | | COMBINE_EQS: (23), (112) imply:
% 136.47/20.30 | | | | | | | (113) all_57_12 = e1
% 136.47/20.30 | | | | | | |
% 136.47/20.30 | | | | | | | REF_CLOSE: (2), (6), (9), (11), (13), (15), (17), (33), (113) are
% 136.47/20.30 | | | | | | | inconsistent by sub-proof #587.
% 136.47/20.30 | | | | | | |
% 136.47/20.30 | | | | | | End of split
% 136.47/20.30 | | | | | |
% 136.47/20.30 | | | | | End of split
% 136.47/20.30 | | | | |
% 136.47/20.30 | | | | End of split
% 136.47/20.30 | | | |
% 136.47/20.30 | | | End of split
% 136.47/20.30 | | |
% 136.47/20.30 | | End of split
% 136.47/20.30 | |
% 136.47/20.30 | End of split
% 136.47/20.30 |
% 136.47/20.30 End of proof
% 136.47/20.30
% 136.47/20.30 Sub-proof #486 shows that the following formulas are inconsistent:
% 136.47/20.30 ----------------------------------------------------------------
% 136.47/20.30 (1) all_57_7 = e3
% 136.47/20.30 (2) all_57_7 = e2
% 136.47/20.30 (3) ~ (e3 = e2)
% 136.47/20.30
% 136.47/20.30 Begin of proof
% 136.47/20.30 |
% 136.47/20.30 | COMBINE_EQS: (1), (2) imply:
% 136.47/20.30 | (4) e3 = e2
% 136.47/20.30 |
% 136.47/20.30 | SIMP: (4) implies:
% 136.47/20.30 | (5) e3 = e2
% 136.47/20.30 |
% 136.47/20.30 | REDUCE: (3), (5) imply:
% 136.47/20.30 | (6) $false
% 136.47/20.30 |
% 136.47/20.30 | CLOSE: (6) is inconsistent.
% 136.47/20.30 |
% 136.47/20.30 End of proof
% 136.47/20.30
% 136.47/20.30 Sub-proof #487 shows that the following formulas are inconsistent:
% 136.47/20.30 ----------------------------------------------------------------
% 136.47/20.30 (1) op(e1, e1) = all_6_2
% 136.47/20.30 (2) ~ (all_52_4 = e0)
% 136.47/20.30 (3) ~ (e2 = e0)
% 136.47/20.30 (4) op(e3, e3) = e1
% 136.47/20.30 (5) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 136.47/20.30 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 136.47/20.30 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.30 (7) all_57_9 = e2
% 136.47/20.30 (8) op(e1, e1) = e0
% 136.47/20.30 (9) ~ (all_52_8 = all_6_2)
% 136.47/20.30 (10) op(e3, e2) = all_52_4
% 136.47/20.30 (11) op(e3, e1) = all_52_8
% 136.47/20.30 (12) ~ (e1 = e0)
% 136.47/20.30
% 136.47/20.30 Begin of proof
% 136.47/20.30 |
% 136.47/20.30 | BETA: splitting (5) gives:
% 136.47/20.30 |
% 136.47/20.30 | Case 1:
% 136.47/20.30 | |
% 136.47/20.30 | | (13) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 136.47/20.30 | | e0)
% 136.47/20.30 | |
% 136.47/20.30 | | REF_CLOSE: (2), (4), (6), (10), (12), (13) are inconsistent by sub-proof
% 136.47/20.30 | | #692.
% 136.47/20.30 | |
% 136.47/20.30 | Case 2:
% 136.47/20.30 | |
% 136.47/20.30 | | (14) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 136.47/20.30 | | e0)
% 136.47/20.30 | |
% 136.47/20.30 | | BETA: splitting (14) gives:
% 136.47/20.30 | |
% 136.47/20.30 | | Case 1:
% 136.47/20.30 | | |
% 136.47/20.30 | | | (15) all_57_4 = e0 & op(e3, e1) = e0
% 136.47/20.30 | | |
% 136.47/20.30 | | | ALPHA: (15) implies:
% 136.47/20.30 | | | (16) op(e3, e1) = e0
% 136.47/20.30 | | |
% 136.47/20.30 | | | REF_CLOSE: (1), (6), (8), (9), (11), (16) are inconsistent by sub-proof
% 136.47/20.30 | | | #619.
% 136.47/20.30 | | |
% 136.47/20.30 | | Case 2:
% 136.47/20.30 | | |
% 136.47/20.30 | | | (17) all_57_9 = e0 & op(e3, e0) = e0
% 136.47/20.30 | | |
% 136.47/20.30 | | | REF_CLOSE: (3), (7), (17) are inconsistent by sub-proof #657.
% 136.47/20.30 | | |
% 136.47/20.30 | | End of split
% 136.47/20.30 | |
% 136.47/20.30 | End of split
% 136.47/20.30 |
% 136.47/20.30 End of proof
% 136.47/20.30
% 136.47/20.30 Sub-proof #488 shows that the following formulas are inconsistent:
% 136.47/20.30 ----------------------------------------------------------------
% 136.47/20.30 (1) all_57_6 = e0
% 136.47/20.30 (2) op(e3, e3) = e1
% 136.47/20.30 (3) all_57_11 = e1
% 136.47/20.30 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.30 (5) ~ (e3 = e0)
% 136.47/20.30 (6) ~ (e3 = e2)
% 136.47/20.30 (7) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 136.47/20.30 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 136.47/20.30 (8) all_57_11 = e3 & op(e1, e0) = e3
% 136.47/20.30 (9) all_57_2 = e2
% 136.47/20.30 (10) all_57_12 = e3
% 136.47/20.30 (11) ~ (e3 = e1)
% 136.47/20.30
% 136.47/20.30 Begin of proof
% 136.47/20.30 |
% 136.47/20.30 | ALPHA: (8) implies:
% 136.47/20.30 | (12) all_57_11 = e3
% 136.47/20.30 |
% 136.47/20.30 | COMBINE_EQS: (3), (12) imply:
% 136.47/20.30 | (13) e3 = e1
% 136.47/20.30 |
% 136.47/20.30 | COMBINE_EQS: (10), (13) imply:
% 136.47/20.30 | (14) all_57_12 = e1
% 136.47/20.30 |
% 136.47/20.30 | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (11), (14) are inconsistent by
% 136.47/20.30 | sub-proof #587.
% 136.47/20.30 |
% 136.47/20.30 End of proof
% 136.47/20.30
% 136.47/20.30 Sub-proof #489 shows that the following formulas are inconsistent:
% 136.47/20.30 ----------------------------------------------------------------
% 136.47/20.30 (1) op(e3, e3) = e2
% 136.47/20.30 (2) ~ (e2 = e0)
% 136.47/20.30 (3) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 136.47/20.30 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 136.47/20.30 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.30 (5) ~ (e2 = e1)
% 136.47/20.30 (6) ~ (e3 = e0)
% 136.47/20.30 (7) all_57_2 = e2
% 136.47/20.30 (8) all_57_12 = e3
% 136.47/20.30 (9) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 136.47/20.30 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 136.47/20.30 (10) ~ (e3 = e1)
% 136.47/20.30 (11) ~ (e1 = e0)
% 136.47/20.30
% 136.47/20.30 Begin of proof
% 136.47/20.30 |
% 136.47/20.30 | BETA: splitting (3) gives:
% 136.47/20.30 |
% 136.47/20.30 | Case 1:
% 136.47/20.30 | |
% 136.47/20.30 | | (12) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 136.47/20.30 | | e1)
% 136.47/20.30 | |
% 136.47/20.30 | | REF_CLOSE: (1), (4), (5), (7), (12) are inconsistent by sub-proof #496.
% 136.47/20.30 | |
% 136.47/20.30 | Case 2:
% 136.47/20.30 | |
% 136.47/20.30 | | (13) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 136.47/20.30 | | e1)
% 136.47/20.30 | |
% 136.47/20.30 | | BETA: splitting (13) gives:
% 136.47/20.30 | |
% 136.47/20.30 | | Case 1:
% 136.47/20.30 | | |
% 136.47/20.30 | | | (14) all_57_6 = e1 & op(e1, e3) = e1
% 136.47/20.30 | | |
% 136.47/20.30 | | | ALPHA: (14) implies:
% 136.47/20.30 | | | (15) all_57_6 = e1
% 136.47/20.30 | | |
% 136.47/20.30 | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (11), (15) are inconsistent
% 136.47/20.30 | | | by sub-proof #491.
% 136.47/20.30 | | |
% 136.47/20.30 | | Case 2:
% 136.47/20.30 | | |
% 136.47/20.30 | | | (16) all_57_12 = e1 & op(e0, e3) = e1
% 136.47/20.30 | | |
% 136.47/20.30 | | | REF_CLOSE: (8), (10), (16) are inconsistent by sub-proof #490.
% 136.47/20.30 | | |
% 136.47/20.30 | | End of split
% 136.47/20.30 | |
% 136.47/20.30 | End of split
% 136.47/20.30 |
% 136.47/20.30 End of proof
% 136.47/20.30
% 136.47/20.30 Sub-proof #490 shows that the following formulas are inconsistent:
% 136.47/20.30 ----------------------------------------------------------------
% 136.47/20.30 (1) all_57_12 = e1 & op(e0, e3) = e1
% 136.47/20.30 (2) all_57_12 = e3
% 136.47/20.30 (3) ~ (e3 = e1)
% 136.47/20.30
% 136.47/20.30 Begin of proof
% 136.47/20.30 |
% 136.47/20.30 | ALPHA: (1) implies:
% 136.47/20.30 | (4) all_57_12 = e1
% 136.47/20.30 |
% 136.47/20.30 | COMBINE_EQS: (2), (4) imply:
% 136.47/20.30 | (5) e3 = e1
% 136.47/20.30 |
% 136.47/20.30 | REDUCE: (3), (5) imply:
% 136.47/20.30 | (6) $false
% 136.47/20.30 |
% 136.47/20.30 | CLOSE: (6) is inconsistent.
% 136.47/20.30 |
% 136.47/20.30 End of proof
% 136.47/20.30
% 136.47/20.30 Sub-proof #491 shows that the following formulas are inconsistent:
% 136.47/20.30 ----------------------------------------------------------------
% 136.47/20.30 (1) op(e3, e3) = e2
% 136.47/20.30 (2) all_57_6 = e1
% 136.47/20.30 (3) ~ (e2 = e0)
% 136.47/20.30 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.30 (5) ~ (e3 = e0)
% 136.47/20.30 (6) all_57_2 = e2
% 136.47/20.30 (7) all_57_12 = e3
% 136.47/20.30 (8) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 136.47/20.30 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 136.47/20.30 (9) ~ (e1 = e0)
% 136.47/20.30
% 136.47/20.30 Begin of proof
% 136.47/20.30 |
% 136.47/20.30 | BETA: splitting (8) gives:
% 136.47/20.30 |
% 136.47/20.30 | Case 1:
% 136.47/20.30 | |
% 136.47/20.30 | | (10) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 136.47/20.30 | | e0)
% 136.47/20.30 | |
% 136.47/20.30 | | BETA: splitting (10) gives:
% 136.47/20.30 | |
% 136.47/20.30 | | Case 1:
% 136.47/20.30 | | |
% 136.47/20.30 | | | (11) all_57_0 = e0 & op(e3, e3) = e0
% 136.47/20.30 | | |
% 136.47/20.30 | | | ALPHA: (11) implies:
% 136.47/20.30 | | | (12) op(e3, e3) = e0
% 136.47/20.30 | | |
% 136.47/20.30 | | | REF_CLOSE: (1), (3), (4), (12) are inconsistent by sub-proof #495.
% 136.47/20.30 | | |
% 136.47/20.30 | | Case 2:
% 136.47/20.30 | | |
% 136.47/20.30 | | | (13) all_57_2 = e0 & op(e2, e3) = e0
% 136.47/20.30 | | |
% 136.47/20.30 | | | REF_CLOSE: (3), (6), (13) are inconsistent by sub-proof #494.
% 136.47/20.30 | | |
% 136.47/20.30 | | End of split
% 136.47/20.30 | |
% 136.47/20.30 | Case 2:
% 136.47/20.30 | |
% 136.47/20.30 | | (14) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 136.47/20.30 | | e0)
% 136.47/20.30 | |
% 136.47/20.30 | | BETA: splitting (14) gives:
% 136.47/20.30 | |
% 136.47/20.30 | | Case 1:
% 136.47/20.30 | | |
% 136.47/20.30 | | | (15) all_57_6 = e0 & op(e1, e3) = e0
% 136.47/20.30 | | |
% 136.47/20.30 | | | ALPHA: (15) implies:
% 136.47/20.30 | | | (16) all_57_6 = e0
% 136.47/20.30 | | |
% 136.47/20.30 | | | REF_CLOSE: (2), (9), (16) are inconsistent by sub-proof #493.
% 136.47/20.30 | | |
% 136.47/20.30 | | Case 2:
% 136.47/20.30 | | |
% 136.47/20.30 | | | (17) all_57_12 = e0 & op(e0, e3) = e0
% 136.47/20.30 | | |
% 136.47/20.30 | | | ALPHA: (17) implies:
% 136.47/20.30 | | | (18) all_57_12 = e0
% 136.47/20.30 | | |
% 136.47/20.30 | | | REF_CLOSE: (5), (7), (18) are inconsistent by sub-proof #492.
% 136.47/20.30 | | |
% 136.47/20.30 | | End of split
% 136.47/20.30 | |
% 136.47/20.30 | End of split
% 136.47/20.30 |
% 136.47/20.30 End of proof
% 136.47/20.30
% 136.47/20.30 Sub-proof #492 shows that the following formulas are inconsistent:
% 136.47/20.30 ----------------------------------------------------------------
% 136.47/20.30 (1) all_57_12 = e3
% 136.47/20.30 (2) all_57_12 = e0
% 136.47/20.30 (3) ~ (e3 = e0)
% 136.47/20.30
% 136.47/20.30 Begin of proof
% 136.47/20.30 |
% 136.47/20.30 | COMBINE_EQS: (1), (2) imply:
% 136.47/20.30 | (4) e3 = e0
% 136.47/20.30 |
% 136.47/20.30 | SIMP: (4) implies:
% 136.47/20.30 | (5) e3 = e0
% 136.47/20.30 |
% 136.47/20.30 | REDUCE: (3), (5) imply:
% 136.47/20.30 | (6) $false
% 136.47/20.30 |
% 136.47/20.30 | CLOSE: (6) is inconsistent.
% 136.47/20.30 |
% 136.47/20.30 End of proof
% 136.47/20.30
% 136.47/20.30 Sub-proof #493 shows that the following formulas are inconsistent:
% 136.47/20.30 ----------------------------------------------------------------
% 136.47/20.30 (1) all_57_6 = e1
% 136.47/20.30 (2) all_57_6 = e0
% 136.47/20.30 (3) ~ (e1 = e0)
% 136.47/20.30
% 136.47/20.30 Begin of proof
% 136.47/20.30 |
% 136.47/20.30 | COMBINE_EQS: (1), (2) imply:
% 136.47/20.30 | (4) e1 = e0
% 136.47/20.30 |
% 136.47/20.30 | SIMP: (4) implies:
% 136.47/20.30 | (5) e1 = e0
% 136.47/20.30 |
% 136.47/20.30 | REDUCE: (3), (5) imply:
% 136.47/20.30 | (6) $false
% 136.47/20.30 |
% 136.47/20.30 | CLOSE: (6) is inconsistent.
% 136.47/20.30 |
% 136.47/20.30 End of proof
% 136.47/20.30
% 136.47/20.30 Sub-proof #494 shows that the following formulas are inconsistent:
% 136.47/20.30 ----------------------------------------------------------------
% 136.47/20.30 (1) all_57_2 = e0 & op(e2, e3) = e0
% 136.47/20.30 (2) all_57_2 = e2
% 136.47/20.30 (3) ~ (e2 = e0)
% 136.47/20.30
% 136.47/20.30 Begin of proof
% 136.47/20.30 |
% 136.47/20.30 | ALPHA: (1) implies:
% 136.47/20.30 | (4) all_57_2 = e0
% 136.47/20.30 |
% 136.47/20.30 | COMBINE_EQS: (2), (4) imply:
% 136.47/20.30 | (5) e2 = e0
% 136.47/20.30 |
% 136.47/20.30 | REDUCE: (3), (5) imply:
% 136.47/20.30 | (6) $false
% 136.47/20.30 |
% 136.47/20.30 | CLOSE: (6) is inconsistent.
% 136.47/20.30 |
% 136.47/20.30 End of proof
% 136.47/20.30
% 136.47/20.30 Sub-proof #495 shows that the following formulas are inconsistent:
% 136.47/20.30 ----------------------------------------------------------------
% 136.47/20.30 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.30 (2) op(e3, e3) = e2
% 136.47/20.30 (3) op(e3, e3) = e0
% 136.47/20.30 (4) ~ (e2 = e0)
% 136.47/20.30
% 136.47/20.30 Begin of proof
% 136.47/20.30 |
% 136.47/20.30 | GROUND_INST: instantiating (1) with e0, e2, e3, e3, simplifying with (2), (3)
% 136.47/20.30 | gives:
% 136.47/20.30 | (5) e2 = e0
% 136.47/20.30 |
% 136.47/20.30 | REDUCE: (4), (5) imply:
% 136.47/20.30 | (6) $false
% 136.47/20.30 |
% 136.47/20.30 | CLOSE: (6) is inconsistent.
% 136.47/20.30 |
% 136.47/20.30 End of proof
% 136.47/20.30
% 136.47/20.30 Sub-proof #496 shows that the following formulas are inconsistent:
% 136.47/20.30 ----------------------------------------------------------------
% 136.47/20.30 (1) op(e3, e3) = e2
% 136.47/20.30 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.30 (3) ~ (e2 = e1)
% 136.47/20.30 (4) all_57_2 = e2
% 136.47/20.30 (5) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1)
% 136.47/20.30
% 136.47/20.30 Begin of proof
% 136.47/20.30 |
% 136.47/20.30 | BETA: splitting (5) gives:
% 136.47/20.30 |
% 136.47/20.30 | Case 1:
% 136.47/20.30 | |
% 136.47/20.30 | | (6) all_57_0 = e1 & op(e3, e3) = e1
% 136.47/20.30 | |
% 136.47/20.30 | | ALPHA: (6) implies:
% 136.47/20.30 | | (7) op(e3, e3) = e1
% 136.47/20.30 | |
% 136.47/20.30 | | REF_CLOSE: (1), (2), (3), (7) are inconsistent by sub-proof #743.
% 136.47/20.30 | |
% 136.47/20.30 | Case 2:
% 136.47/20.30 | |
% 136.47/20.30 | | (8) all_57_2 = e1 & op(e2, e3) = e1
% 136.47/20.30 | |
% 136.47/20.30 | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #497.
% 136.47/20.30 | |
% 136.47/20.30 | End of split
% 136.47/20.30 |
% 136.47/20.30 End of proof
% 136.47/20.30
% 136.47/20.30 Sub-proof #497 shows that the following formulas are inconsistent:
% 136.47/20.30 ----------------------------------------------------------------
% 136.47/20.30 (1) all_57_2 = e1 & op(e2, e3) = e1
% 136.47/20.30 (2) all_57_2 = e2
% 136.47/20.30 (3) ~ (e2 = e1)
% 136.47/20.30
% 136.47/20.30 Begin of proof
% 136.47/20.30 |
% 136.47/20.30 | ALPHA: (1) implies:
% 136.47/20.30 | (4) all_57_2 = e1
% 136.47/20.30 |
% 136.47/20.30 | COMBINE_EQS: (2), (4) imply:
% 136.47/20.30 | (5) e2 = e1
% 136.47/20.30 |
% 136.47/20.30 | REDUCE: (3), (5) imply:
% 136.47/20.30 | (6) $false
% 136.47/20.30 |
% 136.47/20.30 | CLOSE: (6) is inconsistent.
% 136.47/20.30 |
% 136.47/20.30 End of proof
% 136.47/20.30
% 136.47/20.30 Sub-proof #498 shows that the following formulas are inconsistent:
% 136.47/20.30 ----------------------------------------------------------------
% 136.47/20.30 (1) all_57_2 = e0
% 136.47/20.30 (2) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 136.47/20.30 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 136.47/20.30 (3) ~ (all_52_4 = e0)
% 136.47/20.30 (4) op(e2, e2) = e0
% 136.47/20.30 (5) op(e2, e0) = all_52_13
% 136.47/20.30 (6) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 136.47/20.30 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 136.47/20.30 (7) ~ (e2 = e0)
% 136.47/20.30 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.30 (9) ~ (e2 = e1)
% 136.47/20.30 (10) ~ (e3 = e0)
% 136.47/20.30 (11) ~ (e3 = e2)
% 136.47/20.30 (12) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 136.47/20.30 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 136.47/20.30 (13) op(e0, e2) = all_52_7
% 136.47/20.30 (14) ~ (all_52_6 = e0)
% 136.47/20.30 (15) ~ (all_52_13 = e2)
% 136.47/20.30 (16) op(e1, e2) = all_52_6
% 136.47/20.30 (17) ~ (all_52_7 = e0)
% 136.47/20.30 (18) op(e3, e2) = all_52_4
% 136.47/20.30 (19) ~ (e3 = e1)
% 136.47/20.30 (20) ~ (e1 = e0)
% 136.47/20.30 (21) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 136.47/20.30 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 136.47/20.30
% 136.47/20.30 Begin of proof
% 136.47/20.30 |
% 136.47/20.30 | BETA: splitting (2) gives:
% 136.47/20.30 |
% 136.47/20.30 | Case 1:
% 136.47/20.30 | |
% 136.47/20.30 | | (22) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 136.47/20.30 | | e2)
% 136.47/20.30 | |
% 136.47/20.30 | | BETA: splitting (22) gives:
% 136.47/20.30 | |
% 136.47/20.30 | | Case 1:
% 136.47/20.30 | | |
% 136.47/20.30 | | | (23) all_57_2 = e2 & op(e2, e3) = e2
% 136.47/20.30 | | |
% 136.47/20.30 | | | REF_CLOSE: (1), (7), (23) are inconsistent by sub-proof #680.
% 136.47/20.30 | | |
% 136.47/20.30 | | Case 2:
% 136.47/20.30 | | |
% 136.47/20.30 | | | (24) all_57_3 = e2 & op(e2, e2) = e2
% 136.47/20.30 | | |
% 136.47/20.30 | | | ALPHA: (24) implies:
% 136.47/20.30 | | | (25) all_57_3 = e2
% 136.47/20.30 | | |
% 136.47/20.30 | | | REF_CLOSE: (3), (6), (7), (8), (13), (14), (16), (17), (18), (25) are
% 136.47/20.30 | | | inconsistent by sub-proof #503.
% 136.47/20.30 | | |
% 136.47/20.30 | | End of split
% 136.47/20.30 | |
% 136.47/20.30 | Case 2:
% 136.47/20.30 | |
% 136.47/20.30 | | (26) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 136.47/20.30 | | e2)
% 136.47/20.30 | |
% 136.47/20.30 | | BETA: splitting (26) gives:
% 136.47/20.30 | |
% 136.47/20.30 | | Case 1:
% 136.47/20.30 | | |
% 136.47/20.30 | | | (27) all_57_5 = e2 & op(e2, e1) = e2
% 136.47/20.30 | | |
% 136.47/20.30 | | | ALPHA: (27) implies:
% 136.47/20.30 | | | (28) all_57_5 = e2
% 136.47/20.30 | | |
% 136.47/20.30 | | | BETA: splitting (12) gives:
% 136.47/20.30 | | |
% 136.47/20.30 | | | Case 1:
% 136.47/20.30 | | | |
% 136.47/20.30 | | | | (29) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2)
% 136.47/20.30 | | | | = e3)
% 136.47/20.30 | | | |
% 136.47/20.30 | | | | REF_CLOSE: (1), (4), (8), (10), (29) are inconsistent by sub-proof #502.
% 136.47/20.30 | | | |
% 136.47/20.30 | | | Case 2:
% 136.47/20.30 | | | |
% 136.47/20.30 | | | | (30) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0)
% 136.47/20.30 | | | | = e3)
% 136.47/20.30 | | | |
% 136.47/20.30 | | | | BETA: splitting (30) gives:
% 136.47/20.30 | | | |
% 136.47/20.30 | | | | Case 1:
% 136.47/20.30 | | | | |
% 136.47/20.30 | | | | | (31) all_57_5 = e3 & op(e2, e1) = e3
% 136.47/20.30 | | | | |
% 136.47/20.30 | | | | | ALPHA: (31) implies:
% 136.47/20.30 | | | | | (32) all_57_5 = e3
% 136.47/20.30 | | | | |
% 136.47/20.30 | | | | | REF_CLOSE: (11), (28), (32) are inconsistent by sub-proof #501.
% 136.47/20.30 | | | | |
% 136.47/20.30 | | | | Case 2:
% 136.47/20.30 | | | | |
% 136.47/20.30 | | | | | (33) all_57_10 = e3 & op(e2, e0) = e3
% 136.47/20.30 | | | | |
% 136.47/20.30 | | | | | ALPHA: (33) implies:
% 136.47/20.30 | | | | | (34) all_57_10 = e3
% 136.47/20.30 | | | | |
% 136.47/20.30 | | | | | REF_CLOSE: (1), (4), (8), (9), (19), (20), (21), (28), (34) are
% 136.47/20.30 | | | | | inconsistent by sub-proof #499.
% 136.47/20.30 | | | | |
% 136.47/20.30 | | | | End of split
% 136.47/20.30 | | | |
% 136.47/20.30 | | | End of split
% 136.47/20.30 | | |
% 136.47/20.30 | | Case 2:
% 136.47/20.30 | | |
% 136.47/20.30 | | | (35) all_57_10 = e2 & op(e2, e0) = e2
% 136.47/20.30 | | |
% 136.47/20.30 | | | ALPHA: (35) implies:
% 136.47/20.30 | | | (36) op(e2, e0) = e2
% 136.47/20.30 | | |
% 136.47/20.30 | | | REF_CLOSE: (5), (8), (15), (36) are inconsistent by sub-proof #768.
% 136.47/20.30 | | |
% 136.47/20.30 | | End of split
% 136.47/20.30 | |
% 136.47/20.30 | End of split
% 136.47/20.30 |
% 136.47/20.30 End of proof
% 136.47/20.30
% 136.47/20.30 Sub-proof #499 shows that the following formulas are inconsistent:
% 136.47/20.30 ----------------------------------------------------------------
% 136.47/20.30 (1) all_57_2 = e0
% 136.47/20.30 (2) op(e2, e2) = e0
% 136.47/20.30 (3) all_57_5 = e2
% 136.47/20.30 (4) all_57_10 = e3
% 136.47/20.30 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.30 (6) ~ (e2 = e1)
% 136.47/20.30 (7) ~ (e3 = e1)
% 136.47/20.30 (8) ~ (e1 = e0)
% 136.47/20.30 (9) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 136.47/20.30 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 136.47/20.30
% 136.47/20.30 Begin of proof
% 136.47/20.30 |
% 136.47/20.30 | BETA: splitting (9) gives:
% 136.47/20.30 |
% 136.47/20.30 | Case 1:
% 136.47/20.30 | |
% 136.47/20.30 | | (10) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 136.47/20.30 | | e1)
% 136.47/20.30 | |
% 136.47/20.30 | | BETA: splitting (10) gives:
% 136.47/20.30 | |
% 136.47/20.30 | | Case 1:
% 136.47/20.30 | | |
% 136.47/20.30 | | | (11) all_57_2 = e1 & op(e2, e3) = e1
% 136.47/20.30 | | |
% 136.47/20.30 | | | ALPHA: (11) implies:
% 136.47/20.30 | | | (12) all_57_2 = e1
% 136.47/20.30 | | |
% 136.47/20.30 | | | REF_CLOSE: (1), (8), (12) are inconsistent by sub-proof #646.
% 136.47/20.30 | | |
% 136.47/20.30 | | Case 2:
% 136.47/20.30 | | |
% 136.47/20.30 | | | (13) all_57_3 = e1 & op(e2, e2) = e1
% 136.47/20.30 | | |
% 136.47/20.30 | | | ALPHA: (13) implies:
% 136.47/20.30 | | | (14) op(e2, e2) = e1
% 136.47/20.30 | | |
% 136.47/20.30 | | | REF_CLOSE: (2), (5), (8), (14) are inconsistent by sub-proof #675.
% 136.47/20.30 | | |
% 136.47/20.30 | | End of split
% 136.47/20.30 | |
% 136.47/20.30 | Case 2:
% 136.47/20.30 | |
% 136.47/20.30 | | (15) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 136.47/20.30 | | e1)
% 136.47/20.30 | |
% 136.47/20.30 | | BETA: splitting (15) gives:
% 136.47/20.30 | |
% 136.47/20.30 | | Case 1:
% 136.47/20.30 | | |
% 136.47/20.30 | | | (16) all_57_5 = e1 & op(e2, e1) = e1
% 136.47/20.30 | | |
% 136.47/20.30 | | | REF_CLOSE: (3), (6), (16) are inconsistent by sub-proof #500.
% 136.47/20.30 | | |
% 136.47/20.30 | | Case 2:
% 136.47/20.30 | | |
% 136.47/20.30 | | | (17) all_57_10 = e1 & op(e2, e0) = e1
% 136.47/20.30 | | |
% 136.47/20.30 | | | ALPHA: (17) implies:
% 136.47/20.30 | | | (18) all_57_10 = e1
% 136.47/20.30 | | |
% 136.47/20.30 | | | COMBINE_EQS: (4), (18) imply:
% 136.47/20.30 | | | (19) e3 = e1
% 136.47/20.30 | | |
% 136.47/20.30 | | | REDUCE: (7), (19) imply:
% 136.47/20.30 | | | (20) $false
% 136.47/20.30 | | |
% 136.47/20.30 | | | CLOSE: (20) is inconsistent.
% 136.47/20.30 | | |
% 136.47/20.30 | | End of split
% 136.47/20.30 | |
% 136.47/20.30 | End of split
% 136.47/20.30 |
% 136.47/20.30 End of proof
% 136.47/20.30
% 136.47/20.30 Sub-proof #500 shows that the following formulas are inconsistent:
% 136.47/20.30 ----------------------------------------------------------------
% 136.47/20.30 (1) all_57_5 = e1 & op(e2, e1) = e1
% 136.47/20.30 (2) all_57_5 = e2
% 136.47/20.30 (3) ~ (e2 = e1)
% 136.47/20.30
% 136.47/20.30 Begin of proof
% 136.47/20.30 |
% 136.47/20.30 | ALPHA: (1) implies:
% 136.47/20.30 | (4) all_57_5 = e1
% 136.47/20.30 |
% 136.47/20.30 | COMBINE_EQS: (2), (4) imply:
% 136.47/20.30 | (5) e2 = e1
% 136.47/20.30 |
% 136.47/20.30 | REDUCE: (3), (5) imply:
% 136.47/20.30 | (6) $false
% 136.47/20.30 |
% 136.47/20.30 | CLOSE: (6) is inconsistent.
% 136.47/20.30 |
% 136.47/20.30 End of proof
% 136.47/20.30
% 136.47/20.30 Sub-proof #501 shows that the following formulas are inconsistent:
% 136.47/20.30 ----------------------------------------------------------------
% 136.47/20.30 (1) all_57_5 = e3
% 136.47/20.30 (2) all_57_5 = e2
% 136.47/20.30 (3) ~ (e3 = e2)
% 136.47/20.30
% 136.47/20.30 Begin of proof
% 136.47/20.30 |
% 136.47/20.30 | COMBINE_EQS: (1), (2) imply:
% 136.47/20.30 | (4) e3 = e2
% 136.47/20.30 |
% 136.47/20.30 | SIMP: (4) implies:
% 136.47/20.30 | (5) e3 = e2
% 136.47/20.30 |
% 136.47/20.30 | REDUCE: (3), (5) imply:
% 136.47/20.30 | (6) $false
% 136.47/20.30 |
% 136.47/20.30 | CLOSE: (6) is inconsistent.
% 136.47/20.30 |
% 136.47/20.30 End of proof
% 136.47/20.30
% 136.47/20.30 Sub-proof #502 shows that the following formulas are inconsistent:
% 136.47/20.30 ----------------------------------------------------------------
% 136.47/20.30 (1) all_57_2 = e0
% 136.47/20.30 (2) op(e2, e2) = e0
% 136.47/20.30 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.30 (4) ~ (e3 = e0)
% 136.47/20.30 (5) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 136.47/20.31
% 136.47/20.31 Begin of proof
% 136.47/20.31 |
% 136.47/20.31 | BETA: splitting (5) gives:
% 136.47/20.31 |
% 136.47/20.31 | Case 1:
% 136.47/20.31 | |
% 136.47/20.31 | | (6) all_57_2 = e3 & op(e2, e3) = e3
% 136.47/20.31 | |
% 136.47/20.31 | | ALPHA: (6) implies:
% 136.47/20.31 | | (7) all_57_2 = e3
% 136.47/20.31 | |
% 136.47/20.31 | | REF_CLOSE: (1), (4), (7) are inconsistent by sub-proof #593.
% 136.47/20.31 | |
% 136.47/20.31 | Case 2:
% 136.47/20.31 | |
% 136.47/20.31 | | (8) all_57_3 = e3 & op(e2, e2) = e3
% 136.47/20.31 | |
% 136.47/20.31 | | ALPHA: (8) implies:
% 136.47/20.31 | | (9) op(e2, e2) = e3
% 136.47/20.31 | |
% 136.47/20.31 | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #641.
% 136.47/20.31 | |
% 136.47/20.31 | End of split
% 136.47/20.31 |
% 136.47/20.31 End of proof
% 136.47/20.31
% 136.47/20.31 Sub-proof #503 shows that the following formulas are inconsistent:
% 136.47/20.31 ----------------------------------------------------------------
% 136.47/20.31 (1) ~ (all_52_4 = e0)
% 136.47/20.31 (2) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 136.47/20.31 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 136.47/20.31 (3) ~ (e2 = e0)
% 136.47/20.31 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.31 (5) op(e0, e2) = all_52_7
% 136.47/20.31 (6) ~ (all_52_6 = e0)
% 136.47/20.31 (7) op(e1, e2) = all_52_6
% 136.47/20.31 (8) ~ (all_52_7 = e0)
% 136.47/20.31 (9) op(e3, e2) = all_52_4
% 136.47/20.31 (10) all_57_3 = e2
% 136.47/20.31
% 136.47/20.31 Begin of proof
% 136.47/20.31 |
% 136.47/20.31 | BETA: splitting (2) gives:
% 136.47/20.31 |
% 136.47/20.31 | Case 1:
% 136.47/20.31 | |
% 136.47/20.31 | | (11) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 136.47/20.31 | | e0)
% 136.47/20.31 | |
% 136.47/20.31 | | BETA: splitting (11) gives:
% 136.47/20.31 | |
% 136.47/20.31 | | Case 1:
% 136.47/20.31 | | |
% 136.47/20.31 | | | (12) all_57_1 = e0 & op(e3, e2) = e0
% 136.47/20.31 | | |
% 136.47/20.31 | | | REF_CLOSE: (1), (4), (9), (12) are inconsistent by sub-proof #693.
% 136.47/20.31 | | |
% 136.47/20.31 | | Case 2:
% 136.47/20.31 | | |
% 136.47/20.31 | | | (13) all_57_3 = e0 & op(e2, e2) = e0
% 136.47/20.31 | | |
% 136.47/20.31 | | | REF_CLOSE: (3), (10), (13) are inconsistent by sub-proof #627.
% 136.47/20.31 | | |
% 136.47/20.31 | | End of split
% 136.47/20.31 | |
% 136.47/20.31 | Case 2:
% 136.47/20.31 | |
% 136.47/20.31 | | (14) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 136.47/20.31 | | e0)
% 136.47/20.31 | |
% 136.47/20.31 | | REF_CLOSE: (4), (5), (6), (7), (8), (14) are inconsistent by sub-proof #504.
% 136.47/20.31 | |
% 136.47/20.31 | End of split
% 136.47/20.31 |
% 136.47/20.31 End of proof
% 136.47/20.31
% 136.47/20.31 Sub-proof #504 shows that the following formulas are inconsistent:
% 136.47/20.31 ----------------------------------------------------------------
% 136.47/20.31 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.31 (2) op(e0, e2) = all_52_7
% 136.47/20.31 (3) ~ (all_52_6 = e0)
% 136.47/20.31 (4) op(e1, e2) = all_52_6
% 136.47/20.31 (5) ~ (all_52_7 = e0)
% 136.47/20.31 (6) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 136.47/20.31
% 136.47/20.31 Begin of proof
% 136.47/20.31 |
% 136.47/20.31 | BETA: splitting (6) gives:
% 136.47/20.31 |
% 136.47/20.31 | Case 1:
% 136.47/20.31 | |
% 136.47/20.31 | | (7) all_57_7 = e0 & op(e1, e2) = e0
% 136.47/20.31 | |
% 136.47/20.31 | | REF_CLOSE: (1), (3), (4), (7) are inconsistent by sub-proof #505.
% 136.47/20.31 | |
% 136.47/20.31 | Case 2:
% 136.47/20.31 | |
% 136.47/20.31 | | (8) all_57_13 = e0 & op(e0, e2) = e0
% 136.47/20.31 | |
% 136.47/20.31 | | ALPHA: (8) implies:
% 136.47/20.31 | | (9) op(e0, e2) = e0
% 136.47/20.31 | |
% 136.47/20.31 | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #545.
% 136.47/20.31 | |
% 136.47/20.31 | End of split
% 136.47/20.31 |
% 136.47/20.31 End of proof
% 136.47/20.31
% 136.47/20.31 Sub-proof #505 shows that the following formulas are inconsistent:
% 136.47/20.31 ----------------------------------------------------------------
% 136.47/20.31 (1) all_57_7 = e0 & op(e1, e2) = e0
% 136.47/20.31 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.31 (3) op(e1, e2) = all_52_6
% 136.47/20.31 (4) ~ (all_52_6 = e0)
% 136.47/20.31
% 136.47/20.31 Begin of proof
% 136.47/20.31 |
% 136.47/20.31 | ALPHA: (1) implies:
% 136.47/20.31 | (5) op(e1, e2) = e0
% 136.47/20.31 |
% 136.47/20.31 | GROUND_INST: instantiating (2) with all_52_6, e0, e2, e1, simplifying with
% 136.47/20.31 | (3), (5) gives:
% 136.47/20.31 | (6) all_52_6 = e0
% 136.47/20.31 |
% 136.47/20.31 | REDUCE: (4), (6) imply:
% 136.47/20.31 | (7) $false
% 136.47/20.31 |
% 136.47/20.31 | CLOSE: (7) is inconsistent.
% 136.47/20.31 |
% 136.47/20.31 End of proof
% 136.47/20.31
% 136.47/20.31 Sub-proof #506 shows that the following formulas are inconsistent:
% 136.47/20.31 ----------------------------------------------------------------
% 136.47/20.31 (1) all_54_10 = all_6_2
% 136.47/20.31 (2) all_54_10 = e0
% 136.47/20.31 (3) ~ (all_6_2 = e0)
% 136.47/20.31
% 136.47/20.31 Begin of proof
% 136.47/20.31 |
% 136.47/20.31 | COMBINE_EQS: (1), (2) imply:
% 136.47/20.31 | (4) all_6_2 = e0
% 136.47/20.31 |
% 136.47/20.31 | SIMP: (4) implies:
% 136.47/20.31 | (5) all_6_2 = e0
% 136.47/20.31 |
% 136.47/20.31 | REDUCE: (3), (5) imply:
% 136.47/20.31 | (6) $false
% 136.47/20.31 |
% 136.47/20.31 | CLOSE: (6) is inconsistent.
% 136.47/20.31 |
% 136.47/20.31 End of proof
% 136.47/20.31
% 136.47/20.31 Sub-proof #507 shows that the following formulas are inconsistent:
% 136.47/20.31 ----------------------------------------------------------------
% 136.47/20.31 (1) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2)
% 136.47/20.31 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 136.47/20.31 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25
% 136.47/20.31 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 136.47/20.31 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3)
% 136.47/20.31 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.47/20.31 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 136.47/20.31 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) &
% 136.47/20.31 $i(all_56_11) & $i(all_56_19) & $i(all_56_27))
% 136.47/20.31 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.31 (3) ~ (e3 = e2)
% 136.47/20.31 (4) op(e0, e2) = all_52_7
% 136.47/20.31 (5) ~ (all_52_7 = e0)
% 136.47/20.31 (6) op(e0, e0) = e2
% 136.47/20.31 (7) op(e0, e0) = all_56_31
% 136.47/20.31
% 136.47/20.31 Begin of proof
% 136.47/20.31 |
% 136.47/20.31 | BETA: splitting (1) gives:
% 136.47/20.31 |
% 136.47/20.31 | Case 1:
% 136.47/20.31 | |
% 136.47/20.31 | | (8) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.47/20.31 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.47/20.31 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.47/20.31 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 136.47/20.31 | | $i(all_56_17) & $i(all_56_25)
% 136.47/20.31 | |
% 136.47/20.31 | | ALPHA: (8) implies:
% 136.47/20.31 | | (9) all_56_31 = e3
% 136.47/20.31 | |
% 136.47/20.31 | | REDUCE: (7), (9) imply:
% 136.47/20.31 | | (10) op(e0, e0) = e3
% 136.47/20.31 | |
% 136.47/20.31 | | REF_CLOSE: (2), (3), (6), (10) are inconsistent by sub-proof #634.
% 136.47/20.31 | |
% 136.47/20.31 | Case 2:
% 136.47/20.31 | |
% 136.47/20.31 | | (11) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11
% 136.47/20.31 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 136.47/20.31 | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 136.47/20.31 | | e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 136.47/20.31 | | $i(all_56_19) & $i(all_56_27)
% 136.47/20.31 | |
% 136.47/20.31 | | ALPHA: (11) implies:
% 136.47/20.31 | | (12) op(e0, e2) = e0
% 136.47/20.31 | |
% 136.47/20.31 | | REF_CLOSE: (2), (4), (5), (12) are inconsistent by sub-proof #545.
% 136.47/20.31 | |
% 136.47/20.31 | End of split
% 136.47/20.31 |
% 136.47/20.31 End of proof
% 136.47/20.31
% 136.47/20.31 Sub-proof #508 shows that the following formulas are inconsistent:
% 136.47/20.31 ----------------------------------------------------------------
% 136.47/20.31 (1) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2)
% 136.47/20.31 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 136.47/20.31 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25
% 136.47/20.31 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 136.47/20.31 $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~
% 136.47/20.31 (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 136.47/20.31 (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 136.47/20.31 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 136.47/20.31 = all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.47/20.31 $i(all_56_29))
% 136.47/20.31 (2) op(e1, e1) = all_6_2
% 136.47/20.31 (3) op(e2, e2) = e0
% 136.47/20.31 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.31 (5) op(e1, e1) = e1
% 136.47/20.31 (6) ~ (e3 = e1)
% 136.47/20.31 (7) ~ (e1 = e0)
% 136.47/20.31
% 136.47/20.31 Begin of proof
% 136.47/20.31 |
% 136.47/20.31 | BETA: splitting (1) gives:
% 136.47/20.31 |
% 136.47/20.31 | Case 1:
% 136.47/20.31 | |
% 136.47/20.31 | | (8) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.47/20.31 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.47/20.31 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.47/20.31 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1)
% 136.47/20.31 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)
% 136.47/20.31 | |
% 136.47/20.31 | | ALPHA: (8) implies:
% 136.47/20.31 | | (9) op(e1, e1) = e3
% 136.47/20.31 | |
% 136.47/20.31 | | REF_CLOSE: (2), (4), (5), (6), (9) are inconsistent by sub-proof #662.
% 136.47/20.31 | |
% 136.47/20.31 | Case 2:
% 136.47/20.31 | |
% 136.47/20.31 | | (10) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13
% 136.47/20.31 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) =
% 136.47/20.31 | | e1 & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 136.47/20.31 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 136.47/20.31 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 136.47/20.31 | |
% 136.47/20.31 | | ALPHA: (10) implies:
% 136.47/20.31 | | (11) op(e2, e2) = e1
% 136.47/20.31 | |
% 136.47/20.31 | | REF_CLOSE: (3), (4), (7), (11) are inconsistent by sub-proof #675.
% 136.47/20.31 | |
% 136.47/20.31 | End of split
% 136.47/20.31 |
% 136.47/20.31 End of proof
% 136.47/20.31
% 136.47/20.31 Sub-proof #509 shows that the following formulas are inconsistent:
% 136.47/20.31 ----------------------------------------------------------------
% 136.47/20.31 (1) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2)
% 136.47/20.31 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3,
% 136.47/20.31 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 136.47/20.31 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 136.47/20.31 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 136.47/20.31 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.47/20.31 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) =
% 136.47/20.31 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.47/20.31 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 136.47/20.31 $i(all_56_21) & $i(all_56_29))
% 136.47/20.31 (2) op(e3, e3) = e1
% 136.47/20.31 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.31 (4) ~ (e2 = e1)
% 136.47/20.31 (5) op(e1, e1) = e1
% 136.47/20.31
% 136.47/20.31 Begin of proof
% 136.47/20.31 |
% 136.47/20.31 | BETA: splitting (1) gives:
% 136.47/20.31 |
% 136.47/20.31 | Case 1:
% 136.47/20.31 | |
% 136.47/20.31 | | (6) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 136.47/20.31 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 136.47/20.31 | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 136.47/20.31 | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 136.47/20.31 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)
% 136.47/20.31 | |
% 136.47/20.31 | | ALPHA: (6) implies:
% 136.47/20.31 | | (7) op(e3, e3) = e2
% 136.47/20.31 | |
% 136.47/20.31 | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #743.
% 136.47/20.31 | |
% 136.47/20.31 | Case 2:
% 136.47/20.31 | |
% 136.47/20.31 | | (8) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 136.47/20.31 | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 136.47/20.31 | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 136.47/20.31 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 136.47/20.31 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 136.47/20.31 | |
% 136.47/20.31 | | ALPHA: (8) implies:
% 136.47/20.31 | | (9) ~ (all_56_21 = e1)
% 136.47/20.31 | | (10) op(e1, e1) = all_56_21
% 136.47/20.31 | |
% 136.47/20.31 | | REF_CLOSE: (3), (5), (9), (10) are inconsistent by sub-proof #510.
% 136.47/20.31 | |
% 136.47/20.31 | End of split
% 136.47/20.31 |
% 136.47/20.31 End of proof
% 136.47/20.31
% 136.47/20.31 Sub-proof #510 shows that the following formulas are inconsistent:
% 136.47/20.31 ----------------------------------------------------------------
% 136.47/20.31 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.31 (2) op(e1, e1) = all_56_21
% 136.47/20.31 (3) op(e1, e1) = e1
% 136.47/20.31 (4) ~ (all_56_21 = e1)
% 136.47/20.31
% 136.47/20.31 Begin of proof
% 136.47/20.31 |
% 136.47/20.31 | GROUND_INST: instantiating (1) with e1, all_56_21, e1, e1, simplifying with
% 136.47/20.31 | (2), (3) gives:
% 136.47/20.31 | (5) all_56_21 = e1
% 136.47/20.31 |
% 136.47/20.31 | REDUCE: (4), (5) imply:
% 136.47/20.31 | (6) $false
% 136.47/20.31 |
% 136.47/20.31 | CLOSE: (6) is inconsistent.
% 136.47/20.31 |
% 136.47/20.31 End of proof
% 136.47/20.31
% 136.47/20.31 Sub-proof #511 shows that the following formulas are inconsistent:
% 136.47/20.31 ----------------------------------------------------------------
% 136.47/20.31 (1) op(e1, e1) = all_6_2
% 136.47/20.31 (2) ~ (all_52_11 = e2)
% 136.47/20.31 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.31 (4) op(e0, e1) = all_52_11
% 136.47/20.31 (5) ~ (all_6_2 = e2)
% 136.47/20.31 (6) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 136.47/20.31
% 136.47/20.31 Begin of proof
% 136.47/20.31 |
% 136.47/20.31 | BETA: splitting (6) gives:
% 136.47/20.31 |
% 136.47/20.31 | Case 1:
% 136.47/20.31 | |
% 136.47/20.31 | | (7) all_57_8 = e2 & op(e1, e1) = e2
% 136.47/20.31 | |
% 136.47/20.31 | | ALPHA: (7) implies:
% 136.47/20.31 | | (8) op(e1, e1) = e2
% 136.47/20.31 | |
% 136.47/20.31 | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #767.
% 136.47/20.31 | |
% 136.47/20.31 | Case 2:
% 136.47/20.31 | |
% 136.47/20.31 | | (9) all_57_14 = e2 & op(e0, e1) = e2
% 136.47/20.31 | |
% 136.47/20.31 | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #512.
% 136.47/20.31 | |
% 136.47/20.31 | End of split
% 136.47/20.31 |
% 136.47/20.31 End of proof
% 136.47/20.31
% 136.47/20.31 Sub-proof #512 shows that the following formulas are inconsistent:
% 136.47/20.31 ----------------------------------------------------------------
% 136.47/20.31 (1) all_57_14 = e2 & op(e0, e1) = e2
% 136.47/20.31 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.31 (3) op(e0, e1) = all_52_11
% 136.47/20.31 (4) ~ (all_52_11 = e2)
% 136.47/20.31
% 136.47/20.31 Begin of proof
% 136.47/20.31 |
% 136.47/20.31 | ALPHA: (1) implies:
% 136.47/20.31 | (5) op(e0, e1) = e2
% 136.47/20.31 |
% 136.47/20.31 | GROUND_INST: instantiating (2) with all_52_11, e2, e1, e0, simplifying with
% 136.47/20.31 | (3), (5) gives:
% 136.47/20.31 | (6) all_52_11 = e2
% 136.47/20.31 |
% 136.47/20.31 | REDUCE: (4), (6) imply:
% 136.47/20.31 | (7) $false
% 136.47/20.31 |
% 136.47/20.31 | CLOSE: (7) is inconsistent.
% 136.47/20.31 |
% 136.47/20.31 End of proof
% 136.47/20.31
% 136.47/20.31 Sub-proof #513 shows that the following formulas are inconsistent:
% 136.47/20.31 ----------------------------------------------------------------
% 136.47/20.31 (1) op(e1, e1) = all_6_2
% 136.47/20.31 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.31 (3) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 136.47/20.31 (4) ~ (all_52_14 = e2)
% 136.47/20.31 (5) ~ (all_6_2 = e2)
% 136.47/20.31 (6) op(e1, e0) = all_52_14
% 136.47/20.31
% 136.47/20.31 Begin of proof
% 136.47/20.31 |
% 136.47/20.31 | BETA: splitting (3) gives:
% 136.47/20.31 |
% 136.47/20.31 | Case 1:
% 136.47/20.31 | |
% 136.47/20.31 | | (7) all_57_8 = e2 & op(e1, e1) = e2
% 136.47/20.31 | |
% 136.47/20.31 | | ALPHA: (7) implies:
% 136.47/20.31 | | (8) op(e1, e1) = e2
% 136.47/20.31 | |
% 136.47/20.31 | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #767.
% 136.47/20.31 | |
% 136.47/20.31 | Case 2:
% 136.47/20.31 | |
% 136.47/20.31 | | (9) all_57_11 = e2 & op(e1, e0) = e2
% 136.47/20.31 | |
% 136.47/20.31 | | REF_CLOSE: (2), (4), (6), (9) are inconsistent by sub-proof #514.
% 136.47/20.31 | |
% 136.47/20.31 | End of split
% 136.47/20.31 |
% 136.47/20.31 End of proof
% 136.47/20.31
% 136.47/20.31 Sub-proof #514 shows that the following formulas are inconsistent:
% 136.47/20.31 ----------------------------------------------------------------
% 136.47/20.31 (1) all_57_11 = e2 & op(e1, e0) = e2
% 136.47/20.31 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.31 (3) op(e1, e0) = all_52_14
% 136.47/20.31 (4) ~ (all_52_14 = e2)
% 136.47/20.31
% 136.47/20.31 Begin of proof
% 136.47/20.31 |
% 136.47/20.31 | ALPHA: (1) implies:
% 136.47/20.31 | (5) op(e1, e0) = e2
% 136.47/20.31 |
% 136.47/20.31 | GROUND_INST: instantiating (2) with all_52_14, e2, e0, e1, simplifying with
% 136.47/20.31 | (3), (5) gives:
% 136.47/20.31 | (6) all_52_14 = e2
% 136.47/20.31 |
% 136.47/20.31 | REDUCE: (4), (6) imply:
% 136.47/20.31 | (7) $false
% 136.47/20.31 |
% 136.47/20.31 | CLOSE: (7) is inconsistent.
% 136.47/20.31 |
% 136.47/20.31 End of proof
% 136.47/20.31
% 136.47/20.31 Sub-proof #515 shows that the following formulas are inconsistent:
% 136.47/20.31 ----------------------------------------------------------------
% 136.47/20.31 (1) all_57_7 = e2 & op(e1, e2) = e2
% 136.47/20.31 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.31 (3) op(e1, e2) = all_52_6
% 136.47/20.31 (4) ~ (all_52_6 = e2)
% 136.47/20.31
% 136.47/20.31 Begin of proof
% 136.47/20.31 |
% 136.47/20.31 | ALPHA: (1) implies:
% 136.47/20.31 | (5) op(e1, e2) = e2
% 136.47/20.31 |
% 136.47/20.31 | GROUND_INST: instantiating (2) with all_52_6, e2, e2, e1, simplifying with
% 136.47/20.31 | (3), (5) gives:
% 136.47/20.31 | (6) all_52_6 = e2
% 136.47/20.31 |
% 136.47/20.31 | REDUCE: (4), (6) imply:
% 136.47/20.31 | (7) $false
% 136.47/20.31 |
% 136.47/20.31 | CLOSE: (7) is inconsistent.
% 136.47/20.31 |
% 136.47/20.31 End of proof
% 136.47/20.31
% 136.47/20.31 Sub-proof #516 shows that the following formulas are inconsistent:
% 136.47/20.31 ----------------------------------------------------------------
% 136.47/20.31 (1) all_57_12 = e1 & op(e0, e3) = e1
% 136.47/20.31 (2) all_57_12 = e2
% 136.47/20.31 (3) ~ (e2 = e1)
% 136.47/20.31
% 136.47/20.31 Begin of proof
% 136.47/20.31 |
% 136.47/20.31 | ALPHA: (1) implies:
% 136.47/20.31 | (4) all_57_12 = e1
% 136.47/20.31 |
% 136.47/20.31 | COMBINE_EQS: (2), (4) imply:
% 136.47/20.31 | (5) e2 = e1
% 136.47/20.31 |
% 136.47/20.31 | REDUCE: (3), (5) imply:
% 136.47/20.31 | (6) $false
% 136.47/20.31 |
% 136.47/20.31 | CLOSE: (6) is inconsistent.
% 136.47/20.31 |
% 136.47/20.31 End of proof
% 136.47/20.31
% 136.47/20.31 Sub-proof #517 shows that the following formulas are inconsistent:
% 136.47/20.31 ----------------------------------------------------------------
% 136.47/20.31 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.31 (2) ~ (e2 = e1)
% 136.47/20.31 (3) op(e1, e3) = e2
% 136.47/20.31 (4) op(e1, e3) = e1
% 136.47/20.31 (5) op(e1, e3) = all_52_2
% 136.47/20.31
% 136.47/20.31 Begin of proof
% 136.47/20.31 |
% 136.47/20.31 | GROUND_INST: instantiating (1) with all_52_2, e1, e3, e1, simplifying with
% 136.47/20.31 | (4), (5) gives:
% 136.47/20.31 | (6) all_52_2 = e1
% 136.47/20.31 |
% 136.47/20.31 | GROUND_INST: instantiating (1) with all_52_2, e2, e3, e1, simplifying with
% 136.47/20.31 | (3), (5) gives:
% 136.47/20.31 | (7) all_52_2 = e2
% 136.47/20.31 |
% 136.47/20.31 | COMBINE_EQS: (6), (7) imply:
% 136.47/20.31 | (8) e2 = e1
% 136.47/20.31 |
% 136.47/20.31 | REDUCE: (2), (8) imply:
% 136.47/20.31 | (9) $false
% 136.47/20.31 |
% 136.47/20.31 | CLOSE: (9) is inconsistent.
% 136.47/20.31 |
% 136.47/20.31 End of proof
% 136.47/20.31
% 136.47/20.31 Sub-proof #518 shows that the following formulas are inconsistent:
% 136.47/20.31 ----------------------------------------------------------------
% 136.47/20.31 (1) all_57_12 = e3
% 136.47/20.31 (2) all_57_12 = e2
% 136.47/20.31 (3) ~ (e3 = e2)
% 136.47/20.31
% 136.47/20.31 Begin of proof
% 136.47/20.31 |
% 136.47/20.31 | COMBINE_EQS: (1), (2) imply:
% 136.47/20.31 | (4) e3 = e2
% 136.47/20.31 |
% 136.47/20.31 | SIMP: (4) implies:
% 136.47/20.31 | (5) e3 = e2
% 136.47/20.31 |
% 136.47/20.31 | REDUCE: (3), (5) imply:
% 136.47/20.31 | (6) $false
% 136.47/20.31 |
% 136.47/20.31 | CLOSE: (6) is inconsistent.
% 136.47/20.31 |
% 136.47/20.31 End of proof
% 136.47/20.31
% 136.47/20.31 Sub-proof #519 shows that the following formulas are inconsistent:
% 136.47/20.31 ----------------------------------------------------------------
% 136.47/20.31 (1) ~ (e2 = e0)
% 136.47/20.31 (2) op(e3, e3) = e1
% 136.47/20.31 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.31 (4) ~ (e3 = e0)
% 136.47/20.31 (5) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 136.47/20.31 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 136.47/20.31 (6) all_57_2 = e3
% 136.47/20.31 (7) ~ (e1 = e0)
% 136.47/20.31 (8) all_57_6 = e2
% 136.47/20.31 (9) all_57_12 = e2
% 136.47/20.31
% 136.47/20.31 Begin of proof
% 136.47/20.31 |
% 136.47/20.31 | BETA: splitting (5) gives:
% 136.47/20.31 |
% 136.47/20.31 | Case 1:
% 136.47/20.31 | |
% 136.47/20.31 | | (10) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 136.47/20.31 | | e0)
% 136.47/20.31 | |
% 136.47/20.31 | | BETA: splitting (10) gives:
% 136.47/20.31 | |
% 136.47/20.31 | | Case 1:
% 136.47/20.31 | | |
% 136.47/20.31 | | | (11) all_57_0 = e0 & op(e3, e3) = e0
% 136.47/20.31 | | |
% 136.47/20.31 | | | ALPHA: (11) implies:
% 136.47/20.31 | | | (12) op(e3, e3) = e0
% 136.47/20.31 | | |
% 136.47/20.31 | | | REF_CLOSE: (2), (3), (7), (12) are inconsistent by sub-proof #717.
% 136.47/20.31 | | |
% 136.47/20.31 | | Case 2:
% 136.47/20.31 | | |
% 136.47/20.31 | | | (13) all_57_2 = e0 & op(e2, e3) = e0
% 136.47/20.31 | | |
% 136.47/20.31 | | | REF_CLOSE: (4), (6), (13) are inconsistent by sub-proof #521.
% 136.47/20.31 | | |
% 136.47/20.31 | | End of split
% 136.47/20.31 | |
% 136.47/20.31 | Case 2:
% 136.47/20.31 | |
% 136.47/20.31 | | (14) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 136.47/20.31 | | e0)
% 136.47/20.31 | |
% 136.47/20.31 | | BETA: splitting (14) gives:
% 136.47/20.31 | |
% 136.47/20.31 | | Case 1:
% 136.47/20.31 | | |
% 136.47/20.31 | | | (15) all_57_6 = e0 & op(e1, e3) = e0
% 136.47/20.31 | | |
% 136.47/20.31 | | | REF_CLOSE: (1), (8), (15) are inconsistent by sub-proof #520.
% 136.47/20.31 | | |
% 136.47/20.31 | | Case 2:
% 136.47/20.31 | | |
% 136.47/20.31 | | | (16) all_57_12 = e0 & op(e0, e3) = e0
% 136.47/20.31 | | |
% 136.47/20.31 | | | REF_CLOSE: (1), (9), (16) are inconsistent by sub-proof #578.
% 136.47/20.31 | | |
% 136.47/20.31 | | End of split
% 136.47/20.31 | |
% 136.47/20.31 | End of split
% 136.47/20.31 |
% 136.47/20.31 End of proof
% 136.47/20.31
% 136.47/20.31 Sub-proof #520 shows that the following formulas are inconsistent:
% 136.47/20.31 ----------------------------------------------------------------
% 136.47/20.31 (1) all_57_6 = e0 & op(e1, e3) = e0
% 136.47/20.31 (2) all_57_6 = e2
% 136.47/20.31 (3) ~ (e2 = e0)
% 136.47/20.31
% 136.47/20.31 Begin of proof
% 136.47/20.31 |
% 136.47/20.31 | ALPHA: (1) implies:
% 136.47/20.31 | (4) all_57_6 = e0
% 136.47/20.31 |
% 136.47/20.31 | COMBINE_EQS: (2), (4) imply:
% 136.47/20.31 | (5) e2 = e0
% 136.47/20.31 |
% 136.47/20.31 | REDUCE: (3), (5) imply:
% 136.47/20.31 | (6) $false
% 136.47/20.31 |
% 136.47/20.31 | CLOSE: (6) is inconsistent.
% 136.47/20.31 |
% 136.47/20.31 End of proof
% 136.47/20.31
% 136.47/20.31 Sub-proof #521 shows that the following formulas are inconsistent:
% 136.47/20.31 ----------------------------------------------------------------
% 136.47/20.31 (1) all_57_2 = e0 & op(e2, e3) = e0
% 136.47/20.31 (2) all_57_2 = e3
% 136.47/20.31 (3) ~ (e3 = e0)
% 136.47/20.31
% 136.47/20.31 Begin of proof
% 136.47/20.31 |
% 136.47/20.31 | ALPHA: (1) implies:
% 136.47/20.31 | (4) all_57_2 = e0
% 136.47/20.31 |
% 136.47/20.31 | COMBINE_EQS: (2), (4) imply:
% 136.47/20.31 | (5) e3 = e0
% 136.47/20.31 |
% 136.47/20.31 | REDUCE: (3), (5) imply:
% 136.47/20.31 | (6) $false
% 136.47/20.31 |
% 136.47/20.31 | CLOSE: (6) is inconsistent.
% 136.47/20.31 |
% 136.47/20.31 End of proof
% 136.47/20.31
% 136.47/20.31 Sub-proof #522 shows that the following formulas are inconsistent:
% 136.47/20.31 ----------------------------------------------------------------
% 136.47/20.31 (1) op(e1, e1) = all_6_2
% 136.47/20.31 (2) op(e2, e0) = all_52_13
% 136.47/20.31 (3) ~ (all_40_2 = e0) | ( ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 &
% 136.47/20.31 $i(all_40_0)) | ( ~ (all_40_1 = e2) & op(e0, e0) = all_40_1 &
% 136.47/20.31 $i(all_40_1))
% 136.47/20.31 (4) ~ (all_52_8 = all_52_9)
% 136.47/20.31 (5) ~ (all_52_1 = all_52_2)
% 136.47/20.31 (6) all_40_2 = all_6_2
% 136.47/20.31 (7) ~ (all_6_2 = e3)
% 136.47/20.31 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.31 (9) ~ (e2 = e1)
% 136.47/20.31 (10) op(e1, e3) = e2
% 136.47/20.31 (11) ~ (e3 = e2)
% 136.47/20.31 (12) ~ (all_52_11 = all_6_2)
% 136.47/20.31 (13) ~ (all_52_8 = all_52_11)
% 136.47/20.31 (14) op(e0, e1) = all_52_11
% 136.47/20.31 (15) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 136.47/20.31 (16) ~ (all_10_2 = e0)
% 136.47/20.31 (17) ~ (all_52_13 = e2)
% 136.47/20.31 (18) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 136.47/20.31 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 136.47/20.31 op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 136.47/20.31 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 136.47/20.31 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 136.47/20.31 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.47/20.31 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 136.47/20.31 = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.47/20.31 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 136.47/20.31 $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~
% 136.47/20.31 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 136.47/20.31 (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) =
% 136.47/20.31 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0,
% 136.47/20.31 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 136.47/20.31 $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3)
% 136.47/20.31 & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 136.47/20.31 op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17
% 136.47/20.31 & op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 136.47/20.31 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.47/20.31 (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.47/20.31 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.47/20.31 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0)
% 136.47/20.31 = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) &
% 136.47/20.31 $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 &
% 136.47/20.31 all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.47/20.31 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 136.47/20.31 = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.47/20.31 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 136.47/20.31 $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~
% 136.47/20.31 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 136.47/20.31 (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 136.47/20.31 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0,
% 136.47/20.31 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 136.47/20.31 $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3)
% 136.47/20.31 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.47/20.31 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.47/20.31 all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2
% 136.47/20.31 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.47/20.31 (op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 =
% 136.47/20.31 e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 136.47/20.31 & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) =
% 136.47/20.31 all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 136.47/20.31 op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 136.47/20.31 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 136.47/20.31 e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 136.47/20.31 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 136.47/20.31 e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.47/20.31 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.47/20.31 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.47/20.31 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.47/20.31 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 136.47/20.31 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 136.47/20.31 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 136.47/20.31 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 136.47/20.31 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 136.47/20.31 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 136.47/20.31 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.47/20.31 $i(all_56_29))))
% 136.47/20.31 (19) ~ (all_52_8 = all_6_2)
% 136.47/20.31 (20) op(e3, e3) = all_10_2
% 136.47/20.31 (21) op(e3, e1) = e2
% 136.47/20.32 (22) op(e2, e1) = all_52_9
% 136.47/20.32 (23) op(e1, e3) = all_52_2
% 136.47/20.32 (24) op(e0, e0) = e2
% 136.47/20.32 (25) op(e2, e3) = all_52_1
% 136.47/20.32 (26) op(e3, e1) = all_52_8
% 136.47/20.32 (27) all_54_14 = all_52_11
% 136.47/20.32 (28) ~ (all_52_8 = all_10_2)
% 136.47/20.32 (29) op(e2, e2) = e2
% 136.47/20.32
% 136.47/20.32 Begin of proof
% 136.47/20.32 |
% 136.47/20.32 | GROUND_INST: instantiating (8) with all_52_2, e2, e3, e1, simplifying with
% 136.47/20.32 | (10), (23) gives:
% 136.47/20.32 | (30) all_52_2 = e2
% 136.47/20.32 |
% 136.47/20.32 | GROUND_INST: instantiating (8) with all_52_8, e2, e1, e3, simplifying with
% 136.47/20.32 | (21), (26) gives:
% 136.47/20.32 | (31) all_52_8 = e2
% 136.47/20.32 |
% 136.47/20.32 | REDUCE: (5), (30) imply:
% 136.47/20.32 | (32) ~ (all_52_1 = e2)
% 136.47/20.32 |
% 136.47/20.32 | REDUCE: (4), (31) imply:
% 136.47/20.32 | (33) ~ (all_52_9 = e2)
% 136.47/20.32 |
% 136.47/20.32 | SIMP: (33) implies:
% 136.47/20.32 | (34) ~ (all_52_9 = e2)
% 136.47/20.32 |
% 136.47/20.32 | REDUCE: (13), (31) imply:
% 136.47/20.32 | (35) ~ (all_52_11 = e2)
% 136.47/20.32 |
% 136.47/20.32 | SIMP: (35) implies:
% 136.47/20.32 | (36) ~ (all_52_11 = e2)
% 136.47/20.32 |
% 136.47/20.32 | REDUCE: (28), (31) imply:
% 136.47/20.32 | (37) ~ (all_10_2 = e2)
% 136.47/20.32 |
% 136.47/20.32 | SIMP: (37) implies:
% 136.47/20.32 | (38) ~ (all_10_2 = e2)
% 136.47/20.32 |
% 136.47/20.32 | REDUCE: (19), (31) imply:
% 136.47/20.32 | (39) ~ (all_6_2 = e2)
% 136.47/20.32 |
% 136.47/20.32 | SIMP: (39) implies:
% 136.47/20.32 | (40) ~ (all_6_2 = e2)
% 136.47/20.32 |
% 136.47/20.32 | BETA: splitting (18) gives:
% 136.47/20.32 |
% 136.47/20.32 | Case 1:
% 136.47/20.32 | |
% 136.47/20.32 | | (41) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11
% 136.47/20.32 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) =
% 136.47/20.32 | | e2 & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 136.47/20.32 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 136.47/20.32 | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.47/20.32 | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13
% 136.47/20.32 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) =
% 136.47/20.32 | | e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 136.47/20.32 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 136.47/20.32 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 136.47/20.32 | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15
% 136.47/20.32 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) =
% 136.47/20.32 | | e0 & op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 136.47/20.32 | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 &
% 136.47/20.32 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 136.47/20.32 | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 136.47/20.32 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.47/20.32 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.47/20.32 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 136.47/20.32 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25))
% 136.47/20.32 | |
% 136.47/20.32 | | BETA: splitting (41) gives:
% 136.47/20.32 | |
% 136.47/20.32 | | Case 1:
% 136.47/20.32 | | |
% 136.47/20.32 | | | (42) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~
% 136.47/20.32 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.47/20.32 | | | op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = all_56_3 &
% 136.47/20.32 | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 136.47/20.32 | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 136.47/20.32 | | | $i(all_56_27)) | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5
% 136.47/20.32 | | | = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 136.47/20.32 | | | (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1,
% 136.47/20.32 | | | e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.47/20.32 | | | all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 136.47/20.32 | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 136.47/20.32 | | |
% 136.47/20.32 | | | BETA: splitting (42) gives:
% 136.47/20.32 | | |
% 136.47/20.32 | | | Case 1:
% 136.47/20.32 | | | |
% 136.47/20.32 | | | | (43) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~
% 136.47/20.32 | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.47/20.32 | | | | op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = all_56_3 &
% 136.47/20.32 | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 136.47/20.32 | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 136.47/20.32 | | | | $i(all_56_27)
% 136.47/20.32 | | | |
% 136.47/20.32 | | | | ALPHA: (43) implies:
% 136.47/20.32 | | | | (44) op(e3, e3) = e2
% 136.47/20.32 | | | |
% 136.47/20.32 | | | | REF_CLOSE: (8), (20), (38), (44) are inconsistent by sub-proof #536.
% 136.47/20.32 | | | |
% 136.47/20.32 | | | Case 2:
% 136.47/20.32 | | | |
% 136.47/20.32 | | | | (45) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~
% 136.47/20.32 | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 136.47/20.32 | | | | op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 &
% 136.47/20.32 | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 136.47/20.32 | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.47/20.32 | | | | $i(all_56_29)
% 136.47/20.32 | | | |
% 136.47/20.32 | | | | ALPHA: (45) implies:
% 136.47/20.32 | | | | (46) op(e3, e1) = e3
% 136.47/20.32 | | | |
% 136.47/20.32 | | | | GROUND_INST: instantiating (8) with e2, e3, e1, e3, simplifying with
% 136.47/20.32 | | | | (21), (46) gives:
% 136.47/20.32 | | | | (47) e3 = e2
% 136.47/20.32 | | | |
% 136.47/20.32 | | | | REDUCE: (11), (47) imply:
% 136.47/20.32 | | | | (48) $false
% 136.47/20.32 | | | |
% 136.47/20.32 | | | | CLOSE: (48) is inconsistent.
% 136.47/20.32 | | | |
% 136.47/20.32 | | | End of split
% 136.47/20.32 | | |
% 136.47/20.32 | | Case 2:
% 136.47/20.32 | | |
% 136.47/20.32 | | | (49) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~
% 136.47/20.32 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.47/20.32 | | | op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = all_56_7 &
% 136.47/20.32 | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 136.47/20.32 | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 136.47/20.32 | | | $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1
% 136.47/20.32 | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 136.47/20.32 | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9
% 136.47/20.32 | | | & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e2, e3) =
% 136.47/20.32 | | | e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 136.47/20.32 | | | $i(all_56_17) & $i(all_56_25))
% 136.47/20.32 | | |
% 136.47/20.32 | | | REF_CLOSE: (8), (16), (20), (25), (32), (49) are inconsistent by sub-proof
% 136.47/20.32 | | | #533.
% 136.47/20.32 | | |
% 136.47/20.32 | | End of split
% 136.47/20.32 | |
% 136.47/20.32 | Case 2:
% 136.47/20.32 | |
% 136.47/20.32 | | (50) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 136.47/20.32 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.47/20.32 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.47/20.32 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 136.47/20.32 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.47/20.32 | | (all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 136.47/20.32 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 136.47/20.32 | | op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1,
% 136.47/20.32 | | e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 136.47/20.32 | | all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.47/20.32 | | $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 136.47/20.32 | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31
% 136.47/20.32 | | = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 136.47/20.32 | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 136.47/20.32 | | op(e0, e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 136.47/20.32 | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2
% 136.47/20.32 | | & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 136.47/20.32 | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 136.47/20.32 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 136.47/20.32 | | op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 136.47/20.32 | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = all_56_31 &
% 136.47/20.32 | | $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 136.47/20.32 | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 136.47/20.32 | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) =
% 136.47/20.32 | | all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 136.47/20.32 | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17)
% 136.47/20.32 | | & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~
% 136.47/20.32 | | (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 136.47/20.32 | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 136.47/20.32 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 136.47/20.32 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 136.47/20.32 | | & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~
% 136.47/20.32 | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 136.47/20.32 | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 136.47/20.32 | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) =
% 136.47/20.32 | | all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 136.47/20.32 | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 136.47/20.32 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 136.47/20.32 | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.47/20.32 | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 136.47/20.32 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.47/20.32 | | $i(all_56_29))))
% 136.47/20.32 | |
% 136.47/20.32 | | BETA: splitting (50) gives:
% 136.47/20.32 | |
% 136.47/20.32 | | Case 1:
% 136.47/20.32 | | |
% 136.47/20.32 | | | (51) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~
% 136.47/20.32 | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 136.47/20.32 | | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) =
% 136.47/20.32 | | | all_56_17 & op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 136.47/20.32 | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 136.47/20.32 | | | $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5
% 136.47/20.32 | | | = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 136.47/20.32 | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1,
% 136.47/20.32 | | | e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.47/20.32 | | | all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 136.47/20.32 | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 136.47/20.32 | | |
% 136.47/20.32 | | | REF_CLOSE: (1), (7), (8), (22), (34), (51) are inconsistent by sub-proof
% 136.47/20.32 | | | #769.
% 136.47/20.32 | | |
% 136.47/20.32 | | Case 2:
% 136.47/20.32 | | |
% 136.47/20.32 | | | (52) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 136.47/20.32 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.47/20.32 | | | op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 &
% 136.47/20.32 | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 136.47/20.32 | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 136.47/20.32 | | | $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3
% 136.47/20.32 | | | = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 136.47/20.32 | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 136.47/20.32 | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 136.47/20.32 | | | op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11)
% 136.47/20.32 | | | & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = all_56_31 &
% 136.47/20.32 | | | $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 136.47/20.32 | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 136.47/20.32 | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) =
% 136.47/20.32 | | | all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 136.47/20.32 | | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 136.47/20.32 | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 136.47/20.32 | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~
% 136.47/20.32 | | | (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 136.47/20.32 | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 136.47/20.32 | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) &
% 136.47/20.32 | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 136.47/20.32 | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.47/20.32 | | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1,
% 136.47/20.32 | | | e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 136.47/20.32 | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 136.47/20.32 | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 =
% 136.47/20.32 | | | e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 136.47/20.32 | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1,
% 136.47/20.32 | | | e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.47/20.32 | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 136.47/20.32 | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.47/20.32 | | | $i(all_56_29))))
% 136.47/20.32 | | |
% 136.47/20.32 | | | BETA: splitting (52) gives:
% 136.47/20.32 | | |
% 136.47/20.32 | | | Case 1:
% 136.47/20.32 | | | |
% 136.47/20.32 | | | | (53) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 136.47/20.32 | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.47/20.32 | | | | op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 &
% 136.47/20.32 | | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 136.47/20.32 | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 136.47/20.32 | | | | $i(all_56_31)
% 136.47/20.32 | | | |
% 136.47/20.32 | | | | ALPHA: (53) implies:
% 136.47/20.32 | | | | (54) op(e2, e0) = e2
% 136.47/20.32 | | | |
% 136.47/20.32 | | | | REF_CLOSE: (2), (8), (17), (54) are inconsistent by sub-proof #768.
% 136.47/20.32 | | | |
% 136.47/20.32 | | | Case 2:
% 136.47/20.32 | | | |
% 136.47/20.32 | | | | (55) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 136.47/20.32 | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.47/20.32 | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.47/20.32 | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 136.47/20.32 | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 136.47/20.32 | | | | $i(all_56_27)) | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 136.47/20.32 | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 136.47/20.32 | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 =
% 136.47/20.32 | | | | e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 &
% 136.47/20.32 | | | | op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 136.47/20.32 | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 136.47/20.32 | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~
% 136.47/20.32 | | | | (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 136.47/20.32 | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 136.47/20.32 | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 136.47/20.32 | | | | e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) &
% 136.47/20.32 | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.47/20.32 | | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.47/20.32 | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 =
% 136.47/20.32 | | | | e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 136.47/20.32 | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23
% 136.47/20.32 | | | | & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 136.47/20.32 | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 136.47/20.32 | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 =
% 136.47/20.32 | | | | e0) & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 136.47/20.32 | | | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & op(e0,
% 136.47/20.32 | | | | e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 136.47/20.32 | | | | & $i(all_56_29))))
% 136.47/20.32 | | | |
% 136.47/20.32 | | | | BETA: splitting (55) gives:
% 136.47/20.32 | | | |
% 136.47/20.32 | | | | Case 1:
% 136.47/20.32 | | | | |
% 136.47/20.32 | | | | | (56) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 136.47/20.32 | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.47/20.32 | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.47/20.32 | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 136.47/20.32 | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 136.47/20.32 | | | | | $i(all_56_27)
% 136.47/20.32 | | | | |
% 136.47/20.32 | | | | | ALPHA: (56) implies:
% 136.47/20.32 | | | | | (57) op(e1, e1) = e2
% 136.47/20.32 | | | | |
% 136.47/20.32 | | | | | REF_CLOSE: (1), (8), (40), (57) are inconsistent by sub-proof #767.
% 136.47/20.32 | | | | |
% 136.47/20.32 | | | | Case 2:
% 136.47/20.32 | | | | |
% 136.47/20.32 | | | | | (58) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 136.47/20.32 | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) &
% 136.47/20.32 | | | | | ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.47/20.32 | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17
% 136.47/20.32 | | | | | & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1)
% 136.47/20.32 | | | | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.47/20.32 | | | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 136.47/20.32 | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 =
% 136.47/20.32 | | | | | e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 136.47/20.32 | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 136.47/20.32 | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 136.47/20.32 | | | | | & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~
% 136.47/20.32 | | | | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 136.47/20.32 | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 136.47/20.32 | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.47/20.32 | | | | | op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 136.47/20.32 | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 & ~
% 136.47/20.32 | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 136.47/20.32 | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 136.47/20.32 | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1,
% 136.47/20.32 | | | | | e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 136.47/20.32 | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)))
% 136.47/20.32 | | | | |
% 136.47/20.32 | | | | | ALPHA: (58) implies:
% 136.47/20.32 | | | | | (59) op(e0, e0) = all_56_31
% 136.47/20.32 | | | | | (60) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 136.47/20.32 | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0)
% 136.47/20.32 | | | | | & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 136.47/20.32 | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 136.47/20.32 | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25))
% 136.47/20.32 | | | | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 136.47/20.32 | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0)
% 136.47/20.32 | | | | | & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 136.47/20.32 | | | | | e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0
% 136.47/20.32 | | | | | & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 136.47/20.32 | | | | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~
% 136.47/20.32 | | | | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 136.47/20.32 | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 136.47/20.32 | | | | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1)
% 136.47/20.32 | | | | | = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 136.47/20.32 | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 136.47/20.32 | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0)
% 136.47/20.32 | | | | | & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1,
% 136.47/20.32 | | | | | e1) = all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0
% 136.47/20.32 | | | | | & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.47/20.32 | | | | | $i(all_56_29))
% 136.47/20.32 | | | | |
% 136.47/20.32 | | | | | REF_CLOSE: (1), (3), (6), (8), (9), (11), (12), (14), (15), (24),
% 136.47/20.32 | | | | | (27), (29), (36), (59), (60) are inconsistent by sub-proof
% 136.47/20.32 | | | | | #523.
% 136.47/20.32 | | | | |
% 136.47/20.32 | | | | End of split
% 136.47/20.32 | | | |
% 136.47/20.32 | | | End of split
% 136.47/20.32 | | |
% 136.47/20.32 | | End of split
% 136.47/20.32 | |
% 136.47/20.32 | End of split
% 136.47/20.32 |
% 136.47/20.32 End of proof
% 136.47/20.32
% 136.47/20.32 Sub-proof #523 shows that the following formulas are inconsistent:
% 136.47/20.32 ----------------------------------------------------------------
% 136.47/20.32 (1) op(e1, e1) = all_6_2
% 136.47/20.32 (2) ~ (all_40_2 = e0) | ( ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 &
% 136.47/20.32 $i(all_40_0)) | ( ~ (all_40_1 = e2) & op(e0, e0) = all_40_1 &
% 136.47/20.32 $i(all_40_1))
% 136.47/20.32 (3) ~ (all_52_11 = e2)
% 136.47/20.32 (4) all_40_2 = all_6_2
% 136.47/20.32 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.32 (6) ~ (e2 = e1)
% 136.47/20.32 (7) ~ (e3 = e2)
% 136.47/20.32 (8) ~ (all_52_11 = all_6_2)
% 136.47/20.32 (9) op(e0, e1) = all_52_11
% 136.47/20.32 (10) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 136.47/20.32 (11) op(e0, e0) = e2
% 136.47/20.32 (12) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.47/20.32 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.47/20.32 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0)
% 136.47/20.32 = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 136.47/20.32 $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~
% 136.47/20.32 (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 136.47/20.32 (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 136.47/20.32 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.47/20.32 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.47/20.32 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.47/20.32 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 136.47/20.32 op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.47/20.32 op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 136.47/20.32 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13
% 136.47/20.32 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 136.47/20.32 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1,
% 136.47/20.32 e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 136.47/20.32 $i(all_56_21) & $i(all_56_29))
% 136.47/20.32 (13) all_54_14 = all_52_11
% 136.47/20.32 (14) op(e2, e2) = e2
% 136.47/20.32 (15) op(e0, e0) = all_56_31
% 136.47/20.32
% 136.47/20.32 Begin of proof
% 136.47/20.32 |
% 136.47/20.32 | GROUND_INST: instantiating (5) with e2, all_56_31, e0, e0, simplifying with
% 136.47/20.32 | (11), (15) gives:
% 136.47/20.32 | (16) all_56_31 = e2
% 136.47/20.32 |
% 136.47/20.32 | BETA: splitting (12) gives:
% 136.47/20.32 |
% 136.47/20.32 | Case 1:
% 136.47/20.32 | |
% 136.47/20.32 | | (17) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 136.47/20.32 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.47/20.32 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.47/20.32 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9)
% 136.47/20.32 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 136.47/20.32 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 136.47/20.32 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 136.47/20.32 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 136.47/20.32 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 136.47/20.32 | | $i(all_56_27))
% 136.47/20.32 | |
% 136.47/20.32 | | REF_CLOSE: (5), (7), (14), (16), (17) are inconsistent by sub-proof #530.
% 136.47/20.32 | |
% 136.47/20.32 | Case 2:
% 136.47/20.32 | |
% 136.47/20.32 | | (18) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.47/20.32 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.47/20.32 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 136.47/20.32 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 136.47/20.32 | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 136.47/20.32 | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 136.47/20.32 | | ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 136.47/20.32 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 136.47/20.32 | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.47/20.32 | | $i(all_56_29))
% 136.47/20.32 | |
% 136.47/20.32 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (13), (16),
% 136.47/20.32 | | (18) are inconsistent by sub-proof #524.
% 136.47/20.32 | |
% 136.47/20.32 | End of split
% 136.47/20.32 |
% 136.47/20.32 End of proof
% 136.47/20.32
% 136.47/20.32 Sub-proof #524 shows that the following formulas are inconsistent:
% 136.47/20.32 ----------------------------------------------------------------
% 136.47/20.32 (1) op(e1, e1) = all_6_2
% 136.47/20.32 (2) ~ (all_40_2 = e0) | ( ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 &
% 136.47/20.32 $i(all_40_0)) | ( ~ (all_40_1 = e2) & op(e0, e0) = all_40_1 &
% 136.47/20.32 $i(all_40_1))
% 136.47/20.32 (3) ~ (all_52_11 = e2)
% 136.47/20.32 (4) all_56_31 = e2
% 136.47/20.32 (5) all_40_2 = all_6_2
% 136.47/20.32 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.32 (7) ~ (e2 = e1)
% 136.47/20.32 (8) ~ (all_52_11 = all_6_2)
% 136.47/20.32 (9) op(e0, e1) = all_52_11
% 136.47/20.32 (10) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 136.47/20.32 (11) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.47/20.32 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 136.47/20.32 op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.47/20.32 op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 136.47/20.32 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13
% 136.47/20.32 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 136.47/20.32 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1,
% 136.47/20.32 e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 136.47/20.32 $i(all_56_21) & $i(all_56_29))
% 136.47/20.32 (12) op(e0, e0) = e2
% 136.47/20.32 (13) all_54_14 = all_52_11
% 136.47/20.32
% 136.47/20.32 Begin of proof
% 136.47/20.32 |
% 136.47/20.32 | BETA: splitting (11) gives:
% 136.47/20.32 |
% 136.47/20.32 | Case 1:
% 136.47/20.32 | |
% 136.47/20.32 | | (14) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15
% 136.47/20.32 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) =
% 136.47/20.32 | | e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 136.47/20.32 | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 136.47/20.32 | | $i(all_56_23)
% 136.47/20.32 | |
% 136.47/20.32 | | ALPHA: (14) implies:
% 136.47/20.32 | | (15) ~ (all_56_23 = e1)
% 136.47/20.32 | | (16) op(e0, e1) = all_56_23
% 136.47/20.32 | | (17) op(e1, e1) = e0
% 136.47/20.32 | |
% 136.47/20.32 | | GROUND_INST: instantiating (6) with all_52_11, all_56_23, e1, e0,
% 136.47/20.32 | | simplifying with (9), (16) gives:
% 136.47/20.32 | | (18) all_56_23 = all_52_11
% 136.47/20.32 | |
% 136.47/20.32 | | GROUND_INST: instantiating (6) with all_6_2, e0, e1, e1, simplifying with
% 136.47/20.32 | | (1), (17) gives:
% 136.47/20.32 | | (19) all_6_2 = e0
% 136.47/20.32 | |
% 136.47/20.32 | | COMBINE_EQS: (5), (19) imply:
% 136.47/20.32 | | (20) all_40_2 = e0
% 136.47/20.32 | |
% 136.47/20.32 | | REDUCE: (15), (18) imply:
% 136.47/20.32 | | (21) ~ (all_52_11 = e1)
% 136.47/20.32 | |
% 136.47/20.32 | | REDUCE: (8), (19) imply:
% 136.47/20.32 | | (22) ~ (all_52_11 = e0)
% 136.47/20.32 | |
% 136.47/20.32 | | BETA: splitting (2) gives:
% 136.47/20.32 | |
% 136.47/20.32 | | Case 1:
% 136.47/20.32 | | |
% 136.47/20.32 | | | (23) ~ (all_40_2 = e0)
% 136.47/20.32 | | |
% 136.47/20.32 | | | REDUCE: (20), (23) imply:
% 136.47/20.32 | | | (24) $false
% 136.47/20.32 | | |
% 136.47/20.32 | | | CLOSE: (24) is inconsistent.
% 136.47/20.32 | | |
% 136.47/20.32 | | Case 2:
% 136.47/20.32 | | |
% 136.47/20.32 | | | (25) ( ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 & $i(all_40_0)) | ( ~
% 136.47/20.32 | | | (all_40_1 = e2) & op(e0, e0) = all_40_1 & $i(all_40_1))
% 136.47/20.32 | | |
% 136.47/20.32 | | | BETA: splitting (10) gives:
% 136.47/20.32 | | |
% 136.47/20.32 | | | Case 1:
% 136.47/20.32 | | | |
% 136.47/20.32 | | | | (26) all_54_14 = e3
% 136.47/20.32 | | | |
% 136.47/20.32 | | | | COMBINE_EQS: (13), (26) imply:
% 136.47/20.32 | | | | (27) all_52_11 = e3
% 136.47/20.32 | | | |
% 136.47/20.32 | | | | SIMP: (27) implies:
% 136.47/20.32 | | | | (28) all_52_11 = e3
% 136.47/20.32 | | | |
% 136.47/20.32 | | | | REDUCE: (9), (28) imply:
% 136.47/20.32 | | | | (29) op(e0, e1) = e3
% 136.47/20.32 | | | |
% 136.47/20.32 | | | | BETA: splitting (25) gives:
% 136.47/20.32 | | | |
% 136.47/20.32 | | | | Case 1:
% 136.47/20.32 | | | | |
% 136.47/20.32 | | | | | (30) ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 & $i(all_40_0)
% 136.47/20.32 | | | | |
% 136.47/20.32 | | | | | ALPHA: (30) implies:
% 136.47/20.32 | | | | | (31) ~ (all_40_0 = e3)
% 136.47/20.32 | | | | | (32) op(e0, e1) = all_40_0
% 136.47/20.32 | | | | |
% 136.47/20.32 | | | | | REF_CLOSE: (6), (29), (31), (32) are inconsistent by sub-proof #529.
% 136.47/20.32 | | | | |
% 136.47/20.32 | | | | Case 2:
% 136.47/20.32 | | | | |
% 136.47/20.32 | | | | | (33) ~ (all_40_1 = e2) & op(e0, e0) = all_40_1 & $i(all_40_1)
% 136.47/20.32 | | | | |
% 136.47/20.32 | | | | | REF_CLOSE: (6), (12), (33) are inconsistent by sub-proof #528.
% 136.47/20.32 | | | | |
% 136.47/20.32 | | | | End of split
% 136.47/20.32 | | | |
% 136.47/20.32 | | | Case 2:
% 136.47/20.32 | | | |
% 136.47/20.32 | | | | (34) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 136.47/20.32 | | | |
% 136.47/20.32 | | | | REF_CLOSE: (3), (13), (21), (22), (34) are inconsistent by sub-proof
% 136.47/20.32 | | | | #526.
% 136.47/20.32 | | | |
% 136.47/20.32 | | | End of split
% 136.47/20.32 | | |
% 136.47/20.32 | | End of split
% 136.47/20.32 | |
% 136.47/20.32 | Case 2:
% 136.47/20.32 | |
% 136.47/20.32 | | (35) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13
% 136.47/20.32 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 136.47/20.32 | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1,
% 136.47/20.32 | | e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 136.47/20.32 | | $i(all_56_21) & $i(all_56_29)
% 136.47/20.32 | |
% 136.47/20.32 | | REF_CLOSE: (4), (7), (35) are inconsistent by sub-proof #525.
% 136.47/20.32 | |
% 136.47/20.32 | End of split
% 136.47/20.32 |
% 136.47/20.32 End of proof
% 136.47/20.32
% 136.47/20.32 Sub-proof #525 shows that the following formulas are inconsistent:
% 136.47/20.32 ----------------------------------------------------------------
% 136.47/20.32 (1) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 136.47/20.32 e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5
% 136.47/20.32 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 136.47/20.32 all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 136.47/20.32 $i(all_56_21) & $i(all_56_29)
% 136.47/20.32 (2) all_56_31 = e2
% 136.47/20.32 (3) ~ (e2 = e1)
% 136.47/20.32
% 136.47/20.32 Begin of proof
% 136.47/20.32 |
% 136.47/20.32 | ALPHA: (1) implies:
% 136.47/20.32 | (4) all_56_31 = e1
% 136.47/20.32 |
% 136.47/20.32 | COMBINE_EQS: (2), (4) imply:
% 136.47/20.32 | (5) e2 = e1
% 136.47/20.32 |
% 136.47/20.32 | REDUCE: (3), (5) imply:
% 136.47/20.32 | (6) $false
% 136.47/20.32 |
% 136.47/20.32 | CLOSE: (6) is inconsistent.
% 136.47/20.32 |
% 136.47/20.32 End of proof
% 136.47/20.32
% 136.47/20.32 Sub-proof #526 shows that the following formulas are inconsistent:
% 136.47/20.32 ----------------------------------------------------------------
% 136.47/20.32 (1) ~ (all_52_11 = e1)
% 136.47/20.32 (2) ~ (all_52_11 = e2)
% 136.47/20.32 (3) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 136.47/20.32 (4) ~ (all_52_11 = e0)
% 136.47/20.32 (5) all_54_14 = all_52_11
% 136.47/20.32
% 136.47/20.32 Begin of proof
% 136.47/20.32 |
% 136.47/20.32 | BETA: splitting (3) gives:
% 136.47/20.32 |
% 136.47/20.32 | Case 1:
% 136.47/20.32 | |
% 136.47/20.32 | | (6) all_54_14 = e2
% 136.47/20.32 | |
% 136.47/20.32 | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #527.
% 136.47/20.32 | |
% 136.47/20.32 | Case 2:
% 136.47/20.32 | |
% 136.47/20.32 | | (7) all_54_14 = e1 | all_54_14 = e0
% 136.47/20.32 | |
% 136.47/20.32 | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #755.
% 136.47/20.32 | |
% 136.47/20.32 | End of split
% 136.47/20.32 |
% 136.47/20.32 End of proof
% 136.47/20.32
% 136.47/20.32 Sub-proof #527 shows that the following formulas are inconsistent:
% 136.47/20.32 ----------------------------------------------------------------
% 136.47/20.32 (1) all_54_14 = all_52_11
% 136.47/20.33 (2) all_54_14 = e2
% 136.47/20.33 (3) ~ (all_52_11 = e2)
% 136.47/20.33
% 136.47/20.33 Begin of proof
% 136.47/20.33 |
% 136.47/20.33 | COMBINE_EQS: (1), (2) imply:
% 136.47/20.33 | (4) all_52_11 = e2
% 136.47/20.33 |
% 136.47/20.33 | SIMP: (4) implies:
% 136.47/20.33 | (5) all_52_11 = e2
% 136.47/20.33 |
% 136.47/20.33 | REDUCE: (3), (5) imply:
% 136.47/20.33 | (6) $false
% 136.47/20.33 |
% 136.47/20.33 | CLOSE: (6) is inconsistent.
% 136.47/20.33 |
% 136.47/20.33 End of proof
% 136.47/20.33
% 136.47/20.33 Sub-proof #528 shows that the following formulas are inconsistent:
% 136.47/20.33 ----------------------------------------------------------------
% 136.47/20.33 (1) ~ (all_40_1 = e2) & op(e0, e0) = all_40_1 & $i(all_40_1)
% 136.47/20.33 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.33 (3) op(e0, e0) = e2
% 136.47/20.33
% 136.47/20.33 Begin of proof
% 136.47/20.33 |
% 136.47/20.33 | ALPHA: (1) implies:
% 136.47/20.33 | (4) ~ (all_40_1 = e2)
% 136.47/20.33 | (5) op(e0, e0) = all_40_1
% 136.47/20.33 |
% 136.47/20.33 | GROUND_INST: instantiating (2) with e2, all_40_1, e0, e0, simplifying with
% 136.47/20.33 | (3), (5) gives:
% 136.47/20.33 | (6) all_40_1 = e2
% 136.47/20.33 |
% 136.47/20.33 | REDUCE: (4), (6) imply:
% 136.47/20.33 | (7) $false
% 136.47/20.33 |
% 136.47/20.33 | CLOSE: (7) is inconsistent.
% 136.47/20.33 |
% 136.47/20.33 End of proof
% 136.47/20.33
% 136.47/20.33 Sub-proof #529 shows that the following formulas are inconsistent:
% 136.47/20.33 ----------------------------------------------------------------
% 136.47/20.33 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.33 (2) op(e0, e1) = all_40_0
% 136.47/20.33 (3) op(e0, e1) = e3
% 136.47/20.33 (4) ~ (all_40_0 = e3)
% 136.47/20.33
% 136.47/20.33 Begin of proof
% 136.47/20.33 |
% 136.47/20.33 | GROUND_INST: instantiating (1) with e3, all_40_0, e1, e0, simplifying with
% 136.47/20.33 | (2), (3) gives:
% 136.47/20.33 | (5) all_40_0 = e3
% 136.47/20.33 |
% 136.47/20.33 | REDUCE: (4), (5) imply:
% 136.47/20.33 | (6) $false
% 136.47/20.33 |
% 136.47/20.33 | CLOSE: (6) is inconsistent.
% 136.47/20.33 |
% 136.47/20.33 End of proof
% 136.47/20.33
% 136.47/20.33 Sub-proof #530 shows that the following formulas are inconsistent:
% 136.47/20.33 ----------------------------------------------------------------
% 136.47/20.33 (1) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2)
% 136.47/20.33 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 136.47/20.33 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25
% 136.47/20.33 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 136.47/20.33 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3)
% 136.47/20.33 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.47/20.33 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 136.47/20.33 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) &
% 136.47/20.33 $i(all_56_11) & $i(all_56_19) & $i(all_56_27))
% 136.47/20.33 (2) all_56_31 = e2
% 136.47/20.33 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.33 (4) ~ (e3 = e2)
% 136.47/20.33 (5) op(e2, e2) = e2
% 136.47/20.33
% 136.47/20.33 Begin of proof
% 136.47/20.33 |
% 136.47/20.33 | BETA: splitting (1) gives:
% 136.47/20.33 |
% 136.47/20.33 | Case 1:
% 136.47/20.33 | |
% 136.47/20.33 | | (6) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.47/20.33 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.47/20.33 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.47/20.33 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 136.47/20.33 | | $i(all_56_17) & $i(all_56_25)
% 136.47/20.33 | |
% 136.47/20.33 | | ALPHA: (6) implies:
% 136.47/20.33 | | (7) all_56_31 = e3
% 136.47/20.33 | |
% 136.47/20.33 | | REF_CLOSE: (2), (4), (7) are inconsistent by sub-proof #532.
% 136.47/20.33 | |
% 136.47/20.33 | Case 2:
% 136.47/20.33 | |
% 136.47/20.33 | | (8) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11
% 136.47/20.33 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 136.47/20.33 | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 136.47/20.33 | | e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 136.47/20.33 | | $i(all_56_19) & $i(all_56_27)
% 136.47/20.33 | |
% 136.47/20.33 | | ALPHA: (8) implies:
% 136.47/20.33 | | (9) ~ (all_56_11 = e2)
% 136.47/20.33 | | (10) op(e2, e2) = all_56_11
% 136.47/20.33 | |
% 136.47/20.33 | | REF_CLOSE: (3), (5), (9), (10) are inconsistent by sub-proof #531.
% 136.47/20.33 | |
% 136.47/20.33 | End of split
% 136.47/20.33 |
% 136.47/20.33 End of proof
% 136.47/20.33
% 136.47/20.33 Sub-proof #531 shows that the following formulas are inconsistent:
% 136.47/20.33 ----------------------------------------------------------------
% 136.47/20.33 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.33 (2) op(e2, e2) = all_56_11
% 136.47/20.33 (3) op(e2, e2) = e2
% 136.47/20.33 (4) ~ (all_56_11 = e2)
% 136.47/20.33
% 136.47/20.33 Begin of proof
% 136.47/20.33 |
% 136.47/20.33 | GROUND_INST: instantiating (1) with e2, all_56_11, e2, e2, simplifying with
% 136.47/20.33 | (2), (3) gives:
% 136.47/20.33 | (5) all_56_11 = e2
% 136.47/20.33 |
% 136.47/20.33 | REDUCE: (4), (5) imply:
% 136.47/20.33 | (6) $false
% 136.47/20.33 |
% 136.47/20.33 | CLOSE: (6) is inconsistent.
% 136.47/20.33 |
% 136.47/20.33 End of proof
% 136.47/20.33
% 136.47/20.33 Sub-proof #532 shows that the following formulas are inconsistent:
% 136.47/20.33 ----------------------------------------------------------------
% 136.47/20.33 (1) all_56_31 = e3
% 136.47/20.33 (2) all_56_31 = e2
% 136.47/20.33 (3) ~ (e3 = e2)
% 136.47/20.33
% 136.47/20.33 Begin of proof
% 136.47/20.33 |
% 136.47/20.33 | COMBINE_EQS: (1), (2) imply:
% 136.47/20.33 | (4) e3 = e2
% 136.47/20.33 |
% 136.47/20.33 | SIMP: (4) implies:
% 136.47/20.33 | (5) e3 = e2
% 136.47/20.33 |
% 136.47/20.33 | REDUCE: (3), (5) imply:
% 136.47/20.33 | (6) $false
% 136.47/20.33 |
% 136.47/20.33 | CLOSE: (6) is inconsistent.
% 136.47/20.33 |
% 136.47/20.33 End of proof
% 136.47/20.33
% 136.47/20.33 Sub-proof #533 shows that the following formulas are inconsistent:
% 136.47/20.33 ----------------------------------------------------------------
% 136.47/20.33 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.33 (2) ~ (all_10_2 = e0)
% 136.47/20.33 (3) op(e3, e3) = all_10_2
% 136.47/20.33 (4) ~ (all_52_1 = e2)
% 136.47/20.33 (5) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.47/20.33 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 136.47/20.33 op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.47/20.33 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.47/20.33 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 &
% 136.47/20.33 all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~
% 136.47/20.33 (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3,
% 136.47/20.33 e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 136.47/20.33 op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 136.47/20.33 $i(all_56_17) & $i(all_56_25))
% 136.47/20.33 (6) op(e2, e3) = all_52_1
% 136.47/20.33
% 136.47/20.33 Begin of proof
% 136.47/20.33 |
% 136.47/20.33 | BETA: splitting (5) gives:
% 136.47/20.33 |
% 136.47/20.33 | Case 1:
% 136.47/20.33 | |
% 136.47/20.33 | | (7) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.47/20.33 | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 136.47/20.33 | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.47/20.33 | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.47/20.33 | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)
% 136.47/20.33 | |
% 136.47/20.33 | | ALPHA: (7) implies:
% 136.47/20.33 | | (8) op(e3, e3) = e0
% 136.47/20.33 | |
% 136.47/20.33 | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #534.
% 136.47/20.33 | |
% 136.47/20.33 | Case 2:
% 136.47/20.33 | |
% 136.47/20.33 | | (9) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.47/20.33 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.47/20.33 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.47/20.33 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1)
% 136.47/20.33 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)
% 136.47/20.33 | |
% 136.47/20.33 | | ALPHA: (9) implies:
% 136.47/20.33 | | (10) op(e2, e3) = e2
% 136.47/20.33 | |
% 136.47/20.33 | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #779.
% 136.47/20.33 | |
% 136.47/20.33 | End of split
% 136.47/20.33 |
% 136.47/20.33 End of proof
% 136.47/20.33
% 136.47/20.33 Sub-proof #534 shows that the following formulas are inconsistent:
% 136.47/20.33 ----------------------------------------------------------------
% 136.47/20.33 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.33 (2) op(e3, e3) = all_10_2
% 136.47/20.33 (3) op(e3, e3) = e0
% 136.47/20.33 (4) ~ (all_10_2 = e0)
% 136.47/20.33
% 136.47/20.33 Begin of proof
% 136.47/20.33 |
% 136.47/20.33 | GROUND_INST: instantiating (1) with all_10_2, e0, e3, e3, simplifying with
% 136.47/20.33 | (2), (3) gives:
% 136.47/20.33 | (5) all_10_2 = e0
% 136.47/20.33 |
% 136.47/20.33 | REDUCE: (4), (5) imply:
% 136.47/20.33 | (6) $false
% 136.47/20.33 |
% 136.47/20.33 | CLOSE: (6) is inconsistent.
% 136.47/20.33 |
% 136.47/20.33 End of proof
% 136.47/20.33
% 136.47/20.33 Sub-proof #535 shows that the following formulas are inconsistent:
% 136.47/20.33 ----------------------------------------------------------------
% 136.47/20.33 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.33 (2) op(e3, e3) = all_10_2
% 136.47/20.33 (3) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2)
% 136.47/20.33 (4) ~ (all_52_1 = e2)
% 136.47/20.33 (5) ~ (all_10_2 = e2)
% 136.47/20.33 (6) op(e2, e3) = all_52_1
% 136.47/20.33
% 136.47/20.33 Begin of proof
% 136.47/20.33 |
% 136.47/20.33 | BETA: splitting (3) gives:
% 136.47/20.33 |
% 136.47/20.33 | Case 1:
% 136.47/20.33 | |
% 136.47/20.33 | | (7) all_57_0 = e2 & op(e3, e3) = e2
% 136.47/20.33 | |
% 136.47/20.33 | | ALPHA: (7) implies:
% 136.47/20.33 | | (8) op(e3, e3) = e2
% 136.47/20.33 | |
% 136.47/20.33 | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #536.
% 136.47/20.33 | |
% 136.47/20.33 | Case 2:
% 136.47/20.33 | |
% 136.47/20.33 | | (9) all_57_2 = e2 & op(e2, e3) = e2
% 136.47/20.33 | |
% 136.47/20.33 | | ALPHA: (9) implies:
% 136.47/20.33 | | (10) op(e2, e3) = e2
% 136.47/20.33 | |
% 136.47/20.33 | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #779.
% 136.47/20.33 | |
% 136.47/20.33 | End of split
% 136.47/20.33 |
% 136.47/20.33 End of proof
% 136.47/20.33
% 136.47/20.33 Sub-proof #536 shows that the following formulas are inconsistent:
% 136.47/20.33 ----------------------------------------------------------------
% 136.47/20.33 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.33 (2) op(e3, e3) = all_10_2
% 136.47/20.33 (3) op(e3, e3) = e2
% 136.47/20.33 (4) ~ (all_10_2 = e2)
% 136.47/20.33
% 136.47/20.33 Begin of proof
% 136.47/20.33 |
% 136.47/20.33 | GROUND_INST: instantiating (1) with all_10_2, e2, e3, e3, simplifying with
% 136.47/20.33 | (2), (3) gives:
% 136.47/20.33 | (5) all_10_2 = e2
% 136.47/20.33 |
% 136.47/20.33 | REDUCE: (4), (5) imply:
% 136.47/20.33 | (6) $false
% 136.47/20.33 |
% 136.47/20.33 | CLOSE: (6) is inconsistent.
% 136.47/20.33 |
% 136.47/20.33 End of proof
% 136.47/20.33
% 136.47/20.33 Sub-proof #537 shows that the following formulas are inconsistent:
% 136.47/20.33 ----------------------------------------------------------------
% 136.47/20.33 (1) op(e1, e1) = all_6_2
% 136.47/20.33 (2) op(e0, e0) = e3
% 136.47/20.33 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.33 (4) ~ (e3 = e0)
% 136.47/20.33 (5) op(e3, e0) = e0
% 136.47/20.33 (6) op(e1, e1) = e3
% 136.47/20.33 (7) op(e0, e2) = all_52_7
% 136.47/20.33 (8) ~ (all_6_2 = e2)
% 136.47/20.33 (9) ~ (all_52_7 = e0)
% 136.47/20.33 (10) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 136.47/20.33 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 136.47/20.33 all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 136.47/20.33 e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) &
% 136.47/20.33 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) =
% 136.47/20.33 all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~
% 136.47/20.33 (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 136.47/20.33 (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 &
% 136.47/20.33 op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0
% 136.47/20.33 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.47/20.33 (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 136.47/20.33 (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.47/20.33 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.47/20.33 all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.47/20.33 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.47/20.33 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.47/20.33 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.47/20.33 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 136.47/20.33 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 136.47/20.33 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 136.47/20.33 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 136.47/20.33 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 136.47/20.33 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 136.47/20.33 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.47/20.33 $i(all_56_29))))
% 136.47/20.33 (11) ~ (e3 = e1)
% 136.47/20.33
% 136.47/20.33 Begin of proof
% 136.47/20.33 |
% 136.47/20.33 | BETA: splitting (10) gives:
% 136.47/20.33 |
% 136.47/20.33 | Case 1:
% 136.47/20.33 | |
% 136.47/20.33 | | (12) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11
% 136.47/20.33 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 136.47/20.33 | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 136.47/20.33 | | e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3)
% 136.47/20.33 | | & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)
% 136.47/20.33 | |
% 136.47/20.33 | | ALPHA: (12) implies:
% 136.47/20.33 | | (13) op(e1, e1) = e2
% 136.47/20.33 | |
% 136.47/20.33 | | REF_CLOSE: (1), (3), (8), (13) are inconsistent by sub-proof #767.
% 136.47/20.33 | |
% 136.47/20.33 | Case 2:
% 136.47/20.33 | |
% 136.47/20.33 | | (14) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31
% 136.47/20.33 | | = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 =
% 136.47/20.33 | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2)
% 136.47/20.33 | | = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 136.47/20.33 | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 136.47/20.33 | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3
% 136.47/20.33 | | = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 136.47/20.33 | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 136.47/20.33 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 136.47/20.33 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 136.47/20.33 | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7
% 136.47/20.33 | | = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 136.47/20.33 | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0,
% 136.47/20.33 | | e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) =
% 136.47/20.33 | | all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 136.47/20.33 | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 136.47/20.33 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 136.47/20.33 | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.47/20.33 | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 136.47/20.33 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)))
% 136.47/20.33 | |
% 136.47/20.33 | | ALPHA: (14) implies:
% 136.47/20.33 | | (15) op(e0, e0) = all_56_31
% 136.47/20.33 | | (16) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 136.47/20.33 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.47/20.33 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.47/20.33 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9)
% 136.47/20.33 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 136.47/20.33 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 136.47/20.33 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 136.47/20.33 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 136.47/20.33 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 136.47/20.33 | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 =
% 136.47/20.33 | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31
% 136.47/20.33 | | = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 136.47/20.33 | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 136.47/20.33 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 &
% 136.47/20.33 | | all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.47/20.33 | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 136.47/20.33 | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 136.47/20.33 | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 136.47/20.33 | | $i(all_56_21) & $i(all_56_29))
% 136.47/20.33 | |
% 136.47/20.33 | | BETA: splitting (16) gives:
% 136.47/20.33 | |
% 136.47/20.33 | | Case 1:
% 136.47/20.33 | | |
% 136.47/20.33 | | | (17) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 136.47/20.33 | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 136.47/20.33 | | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) =
% 136.47/20.33 | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 136.47/20.33 | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.47/20.33 | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 136.47/20.33 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.47/20.33 | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.47/20.33 | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.47/20.33 | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27))
% 136.47/20.33 | | |
% 136.47/20.33 | | | REF_CLOSE: (3), (5), (7), (9), (17) are inconsistent by sub-proof #538.
% 136.47/20.33 | | |
% 136.47/20.33 | | Case 2:
% 136.47/20.33 | | |
% 136.47/20.33 | | | (18) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.47/20.33 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.47/20.33 | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 136.47/20.33 | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 136.47/20.33 | | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 =
% 136.47/20.33 | | | e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 136.47/20.33 | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2)
% 136.47/20.33 | | | = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 136.47/20.33 | | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.47/20.33 | | | $i(all_56_29))
% 136.47/20.33 | | |
% 136.47/20.33 | | | BETA: splitting (18) gives:
% 136.47/20.33 | | |
% 136.47/20.33 | | | Case 1:
% 136.47/20.33 | | | |
% 136.47/20.33 | | | | (19) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.47/20.33 | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.47/20.33 | | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 136.47/20.33 | | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 136.47/20.33 | | | | $i(all_56_15) & $i(all_56_23)
% 136.47/20.33 | | | |
% 136.47/20.33 | | | | ALPHA: (19) implies:
% 136.47/20.33 | | | | (20) op(e1, e1) = e0
% 136.47/20.33 | | | |
% 136.47/20.33 | | | | REF_CLOSE: (3), (4), (6), (20) are inconsistent by sub-proof #753.
% 136.47/20.33 | | | |
% 136.47/20.33 | | | Case 2:
% 136.47/20.33 | | | |
% 136.47/20.33 | | | | (21) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 136.47/20.33 | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 136.47/20.33 | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.47/20.33 | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 136.47/20.33 | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 136.47/20.33 | | | |
% 136.47/20.33 | | | | ALPHA: (21) implies:
% 136.47/20.33 | | | | (22) all_56_31 = e1
% 136.47/20.33 | | | |
% 136.47/20.33 | | | | REDUCE: (15), (22) imply:
% 136.47/20.33 | | | | (23) op(e0, e0) = e1
% 136.47/20.33 | | | |
% 136.47/20.33 | | | | REF_CLOSE: (2), (3), (11), (23) are inconsistent by sub-proof #606.
% 136.47/20.33 | | | |
% 136.47/20.33 | | | End of split
% 136.47/20.33 | | |
% 136.47/20.33 | | End of split
% 136.47/20.33 | |
% 136.47/20.33 | End of split
% 136.47/20.33 |
% 136.47/20.33 End of proof
% 136.47/20.33
% 136.47/20.33 Sub-proof #538 shows that the following formulas are inconsistent:
% 136.47/20.33 ----------------------------------------------------------------
% 136.47/20.33 (1) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2)
% 136.47/20.33 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 136.47/20.33 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25
% 136.47/20.33 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 136.47/20.33 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3)
% 136.47/20.33 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.47/20.33 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 136.47/20.33 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) &
% 136.47/20.33 $i(all_56_11) & $i(all_56_19) & $i(all_56_27))
% 136.47/20.33 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.33 (3) op(e3, e0) = e0
% 136.47/20.33 (4) op(e0, e2) = all_52_7
% 136.47/20.33 (5) ~ (all_52_7 = e0)
% 136.47/20.33
% 136.47/20.33 Begin of proof
% 136.47/20.33 |
% 136.47/20.33 | BETA: splitting (1) gives:
% 136.47/20.33 |
% 136.47/20.33 | Case 1:
% 136.47/20.33 | |
% 136.47/20.33 | | (6) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.47/20.33 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.47/20.33 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.47/20.33 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 136.47/20.33 | | $i(all_56_17) & $i(all_56_25)
% 136.47/20.33 | |
% 136.47/20.33 | | ALPHA: (6) implies:
% 136.47/20.33 | | (7) ~ (all_56_25 = e0)
% 136.47/20.33 | | (8) op(e3, e0) = all_56_25
% 136.47/20.33 | |
% 136.47/20.33 | | REF_CLOSE: (2), (3), (7), (8) are inconsistent by sub-proof #642.
% 136.47/20.33 | |
% 136.47/20.33 | Case 2:
% 136.47/20.33 | |
% 136.47/20.33 | | (9) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11
% 136.47/20.33 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 136.47/20.33 | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 136.47/20.33 | | e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 136.47/20.33 | | $i(all_56_19) & $i(all_56_27)
% 136.47/20.33 | |
% 136.47/20.33 | | ALPHA: (9) implies:
% 136.47/20.33 | | (10) op(e0, e2) = e0
% 136.47/20.33 | |
% 136.47/20.33 | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #545.
% 136.47/20.33 | |
% 136.47/20.33 | End of split
% 136.47/20.33 |
% 136.47/20.33 End of proof
% 136.47/20.33
% 136.47/20.33 Sub-proof #539 shows that the following formulas are inconsistent:
% 136.47/20.33 ----------------------------------------------------------------
% 136.47/20.33 (1) ~ (all_42_0 = e1)
% 136.47/20.33 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.33 (3) op(e0, e2) = all_42_0
% 136.47/20.33 (4) ~ (all_56_15 = e2)
% 136.47/20.33 (5) op(e0, e2) = all_56_15
% 136.47/20.33 (6) ~ (all_42_0 = e0)
% 136.47/20.33 (7) all_54_13 = all_42_0
% 136.47/20.33 (8) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 136.47/20.33
% 136.47/20.33 Begin of proof
% 136.47/20.33 |
% 136.47/20.33 | BETA: splitting (8) gives:
% 136.47/20.33 |
% 136.47/20.33 | Case 1:
% 136.47/20.33 | |
% 136.47/20.33 | | (9) all_54_13 = e2
% 136.47/20.33 | |
% 136.47/20.33 | | COMBINE_EQS: (7), (9) imply:
% 136.47/20.33 | | (10) all_42_0 = e2
% 136.47/20.33 | |
% 136.47/20.33 | | SIMP: (10) implies:
% 136.47/20.33 | | (11) all_42_0 = e2
% 136.47/20.33 | |
% 136.47/20.33 | | REDUCE: (3), (11) imply:
% 136.47/20.33 | | (12) op(e0, e2) = e2
% 136.47/20.33 | |
% 136.47/20.33 | | REF_CLOSE: (2), (4), (5), (12) are inconsistent by sub-proof #609.
% 136.47/20.33 | |
% 136.47/20.33 | Case 2:
% 136.47/20.33 | |
% 136.47/20.33 | | (13) all_54_13 = e1 | all_54_13 = e0
% 136.47/20.33 | |
% 136.47/20.33 | | REF_CLOSE: (1), (6), (7), (13) are inconsistent by sub-proof #604.
% 136.47/20.33 | |
% 136.47/20.33 | End of split
% 136.47/20.33 |
% 136.47/20.33 End of proof
% 136.47/20.33
% 136.47/20.33 Sub-proof #540 shows that the following formulas are inconsistent:
% 136.47/20.33 ----------------------------------------------------------------
% 136.47/20.33 (1) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2)
% 136.47/20.33 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 136.47/20.33 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25
% 136.47/20.33 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) &
% 136.47/20.33 $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~
% 136.47/20.33 (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 136.47/20.33 (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) =
% 136.47/20.33 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0)
% 136.47/20.33 = all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.47/20.33 $i(all_56_29))
% 136.47/20.33 (2) op(e2, e2) = e0
% 136.47/20.33 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.33 (4) op(e3, e0) = e0
% 136.47/20.33 (5) ~ (e1 = e0)
% 136.47/20.33
% 136.47/20.33 Begin of proof
% 136.47/20.33 |
% 136.47/20.33 | BETA: splitting (1) gives:
% 136.47/20.33 |
% 136.47/20.33 | Case 1:
% 136.47/20.33 | |
% 136.47/20.33 | | (6) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.47/20.33 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.47/20.33 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.47/20.33 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1)
% 136.47/20.33 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)
% 136.47/20.33 | |
% 136.47/20.33 | | ALPHA: (6) implies:
% 136.47/20.33 | | (7) ~ (all_56_25 = e0)
% 136.47/20.33 | | (8) op(e3, e0) = all_56_25
% 136.47/20.33 | |
% 136.47/20.33 | | REF_CLOSE: (3), (4), (7), (8) are inconsistent by sub-proof #642.
% 136.47/20.33 | |
% 136.47/20.33 | Case 2:
% 136.47/20.33 | |
% 136.47/20.33 | | (9) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13
% 136.47/20.33 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1
% 136.47/20.33 | | & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 136.47/20.33 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 136.47/20.33 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 136.47/20.33 | |
% 136.47/20.33 | | ALPHA: (9) implies:
% 136.47/20.33 | | (10) op(e2, e2) = e1
% 136.47/20.33 | |
% 136.47/20.33 | | REF_CLOSE: (2), (3), (5), (10) are inconsistent by sub-proof #675.
% 136.47/20.33 | |
% 136.47/20.33 | End of split
% 136.47/20.33 |
% 136.47/20.33 End of proof
% 136.47/20.33
% 136.47/20.33 Sub-proof #541 shows that the following formulas are inconsistent:
% 136.47/20.33 ----------------------------------------------------------------
% 136.47/20.33 (1) all_54_0 = all_10_2
% 136.47/20.33 (2) op(e0, e0) = all_4_2
% 136.47/20.33 (3) op(e1, e1) = all_6_2
% 136.47/20.33 (4) op(e2, e2) = e0
% 136.47/20.33 (5) op(e2, e0) = all_52_13
% 136.47/20.33 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.33 (7) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 136.47/20.33 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 136.47/20.33 (8) op(e1, e1) = e3
% 136.47/20.33 (9) op(e0, e2) = all_52_7
% 136.47/20.33 (10) ~ (all_52_12 = all_10_2)
% 136.47/20.33 (11) ~ (all_10_2 = e0)
% 136.47/20.33 (12) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 136.47/20.33 (13) ~ (all_4_2 = e1)
% 136.47/20.33 (14) ~ (all_6_2 = e2)
% 136.47/20.34 (15) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 136.47/20.34 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 136.47/20.34 op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 136.47/20.34 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 136.47/20.34 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 136.47/20.34 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.47/20.34 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 136.47/20.34 = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.47/20.34 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 136.47/20.34 $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~
% 136.47/20.34 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 136.47/20.34 (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) =
% 136.47/20.34 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0,
% 136.47/20.34 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 136.47/20.34 $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3)
% 136.47/20.34 & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 136.47/20.34 op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17
% 136.47/20.34 & op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 136.47/20.34 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.47/20.34 (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.47/20.34 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.47/20.34 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0)
% 136.47/20.34 = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) &
% 136.47/20.34 $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 &
% 136.47/20.34 all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.47/20.34 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 136.47/20.34 = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.47/20.34 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 136.47/20.34 $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~
% 136.47/20.34 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 136.47/20.34 (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 136.47/20.34 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0,
% 136.47/20.34 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 136.47/20.34 $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3)
% 136.47/20.34 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.47/20.34 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.47/20.34 all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2
% 136.47/20.34 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.47/20.34 (op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 =
% 136.47/20.34 e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 136.47/20.34 & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) =
% 136.47/20.34 all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 136.47/20.34 op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 136.47/20.34 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 136.47/20.34 e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 136.47/20.34 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 136.47/20.34 e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.47/20.34 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.47/20.34 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.47/20.34 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.47/20.34 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 136.47/20.34 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 136.47/20.34 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 136.47/20.34 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 136.47/20.34 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 136.47/20.34 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 136.47/20.34 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.47/20.34 $i(all_56_29))))
% 136.47/20.34 (16) op(e3, e3) = all_10_2
% 136.47/20.34 (17) ~ (all_52_7 = e0)
% 136.47/20.34 (18) ~ (all_52_9 = e3)
% 136.47/20.34 (19) op(e2, e1) = all_52_9
% 136.47/20.34 (20) ~ (all_52_1 = all_10_2)
% 136.47/20.34 (21) op(e3, e0) = all_52_12
% 136.47/20.34 (22) ~ (all_10_2 = e2)
% 136.47/20.34 (23) op(e2, e3) = all_52_1
% 136.47/20.34 (24) ~ (e1 = e0)
% 136.47/20.34 (25) ~ (all_10_2 = e1)
% 136.47/20.34
% 136.47/20.34 Begin of proof
% 136.47/20.34 |
% 136.47/20.34 | BETA: splitting (12) gives:
% 136.47/20.34 |
% 136.47/20.34 | Case 1:
% 136.47/20.34 | |
% 136.47/20.34 | | (26) all_54_0 = e3
% 136.47/20.34 | |
% 136.47/20.34 | | COMBINE_EQS: (1), (26) imply:
% 136.47/20.34 | | (27) all_10_2 = e3
% 136.47/20.34 | |
% 136.47/20.34 | | SIMP: (27) implies:
% 136.47/20.34 | | (28) all_10_2 = e3
% 136.47/20.34 | |
% 136.47/20.34 | | REDUCE: (20), (28) imply:
% 136.47/20.34 | | (29) ~ (all_52_1 = e3)
% 136.47/20.34 | |
% 136.47/20.34 | | REDUCE: (10), (28) imply:
% 136.47/20.34 | | (30) ~ (all_52_12 = e3)
% 136.47/20.34 | |
% 136.47/20.34 | | REDUCE: (22), (28) imply:
% 136.47/20.34 | | (31) ~ (e3 = e2)
% 136.47/20.34 | |
% 136.47/20.34 | | REDUCE: (25), (28) imply:
% 136.47/20.34 | | (32) ~ (e3 = e1)
% 136.47/20.34 | |
% 136.47/20.34 | | REDUCE: (11), (28) imply:
% 136.47/20.34 | | (33) ~ (e3 = e0)
% 136.47/20.34 | |
% 136.47/20.34 | | REDUCE: (16), (28) imply:
% 136.47/20.34 | | (34) op(e3, e3) = e3
% 136.47/20.34 | |
% 136.47/20.34 | | BETA: splitting (7) gives:
% 136.47/20.34 | |
% 136.47/20.34 | | Case 1:
% 136.47/20.34 | | |
% 136.47/20.34 | | | (35) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 136.47/20.34 | | | e3)
% 136.47/20.34 | | |
% 136.47/20.34 | | | BETA: splitting (35) gives:
% 136.47/20.34 | | |
% 136.47/20.34 | | | Case 1:
% 136.47/20.34 | | | |
% 136.47/20.34 | | | | (36) all_57_2 = e3 & op(e2, e3) = e3
% 136.47/20.34 | | | |
% 136.47/20.34 | | | | ALPHA: (36) implies:
% 136.47/20.34 | | | | (37) op(e2, e3) = e3
% 136.47/20.34 | | | |
% 136.47/20.34 | | | | REF_CLOSE: (6), (23), (29), (37) are inconsistent by sub-proof #763.
% 136.47/20.34 | | | |
% 136.47/20.34 | | | Case 2:
% 136.47/20.34 | | | |
% 136.47/20.34 | | | | (38) all_57_3 = e3 & op(e2, e2) = e3
% 136.47/20.34 | | | |
% 136.47/20.34 | | | | ALPHA: (38) implies:
% 136.47/20.34 | | | | (39) op(e2, e2) = e3
% 136.47/20.34 | | | |
% 136.47/20.34 | | | | REF_CLOSE: (4), (6), (33), (39) are inconsistent by sub-proof #641.
% 136.47/20.34 | | | |
% 136.47/20.34 | | | End of split
% 136.47/20.34 | | |
% 136.47/20.34 | | Case 2:
% 136.47/20.34 | | |
% 136.47/20.34 | | | (40) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 136.47/20.34 | | | e3)
% 136.47/20.34 | | |
% 136.47/20.34 | | | BETA: splitting (40) gives:
% 136.47/20.34 | | |
% 136.47/20.34 | | | Case 1:
% 136.47/20.34 | | | |
% 136.47/20.34 | | | | (41) all_57_5 = e3 & op(e2, e1) = e3
% 136.47/20.34 | | | |
% 136.47/20.34 | | | | REF_CLOSE: (6), (18), (19), (41) are inconsistent by sub-proof #547.
% 136.47/20.34 | | | |
% 136.47/20.34 | | | Case 2:
% 136.47/20.34 | | | |
% 136.47/20.34 | | | | (42) all_57_10 = e3 & op(e2, e0) = e3
% 136.47/20.34 | | | |
% 136.47/20.34 | | | | ALPHA: (42) implies:
% 136.47/20.34 | | | | (43) op(e2, e0) = e3
% 136.47/20.34 | | | |
% 136.47/20.34 | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (13), (14), (15), (17),
% 136.47/20.34 | | | | (21), (24), (30), (31), (32), (33), (34), (43) are
% 136.47/20.34 | | | | inconsistent by sub-proof #542.
% 136.47/20.34 | | | |
% 136.47/20.34 | | | End of split
% 136.47/20.34 | | |
% 136.47/20.34 | | End of split
% 136.47/20.34 | |
% 136.47/20.34 | Case 2:
% 136.47/20.34 | |
% 136.47/20.34 | | (44) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 136.47/20.34 | |
% 136.47/20.34 | | REF_CLOSE: (1), (11), (22), (25), (44) are inconsistent by sub-proof #777.
% 136.47/20.34 | |
% 136.47/20.34 | End of split
% 136.47/20.34 |
% 136.47/20.34 End of proof
% 136.47/20.34
% 136.47/20.34 Sub-proof #542 shows that the following formulas are inconsistent:
% 136.47/20.34 ----------------------------------------------------------------
% 136.47/20.34 (1) op(e0, e0) = all_4_2
% 136.47/20.34 (2) op(e1, e1) = all_6_2
% 136.47/20.34 (3) op(e2, e2) = e0
% 136.47/20.34 (4) op(e2, e0) = all_52_13
% 136.47/20.34 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.34 (6) ~ (e3 = e0)
% 136.47/20.34 (7) op(e2, e0) = e3
% 136.47/20.34 (8) ~ (e3 = e2)
% 136.47/20.34 (9) op(e1, e1) = e3
% 136.47/20.34 (10) op(e0, e2) = all_52_7
% 136.47/20.34 (11) ~ (all_4_2 = e1)
% 136.47/20.34 (12) ~ (all_6_2 = e2)
% 136.47/20.34 (13) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 136.47/20.34 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 136.47/20.34 op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 136.47/20.34 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 136.47/20.34 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 136.47/20.34 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.47/20.34 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 136.47/20.34 = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.47/20.34 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 136.47/20.34 $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~
% 136.47/20.34 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 136.47/20.34 (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) =
% 136.47/20.34 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0,
% 136.47/20.34 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 136.47/20.34 $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3)
% 136.47/20.34 & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 136.47/20.34 op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17
% 136.47/20.34 & op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 136.47/20.34 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.47/20.34 (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.47/20.34 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.47/20.34 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0)
% 136.47/20.34 = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) &
% 136.47/20.34 $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 &
% 136.47/20.34 all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.47/20.34 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 136.47/20.34 = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.47/20.34 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 136.47/20.34 $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~
% 136.47/20.34 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 136.47/20.34 (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 136.47/20.34 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0,
% 136.47/20.34 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 136.47/20.34 $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3)
% 136.47/20.34 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.47/20.34 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.47/20.34 all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2
% 136.47/20.34 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.47/20.34 (op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 =
% 136.47/20.34 e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 136.47/20.34 & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) =
% 136.47/20.34 all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 136.47/20.34 op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 136.47/20.34 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 136.47/20.34 e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 136.47/20.34 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 136.47/20.34 e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.47/20.34 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.47/20.34 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.47/20.34 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.47/20.34 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 136.47/20.34 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 136.47/20.34 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 136.47/20.34 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 136.47/20.34 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 136.47/20.34 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 136.47/20.34 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.47/20.34 $i(all_56_29))))
% 136.47/20.34 (14) ~ (all_52_7 = e0)
% 136.47/20.34 (15) op(e3, e3) = e3
% 136.47/20.34 (16) op(e3, e0) = all_52_12
% 136.47/20.34 (17) ~ (e3 = e1)
% 136.47/20.34 (18) ~ (e1 = e0)
% 136.47/20.34 (19) ~ (all_52_12 = e3)
% 136.47/20.34
% 136.47/20.34 Begin of proof
% 136.47/20.34 |
% 136.47/20.34 | BETA: splitting (13) gives:
% 136.47/20.34 |
% 136.47/20.34 | Case 1:
% 136.47/20.34 | |
% 136.47/20.34 | | (20) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11
% 136.47/20.34 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) =
% 136.47/20.34 | | e2 & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 136.47/20.34 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 136.47/20.34 | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.47/20.34 | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13
% 136.47/20.34 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) =
% 136.47/20.34 | | e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 136.47/20.34 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 136.47/20.34 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 136.47/20.34 | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15
% 136.47/20.34 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) =
% 136.47/20.34 | | e0 & op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 136.47/20.34 | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 &
% 136.47/20.34 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 136.47/20.34 | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 136.47/20.34 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.47/20.34 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.47/20.34 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 136.47/20.34 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25))
% 136.47/20.34 | |
% 136.47/20.34 | | BETA: splitting (20) gives:
% 136.47/20.34 | |
% 136.47/20.34 | | Case 1:
% 136.47/20.34 | | |
% 136.47/20.34 | | | (21) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~
% 136.47/20.34 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.47/20.34 | | | op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = all_56_3 &
% 136.47/20.34 | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) =
% 136.47/20.34 | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 136.47/20.34 | | | $i(all_56_27)) | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5
% 136.47/20.34 | | | = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 136.47/20.34 | | | (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1,
% 136.47/20.34 | | | e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.47/20.34 | | | all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 136.47/20.34 | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 136.47/20.34 | | |
% 136.47/20.34 | | | REF_CLOSE: (5), (8), (15), (17), (21) are inconsistent by sub-proof #623.
% 136.47/20.34 | | |
% 136.47/20.34 | | Case 2:
% 136.47/20.34 | | |
% 136.47/20.34 | | | (22) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~
% 136.47/20.34 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.47/20.34 | | | op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = all_56_7 &
% 136.47/20.34 | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 136.47/20.34 | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 136.47/20.34 | | | $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1
% 136.47/20.34 | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 136.47/20.34 | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9
% 136.47/20.34 | | | & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e2, e3) =
% 136.47/20.34 | | | e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 136.47/20.34 | | | $i(all_56_17) & $i(all_56_25))
% 136.47/20.34 | | |
% 136.47/20.34 | | | REF_CLOSE: (3), (5), (6), (16), (19), (22) are inconsistent by sub-proof
% 136.47/20.34 | | | #622.
% 136.47/20.34 | | |
% 136.47/20.34 | | End of split
% 136.47/20.34 | |
% 136.47/20.34 | Case 2:
% 136.47/20.34 | |
% 136.47/20.34 | | (23) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 136.47/20.34 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.47/20.34 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.47/20.34 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 136.47/20.34 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.47/20.34 | | (all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 136.47/20.34 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 136.47/20.34 | | op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1,
% 136.47/20.34 | | e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 136.47/20.34 | | all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.47/20.34 | | $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 =
% 136.47/20.34 | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31
% 136.47/20.34 | | = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 136.47/20.34 | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 136.47/20.34 | | op(e0, e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) &
% 136.47/20.34 | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2
% 136.47/20.34 | | & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 136.47/20.34 | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 136.47/20.34 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 136.47/20.34 | | op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) &
% 136.47/20.34 | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = all_56_31 &
% 136.47/20.34 | | $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 =
% 136.47/20.34 | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 136.47/20.34 | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) =
% 136.47/20.34 | | all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 136.47/20.34 | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17)
% 136.47/20.34 | | & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~
% 136.47/20.34 | | (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) &
% 136.47/20.34 | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 136.47/20.34 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 136.47/20.34 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 136.47/20.34 | | & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~
% 136.47/20.34 | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) &
% 136.47/20.34 | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 136.47/20.34 | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) =
% 136.47/20.34 | | all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 136.47/20.34 | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 136.47/20.34 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 136.47/20.34 | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.47/20.34 | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 136.47/20.34 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.47/20.34 | | $i(all_56_29))))
% 136.47/20.34 | |
% 136.47/20.34 | | BETA: splitting (23) gives:
% 136.47/20.34 | |
% 136.47/20.34 | | Case 1:
% 136.47/20.34 | | |
% 136.47/20.34 | | | (24) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~
% 136.47/20.34 | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 136.47/20.34 | | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) =
% 136.47/20.34 | | | all_56_17 & op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 136.47/20.34 | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 136.47/20.34 | | | $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5
% 136.47/20.34 | | | = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~
% 136.47/20.34 | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1,
% 136.47/20.34 | | | e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.47/20.34 | | | all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 136.47/20.34 | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))
% 136.47/20.34 | | |
% 136.47/20.34 | | | BETA: splitting (24) gives:
% 136.47/20.34 | | |
% 136.47/20.34 | | | Case 1:
% 136.47/20.34 | | | |
% 136.47/20.34 | | | | (25) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~
% 136.47/20.34 | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 136.47/20.34 | | | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) =
% 136.47/20.34 | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1,
% 136.47/20.34 | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 136.47/20.34 | | | | $i(all_56_25)
% 136.47/20.34 | | | |
% 136.47/20.34 | | | | ALPHA: (25) implies:
% 136.47/20.34 | | | | (26) ~ (all_56_1 = e3)
% 136.47/20.34 | | | | (27) op(e3, e3) = all_56_1
% 136.47/20.34 | | | |
% 136.47/20.34 | | | | REF_CLOSE: (5), (15), (26), (27) are inconsistent by sub-proof #766.
% 136.47/20.34 | | | |
% 136.47/20.34 | | | Case 2:
% 136.47/20.34 | | | |
% 136.47/20.34 | | | | (28) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 136.47/20.34 | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 136.47/20.34 | | | | op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = all_56_5 &
% 136.47/20.34 | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 136.47/20.34 | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.47/20.34 | | | | $i(all_56_29)
% 136.47/20.34 | | | |
% 136.47/20.34 | | | | ALPHA: (28) implies:
% 136.47/20.34 | | | | (29) op(e2, e2) = e1
% 136.47/20.34 | | | |
% 136.47/20.34 | | | | REF_CLOSE: (3), (5), (18), (29) are inconsistent by sub-proof #675.
% 136.47/20.34 | | | |
% 136.47/20.34 | | | End of split
% 136.47/20.34 | | |
% 136.47/20.34 | | Case 2:
% 136.47/20.34 | | |
% 136.47/20.34 | | | (30) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 136.47/20.34 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.47/20.34 | | | op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 &
% 136.47/20.34 | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 136.47/20.34 | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 136.47/20.34 | | | $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3
% 136.47/20.34 | | | = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 136.47/20.34 | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 136.47/20.34 | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 136.47/20.34 | | | op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11)
% 136.47/20.34 | | | & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = all_56_31 &
% 136.47/20.34 | | | $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1
% 136.47/20.34 | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~
% 136.47/20.34 | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) =
% 136.47/20.34 | | | all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 136.47/20.34 | | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 136.47/20.34 | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31
% 136.47/20.34 | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~
% 136.47/20.34 | | | (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 136.47/20.34 | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 &
% 136.47/20.34 | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) &
% 136.47/20.34 | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_21
% 136.47/20.34 | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.47/20.34 | | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1,
% 136.47/20.34 | | | e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 &
% 136.47/20.34 | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 &
% 136.47/20.34 | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 =
% 136.47/20.34 | | | e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 136.47/20.34 | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1,
% 136.47/20.34 | | | e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.47/20.34 | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 136.47/20.34 | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.47/20.34 | | | $i(all_56_29))))
% 136.47/20.34 | | |
% 136.47/20.34 | | | BETA: splitting (30) gives:
% 136.47/20.34 | | |
% 136.47/20.34 | | | Case 1:
% 136.47/20.34 | | | |
% 136.47/20.34 | | | | (31) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~
% 136.47/20.34 | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.47/20.34 | | | | op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 &
% 136.47/20.34 | | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) =
% 136.47/20.34 | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 136.47/20.34 | | | | $i(all_56_31)
% 136.47/20.34 | | | |
% 136.47/20.34 | | | | ALPHA: (31) implies:
% 136.47/20.34 | | | | (32) op(e2, e0) = e2
% 136.47/20.34 | | | |
% 136.47/20.34 | | | | REF_CLOSE: (4), (5), (7), (8), (32) are inconsistent by sub-proof #546.
% 136.47/20.34 | | | |
% 136.47/20.34 | | | Case 2:
% 136.47/20.34 | | | |
% 136.47/20.34 | | | | (33) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 136.47/20.34 | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.47/20.34 | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.47/20.34 | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 136.47/20.34 | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 136.47/20.34 | | | | $i(all_56_27)) | (op(e0, e0) = all_56_31 & $i(all_56_31) &
% 136.47/20.34 | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 136.47/20.34 | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 =
% 136.47/20.34 | | | | e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 &
% 136.47/20.34 | | | | op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0,
% 136.47/20.34 | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 136.47/20.34 | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~
% 136.47/20.34 | | | | (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 136.47/20.34 | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 &
% 136.47/20.34 | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 136.47/20.34 | | | | e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) &
% 136.47/20.34 | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.47/20.34 | | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.47/20.34 | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 =
% 136.47/20.34 | | | | e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) =
% 136.47/20.34 | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23
% 136.47/20.34 | | | | & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) |
% 136.47/20.34 | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 136.47/20.34 | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 =
% 136.47/20.34 | | | | e0) & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 136.47/20.34 | | | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & op(e0,
% 136.47/20.34 | | | | e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21)
% 136.47/20.34 | | | | & $i(all_56_29))))
% 136.47/20.34 | | | |
% 136.47/20.34 | | | | BETA: splitting (33) gives:
% 136.47/20.34 | | | |
% 136.47/20.34 | | | | Case 1:
% 136.47/20.34 | | | | |
% 136.47/20.34 | | | | | (34) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~
% 136.47/20.34 | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.47/20.34 | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.47/20.34 | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1,
% 136.47/20.34 | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 136.47/20.34 | | | | | $i(all_56_27)
% 136.47/20.34 | | | | |
% 136.47/20.34 | | | | | ALPHA: (34) implies:
% 136.47/20.34 | | | | | (35) op(e1, e1) = e2
% 136.47/20.34 | | | | |
% 136.47/20.34 | | | | | REF_CLOSE: (2), (5), (12), (35) are inconsistent by sub-proof #767.
% 136.47/20.34 | | | | |
% 136.47/20.34 | | | | Case 2:
% 136.47/20.34 | | | | |
% 136.47/20.34 | | | | | (36) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 &
% 136.47/20.34 | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) &
% 136.47/20.34 | | | | | ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.47/20.34 | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17
% 136.47/20.34 | | | | | & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1)
% 136.47/20.34 | | | | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.47/20.34 | | | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 136.47/20.34 | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 =
% 136.47/20.34 | | | | | e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 136.47/20.34 | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0,
% 136.47/20.34 | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19)
% 136.47/20.34 | | | | | & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~
% 136.47/20.34 | | | | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 =
% 136.47/20.34 | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0)
% 136.47/20.34 | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.47/20.34 | | | | | op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) &
% 136.47/20.34 | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 & ~
% 136.47/20.34 | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 =
% 136.47/20.34 | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 &
% 136.47/20.34 | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1,
% 136.47/20.34 | | | | | e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) &
% 136.47/20.34 | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)))
% 136.47/20.34 | | | | |
% 136.47/20.34 | | | | | ALPHA: (36) implies:
% 136.47/20.34 | | | | | (37) op(e0, e0) = all_56_31
% 136.47/20.34 | | | | | (38) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~
% 136.47/20.34 | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0)
% 136.47/20.34 | | | | | & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1)
% 136.47/20.34 | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 &
% 136.47/20.34 | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25))
% 136.47/20.34 | | | | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 136.47/20.34 | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0)
% 136.47/20.34 | | | | | & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 136.47/20.34 | | | | | e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0
% 136.47/20.34 | | | | | & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 136.47/20.34 | | | | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~
% 136.47/20.34 | | | | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1)
% 136.47/20.34 | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 &
% 136.47/20.34 | | | | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1)
% 136.47/20.34 | | | | | = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 136.47/20.34 | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 136.47/20.34 | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0)
% 136.47/20.34 | | | | | & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1,
% 136.47/20.34 | | | | | e1) = all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0
% 136.47/20.34 | | | | | & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.47/20.34 | | | | | $i(all_56_29))
% 136.47/20.34 | | | | |
% 136.47/20.34 | | | | | REF_CLOSE: (1), (5), (6), (9), (10), (11), (14), (15), (37), (38) are
% 136.47/20.34 | | | | | inconsistent by sub-proof #543.
% 136.47/20.34 | | | | |
% 136.47/20.34 | | | | End of split
% 136.47/20.34 | | | |
% 136.47/20.34 | | | End of split
% 136.47/20.34 | | |
% 136.47/20.34 | | End of split
% 136.47/20.34 | |
% 136.47/20.34 | End of split
% 136.47/20.34 |
% 136.47/20.34 End of proof
% 136.47/20.34
% 136.47/20.34 Sub-proof #543 shows that the following formulas are inconsistent:
% 136.47/20.34 ----------------------------------------------------------------
% 136.47/20.34 (1) op(e0, e0) = all_4_2
% 136.47/20.34 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.34 (3) ~ (e3 = e0)
% 136.47/20.34 (4) op(e1, e1) = e3
% 136.47/20.34 (5) op(e0, e2) = all_52_7
% 136.47/20.34 (6) ~ (all_4_2 = e1)
% 136.47/20.34 (7) ~ (all_52_7 = e0)
% 136.47/20.34 (8) op(e3, e3) = e3
% 136.47/20.35 (9) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2)
% 136.47/20.35 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 136.47/20.35 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25
% 136.47/20.35 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 136.47/20.35 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3)
% 136.47/20.35 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.47/20.35 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 136.47/20.35 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) &
% 136.47/20.35 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 &
% 136.47/20.35 all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~
% 136.47/20.35 (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) =
% 136.47/20.35 e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) =
% 136.47/20.35 all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23
% 136.47/20.35 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.47/20.35 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1,
% 136.47/20.35 e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 136.47/20.35 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.47/20.35 $i(all_56_29))
% 136.47/20.35 (10) op(e0, e0) = all_56_31
% 136.47/20.35
% 136.47/20.35 Begin of proof
% 136.47/20.35 |
% 136.47/20.35 | BETA: splitting (9) gives:
% 136.47/20.35 |
% 136.47/20.35 | Case 1:
% 136.47/20.35 | |
% 136.47/20.35 | | (11) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 136.47/20.35 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.47/20.35 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.47/20.35 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9)
% 136.47/20.35 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 136.47/20.35 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 136.47/20.35 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 136.47/20.35 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 136.47/20.35 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 136.47/20.35 | | $i(all_56_27))
% 136.47/20.35 | |
% 136.47/20.35 | | REF_CLOSE: (2), (5), (7), (8), (11) are inconsistent by sub-proof #544.
% 136.47/20.35 | |
% 136.47/20.35 | Case 2:
% 136.47/20.35 | |
% 136.47/20.35 | | (12) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.47/20.35 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.47/20.35 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 136.47/20.35 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 136.47/20.35 | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 136.47/20.35 | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 136.47/20.35 | | ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 136.47/20.35 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 136.47/20.35 | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.47/20.35 | | $i(all_56_29))
% 136.47/20.35 | |
% 136.47/20.35 | | BETA: splitting (12) gives:
% 136.47/20.35 | |
% 136.47/20.35 | | Case 1:
% 136.47/20.35 | | |
% 136.47/20.35 | | | (13) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.47/20.35 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.47/20.35 | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 136.47/20.35 | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 136.47/20.35 | | | $i(all_56_15) & $i(all_56_23)
% 136.47/20.35 | | |
% 136.47/20.35 | | | ALPHA: (13) implies:
% 136.47/20.35 | | | (14) op(e1, e1) = e0
% 136.47/20.35 | | |
% 136.47/20.35 | | | REF_CLOSE: (2), (3), (4), (14) are inconsistent by sub-proof #753.
% 136.47/20.35 | | |
% 136.47/20.35 | | Case 2:
% 136.47/20.35 | | |
% 136.47/20.35 | | | (15) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 136.47/20.35 | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 136.47/20.35 | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.47/20.35 | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 136.47/20.35 | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 136.47/20.35 | | |
% 136.47/20.35 | | | ALPHA: (15) implies:
% 136.47/20.35 | | | (16) all_56_31 = e1
% 136.47/20.35 | | |
% 136.47/20.35 | | | REDUCE: (10), (16) imply:
% 136.47/20.35 | | | (17) op(e0, e0) = e1
% 136.47/20.35 | | |
% 136.47/20.35 | | | GROUND_INST: instantiating (2) with all_4_2, e1, e0, e0, simplifying with
% 136.47/20.35 | | | (1), (17) gives:
% 136.47/20.35 | | | (18) all_4_2 = e1
% 136.47/20.35 | | |
% 136.47/20.35 | | | REDUCE: (6), (18) imply:
% 136.47/20.35 | | | (19) $false
% 136.47/20.35 | | |
% 136.47/20.35 | | | CLOSE: (19) is inconsistent.
% 136.47/20.35 | | |
% 136.47/20.35 | | End of split
% 136.47/20.35 | |
% 136.47/20.35 | End of split
% 136.47/20.35 |
% 136.47/20.35 End of proof
% 136.47/20.35
% 136.47/20.35 Sub-proof #544 shows that the following formulas are inconsistent:
% 136.47/20.35 ----------------------------------------------------------------
% 136.47/20.35 (1) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2)
% 136.47/20.35 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 &
% 136.47/20.35 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25
% 136.47/20.35 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 136.47/20.35 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3)
% 136.47/20.35 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.47/20.35 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19
% 136.47/20.35 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) &
% 136.47/20.35 $i(all_56_11) & $i(all_56_19) & $i(all_56_27))
% 136.47/20.35 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.35 (3) op(e0, e2) = all_52_7
% 136.47/20.35 (4) ~ (all_52_7 = e0)
% 136.47/20.35 (5) op(e3, e3) = e3
% 136.47/20.35
% 136.47/20.35 Begin of proof
% 136.47/20.35 |
% 136.47/20.35 | BETA: splitting (1) gives:
% 136.47/20.35 |
% 136.47/20.35 | Case 1:
% 136.47/20.35 | |
% 136.47/20.35 | | (6) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.47/20.35 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.47/20.35 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.47/20.35 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 136.47/20.35 | | $i(all_56_17) & $i(all_56_25)
% 136.47/20.35 | |
% 136.47/20.35 | | ALPHA: (6) implies:
% 136.47/20.35 | | (7) ~ (all_56_1 = e3)
% 136.47/20.35 | | (8) op(e3, e3) = all_56_1
% 136.47/20.35 | |
% 136.47/20.35 | | REF_CLOSE: (2), (5), (7), (8) are inconsistent by sub-proof #766.
% 136.47/20.35 | |
% 136.47/20.35 | Case 2:
% 136.47/20.35 | |
% 136.47/20.35 | | (9) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11
% 136.47/20.35 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) =
% 136.47/20.35 | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2,
% 136.47/20.35 | | e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) &
% 136.47/20.35 | | $i(all_56_19) & $i(all_56_27)
% 136.47/20.35 | |
% 136.47/20.35 | | ALPHA: (9) implies:
% 136.47/20.35 | | (10) op(e0, e2) = e0
% 136.47/20.35 | |
% 136.47/20.35 | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #545.
% 136.47/20.35 | |
% 136.47/20.35 | End of split
% 136.47/20.35 |
% 136.47/20.35 End of proof
% 136.47/20.35
% 136.47/20.35 Sub-proof #545 shows that the following formulas are inconsistent:
% 136.47/20.35 ----------------------------------------------------------------
% 136.47/20.35 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.35 (2) op(e0, e2) = all_52_7
% 136.47/20.35 (3) op(e0, e2) = e0
% 136.47/20.35 (4) ~ (all_52_7 = e0)
% 136.47/20.35
% 136.47/20.35 Begin of proof
% 136.47/20.35 |
% 136.47/20.35 | GROUND_INST: instantiating (1) with all_52_7, e0, e2, e0, simplifying with
% 136.47/20.35 | (2), (3) gives:
% 136.47/20.35 | (5) all_52_7 = e0
% 136.47/20.35 |
% 136.47/20.35 | REDUCE: (4), (5) imply:
% 136.47/20.35 | (6) $false
% 136.47/20.35 |
% 136.47/20.35 | CLOSE: (6) is inconsistent.
% 136.47/20.35 |
% 136.47/20.35 End of proof
% 136.47/20.35
% 136.47/20.35 Sub-proof #546 shows that the following formulas are inconsistent:
% 136.47/20.35 ----------------------------------------------------------------
% 136.47/20.35 (1) op(e2, e0) = all_52_13
% 136.47/20.35 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.35 (3) op(e2, e0) = e3
% 136.47/20.35 (4) ~ (e3 = e2)
% 136.47/20.35 (5) op(e2, e0) = e2
% 136.47/20.35
% 136.47/20.35 Begin of proof
% 136.47/20.35 |
% 136.47/20.35 | GROUND_INST: instantiating (2) with all_52_13, e2, e0, e2, simplifying with
% 136.47/20.35 | (1), (5) gives:
% 136.47/20.35 | (6) all_52_13 = e2
% 136.47/20.35 |
% 136.47/20.35 | GROUND_INST: instantiating (2) with all_52_13, e3, e0, e2, simplifying with
% 136.47/20.35 | (1), (3) gives:
% 136.47/20.35 | (7) all_52_13 = e3
% 136.47/20.35 |
% 136.47/20.35 | COMBINE_EQS: (6), (7) imply:
% 136.47/20.35 | (8) e3 = e2
% 136.47/20.35 |
% 136.47/20.35 | REDUCE: (4), (8) imply:
% 136.47/20.35 | (9) $false
% 136.47/20.35 |
% 136.47/20.35 | CLOSE: (9) is inconsistent.
% 136.47/20.35 |
% 136.47/20.35 End of proof
% 136.47/20.35
% 136.47/20.35 Sub-proof #547 shows that the following formulas are inconsistent:
% 136.47/20.35 ----------------------------------------------------------------
% 136.47/20.35 (1) all_57_5 = e3 & op(e2, e1) = e3
% 136.47/20.35 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.35 (3) op(e2, e1) = all_52_9
% 136.47/20.35 (4) ~ (all_52_9 = e3)
% 136.47/20.35
% 136.47/20.35 Begin of proof
% 136.47/20.35 |
% 136.47/20.35 | ALPHA: (1) implies:
% 136.47/20.35 | (5) op(e2, e1) = e3
% 136.47/20.35 |
% 136.47/20.35 | GROUND_INST: instantiating (2) with all_52_9, e3, e1, e2, simplifying with
% 136.47/20.35 | (3), (5) gives:
% 136.47/20.35 | (6) all_52_9 = e3
% 136.47/20.35 |
% 136.47/20.35 | REDUCE: (4), (6) imply:
% 136.47/20.35 | (7) $false
% 136.47/20.35 |
% 136.47/20.35 | CLOSE: (7) is inconsistent.
% 136.47/20.35 |
% 136.47/20.35 End of proof
% 136.47/20.35
% 136.47/20.35 Sub-proof #548 shows that the following formulas are inconsistent:
% 136.47/20.35 ----------------------------------------------------------------
% 136.47/20.35 (1) op(e0, e0) = all_4_2
% 136.47/20.35 (2) ~ (e2 = e0)
% 136.47/20.35 (3) op(e3, e3) = e1
% 136.47/20.35 (4) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 136.47/20.35 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 136.47/20.35 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.35 (6) ~ (e2 = e1)
% 136.47/20.35 (7) ~ (all_4_2 = e2)
% 136.47/20.35 (8) ~ (e3 = e0)
% 136.47/20.35 (9) op(e1, e1) = e3
% 136.47/20.35 (10) ~ (all_4_2 = e1)
% 136.47/20.35 (11) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 136.47/20.35 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 136.47/20.35 (12) ~ (all_52_4 = e2)
% 136.47/20.35 (13) ~ (all_52_3 = e1)
% 136.47/20.35 (14) op(e3, e2) = all_52_4
% 136.47/20.35 (15) op(e0, e3) = all_52_3
% 136.47/20.35 (16) op(e3, e0) = all_52_12
% 136.47/20.35 (17) op(e3, e1) = all_52_8
% 136.47/20.35 (18) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.47/20.35 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.47/20.35 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0)
% 136.47/20.35 = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) &
% 136.47/20.35 $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~
% 136.47/20.35 (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~
% 136.47/20.35 (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 136.47/20.35 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.47/20.35 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.47/20.35 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.47/20.35 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 &
% 136.47/20.35 op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.47/20.35 op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23))
% 136.47/20.35 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13
% 136.47/20.35 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) =
% 136.47/20.35 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1,
% 136.47/20.35 e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) &
% 136.47/20.35 $i(all_56_21) & $i(all_56_29))
% 136.47/20.35 (19) ~ (all_52_3 = all_4_2)
% 136.47/20.35 (20) ~ (all_34_2 = e3) | ( ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 &
% 136.47/20.35 $i(all_34_0)) | ( ~ (all_34_1 = e1) & op(e3, e3) = all_34_1 &
% 136.47/20.35 $i(all_34_1))
% 136.47/20.35 (21) ~ (all_52_12 = all_4_2)
% 136.47/20.35 (22) all_34_2 = all_4_2
% 136.47/20.35 (23) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 136.47/20.35 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 136.47/20.35 (24) op(e0, e0) = all_56_31
% 136.47/20.35 (25) ~ (all_52_8 = e3)
% 136.47/20.35
% 136.47/20.35 Begin of proof
% 136.47/20.35 |
% 136.47/20.35 | GROUND_INST: instantiating (5) with all_4_2, all_56_31, e0, e0, simplifying
% 136.47/20.35 | with (1), (24) gives:
% 136.47/20.35 | (26) all_56_31 = all_4_2
% 136.47/20.35 |
% 136.47/20.35 | BETA: splitting (18) gives:
% 136.47/20.35 |
% 136.47/20.35 | Case 1:
% 136.47/20.35 | |
% 136.47/20.35 | | (27) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 136.47/20.35 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.47/20.35 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.47/20.35 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9)
% 136.47/20.35 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 =
% 136.47/20.35 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 =
% 136.47/20.35 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) =
% 136.47/20.35 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 136.47/20.35 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) &
% 136.47/20.35 | | $i(all_56_27))
% 136.47/20.35 | |
% 136.47/20.35 | | BETA: splitting (27) gives:
% 136.47/20.35 | |
% 136.47/20.35 | | Case 1:
% 136.47/20.35 | | |
% 136.47/20.35 | | | (28) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 136.47/20.35 | | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.47/20.35 | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.47/20.35 | | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9)
% 136.47/20.35 | | | & $i(all_56_17) & $i(all_56_25)
% 136.47/20.35 | | |
% 136.47/20.35 | | | ALPHA: (28) implies:
% 136.47/20.35 | | | (29) all_56_31 = e3
% 136.47/20.35 | | | (30) ~ (all_56_25 = e0)
% 136.47/20.35 | | | (31) op(e0, e3) = e0
% 136.47/20.35 | | | (32) op(e3, e0) = all_56_25
% 136.47/20.35 | | | (33) op(e3, e2) = all_56_9
% 136.47/20.35 | | | (34) op(e3, e3) = all_56_1
% 136.47/20.35 | | |
% 136.47/20.35 | | | COMBINE_EQS: (26), (29) imply:
% 136.47/20.35 | | | (35) all_4_2 = e3
% 136.47/20.35 | | |
% 136.47/20.35 | | | COMBINE_EQS: (22), (35) imply:
% 136.47/20.35 | | | (36) all_34_2 = e3
% 136.47/20.35 | | |
% 136.47/20.35 | | | REDUCE: (19), (35) imply:
% 136.47/20.35 | | | (37) ~ (all_52_3 = e3)
% 136.47/20.35 | | |
% 136.47/20.35 | | | REDUCE: (21), (35) imply:
% 136.47/20.35 | | | (38) ~ (all_52_12 = e3)
% 136.47/20.35 | | |
% 136.47/20.35 | | | REDUCE: (1), (35) imply:
% 136.47/20.35 | | | (39) op(e0, e0) = e3
% 136.47/20.35 | | |
% 136.47/20.35 | | | BETA: splitting (20) gives:
% 136.47/20.35 | | |
% 136.47/20.35 | | | Case 1:
% 136.47/20.35 | | | |
% 136.47/20.35 | | | | (40) ~ (all_34_2 = e3)
% 136.47/20.35 | | | |
% 136.47/20.35 | | | | REDUCE: (36), (40) imply:
% 136.47/20.35 | | | | (41) $false
% 136.47/20.35 | | | |
% 136.47/20.35 | | | | CLOSE: (41) is inconsistent.
% 136.47/20.35 | | | |
% 136.47/20.35 | | | Case 2:
% 136.47/20.35 | | | |
% 136.47/20.35 | | | | (42) ( ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 & $i(all_34_0)) | (
% 136.47/20.35 | | | | ~ (all_34_1 = e1) & op(e3, e3) = all_34_1 & $i(all_34_1))
% 136.47/20.35 | | | |
% 136.47/20.35 | | | | BETA: splitting (23) gives:
% 136.47/20.35 | | | |
% 136.47/20.35 | | | | Case 1:
% 136.47/20.35 | | | | |
% 136.47/20.35 | | | | | (43) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3,
% 136.47/20.35 | | | | | e2) = e3)
% 136.47/20.35 | | | | |
% 136.47/20.35 | | | | | BETA: splitting (43) gives:
% 136.47/20.35 | | | | |
% 136.47/20.35 | | | | | Case 1:
% 136.47/20.35 | | | | | |
% 136.47/20.35 | | | | | | (44) all_57_0 = e3 & op(e3, e3) = e3
% 136.47/20.35 | | | | | |
% 136.47/20.35 | | | | | | ALPHA: (44) implies:
% 136.47/20.35 | | | | | | (45) op(e3, e3) = e3
% 136.47/20.35 | | | | | |
% 136.47/20.35 | | | | | | REF_CLOSE: (1), (5), (7), (8), (9), (10), (18), (24), (39), (45) are
% 136.47/20.35 | | | | | | inconsistent by sub-proof #751.
% 136.47/20.35 | | | | | |
% 136.47/20.35 | | | | | Case 2:
% 136.47/20.35 | | | | | |
% 136.47/20.35 | | | | | | (46) all_57_1 = e3 & op(e3, e2) = e3
% 136.47/20.35 | | | | | |
% 136.47/20.35 | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (11), (12), (13), (14), (15),
% 136.47/20.35 | | | | | | (16), (30), (31), (32), (33), (34), (37), (42), (46) are
% 136.47/20.35 | | | | | | inconsistent by sub-proof #549.
% 136.47/20.35 | | | | | |
% 136.47/20.35 | | | | | End of split
% 136.47/20.35 | | | | |
% 136.47/20.35 | | | | Case 2:
% 136.47/20.35 | | | | |
% 136.47/20.35 | | | | | (47) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3,
% 136.47/20.35 | | | | | e0) = e3)
% 136.47/20.35 | | | | |
% 136.47/20.35 | | | | | REF_CLOSE: (5), (16), (17), (25), (38), (47) are inconsistent by
% 136.47/20.35 | | | | | sub-proof #650.
% 136.47/20.35 | | | | |
% 136.47/20.35 | | | | End of split
% 136.47/20.35 | | | |
% 136.47/20.35 | | | End of split
% 136.47/20.35 | | |
% 136.47/20.35 | | Case 2:
% 136.47/20.35 | | |
% 136.47/20.35 | | | (48) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~
% 136.47/20.35 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.47/20.35 | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.47/20.35 | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.47/20.35 | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)
% 136.47/20.35 | | |
% 136.47/20.35 | | | REF_CLOSE: (7), (26), (48) are inconsistent by sub-proof #765.
% 136.47/20.35 | | |
% 136.47/20.35 | | End of split
% 136.47/20.35 | |
% 136.47/20.35 | Case 2:
% 136.47/20.35 | |
% 136.47/20.35 | | (49) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.47/20.35 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.47/20.35 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 136.47/20.35 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 136.47/20.35 | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 136.47/20.35 | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 136.47/20.35 | | ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 136.47/20.35 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 136.47/20.35 | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.47/20.35 | | $i(all_56_29))
% 136.47/20.35 | |
% 136.47/20.35 | | BETA: splitting (49) gives:
% 136.47/20.35 | |
% 136.47/20.35 | | Case 1:
% 136.47/20.35 | | |
% 136.47/20.35 | | | (50) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.47/20.35 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.47/20.35 | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 136.47/20.35 | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 136.47/20.35 | | | $i(all_56_15) & $i(all_56_23)
% 136.47/20.35 | | |
% 136.47/20.35 | | | ALPHA: (50) implies:
% 136.47/20.35 | | | (51) op(e1, e1) = e0
% 136.47/20.35 | | |
% 136.47/20.35 | | | REF_CLOSE: (5), (8), (9), (51) are inconsistent by sub-proof #753.
% 136.47/20.35 | | |
% 136.47/20.35 | | Case 2:
% 136.47/20.35 | | |
% 136.47/20.35 | | | (52) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~
% 136.47/20.35 | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 136.47/20.35 | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.47/20.35 | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 &
% 136.47/20.35 | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 136.47/20.35 | | |
% 136.47/20.35 | | | REF_CLOSE: (10), (26), (52) are inconsistent by sub-proof #745.
% 136.47/20.35 | | |
% 136.47/20.35 | | End of split
% 136.47/20.35 | |
% 136.47/20.35 | End of split
% 136.47/20.35 |
% 136.47/20.35 End of proof
% 136.47/20.35
% 136.47/20.35 Sub-proof #549 shows that the following formulas are inconsistent:
% 136.47/20.35 ----------------------------------------------------------------
% 136.47/20.35 (1) all_57_1 = e3 & op(e3, e2) = e3
% 136.47/20.35 (2) ~ (e2 = e0)
% 136.47/20.35 (3) op(e3, e3) = e1
% 136.47/20.35 (4) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 136.47/20.35 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 136.47/20.35 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.35 (6) ~ (e2 = e1)
% 136.47/20.35 (7) ~ (all_56_25 = e0)
% 136.47/20.35 (8) ~ (all_52_3 = e3)
% 136.47/20.35 (9) op(e3, e3) = all_56_1
% 136.47/20.35 (10) op(e3, e0) = all_56_25
% 136.47/20.35 (11) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 136.47/20.35 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 136.47/20.35 (12) ( ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 & $i(all_34_0)) | ( ~
% 136.47/20.35 (all_34_1 = e1) & op(e3, e3) = all_34_1 & $i(all_34_1))
% 136.47/20.35 (13) ~ (all_52_4 = e2)
% 136.47/20.35 (14) ~ (all_52_3 = e1)
% 136.47/20.35 (15) op(e3, e2) = all_52_4
% 136.47/20.35 (16) op(e0, e3) = all_52_3
% 136.47/20.35 (17) op(e3, e0) = all_52_12
% 136.47/20.35 (18) op(e3, e2) = all_56_9
% 136.47/20.35 (19) op(e0, e3) = e0
% 136.47/20.35
% 136.47/20.35 Begin of proof
% 136.47/20.35 |
% 136.47/20.35 | ALPHA: (1) implies:
% 136.47/20.35 | (20) all_57_1 = e3
% 136.47/20.35 | (21) op(e3, e2) = e3
% 136.47/20.35 |
% 136.47/20.35 | GROUND_INST: instantiating (5) with all_52_3, e0, e3, e0, simplifying with
% 136.47/20.35 | (16), (19) gives:
% 136.47/20.35 | (22) all_52_3 = e0
% 136.47/20.35 |
% 136.47/20.35 | GROUND_INST: instantiating (5) with all_52_12, all_56_25, e0, e3, simplifying
% 136.47/20.35 | with (10), (17) gives:
% 136.47/20.35 | (23) all_56_25 = all_52_12
% 136.47/20.35 |
% 136.47/20.35 | GROUND_INST: instantiating (5) with all_52_4, all_56_9, e2, e3, simplifying
% 136.47/20.35 | with (15), (18) gives:
% 136.47/20.35 | (24) all_56_9 = all_52_4
% 136.47/20.35 |
% 136.47/20.35 | GROUND_INST: instantiating (5) with e3, all_56_9, e2, e3, simplifying with
% 136.47/20.35 | (18), (21) gives:
% 136.47/20.35 | (25) all_56_9 = e3
% 136.47/20.35 |
% 136.47/20.35 | GROUND_INST: instantiating (5) with e1, all_56_1, e3, e3, simplifying with
% 136.47/20.35 | (3), (9) gives:
% 136.47/20.35 | (26) all_56_1 = e1
% 136.47/20.35 |
% 136.47/20.35 | COMBINE_EQS: (24), (25) imply:
% 136.47/20.35 | (27) all_52_4 = e3
% 136.47/20.35 |
% 136.47/20.35 | SIMP: (27) implies:
% 136.47/20.35 | (28) all_52_4 = e3
% 136.47/20.35 |
% 136.47/20.35 | REDUCE: (7), (23) imply:
% 136.47/20.35 | (29) ~ (all_52_12 = e0)
% 136.47/20.35 |
% 136.47/20.35 | REDUCE: (8), (22) imply:
% 136.47/20.35 | (30) ~ (e3 = e0)
% 136.47/20.35 |
% 136.47/20.35 | SIMP: (30) implies:
% 136.47/20.35 | (31) ~ (e3 = e0)
% 136.47/20.35 |
% 136.47/20.35 | REDUCE: (14), (22) imply:
% 136.47/20.35 | (32) ~ (e1 = e0)
% 136.47/20.35 |
% 136.47/20.35 | SIMP: (32) implies:
% 136.47/20.35 | (33) ~ (e1 = e0)
% 136.47/20.35 |
% 136.47/20.35 | REDUCE: (13), (28) imply:
% 136.47/20.35 | (34) ~ (e3 = e2)
% 136.47/20.35 |
% 136.47/20.35 | BETA: splitting (4) gives:
% 136.47/20.35 |
% 136.47/20.35 | Case 1:
% 136.47/20.35 | |
% 136.47/20.35 | | (35) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 136.47/20.35 | | e0)
% 136.47/20.35 | |
% 136.47/20.35 | | REF_CLOSE: (3), (5), (20), (31), (33), (35) are inconsistent by sub-proof
% 136.47/20.35 | | #648.
% 136.47/20.35 | |
% 136.47/20.35 | Case 2:
% 136.47/20.35 | |
% 136.47/20.35 | | (36) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 136.47/20.35 | | e0)
% 136.47/20.35 | |
% 136.47/20.35 | | BETA: splitting (36) gives:
% 136.47/20.35 | |
% 136.47/20.35 | | Case 1:
% 136.47/20.35 | | |
% 136.47/20.35 | | | (37) all_57_4 = e0 & op(e3, e1) = e0
% 136.47/20.35 | | |
% 136.47/20.35 | | | ALPHA: (37) implies:
% 136.47/20.35 | | | (38) all_57_4 = e0
% 136.47/20.35 | | |
% 136.47/20.35 | | | REF_CLOSE: (2), (3), (5), (6), (11), (12), (20), (34), (38) are
% 136.47/20.35 | | | inconsistent by sub-proof #550.
% 136.47/20.35 | | |
% 136.47/20.35 | | Case 2:
% 136.47/20.35 | | |
% 136.47/20.35 | | | (39) all_57_9 = e0 & op(e3, e0) = e0
% 136.47/20.35 | | |
% 136.47/20.35 | | | REF_CLOSE: (5), (17), (29), (39) are inconsistent by sub-proof #618.
% 136.47/20.35 | | |
% 136.47/20.35 | | End of split
% 136.47/20.35 | |
% 136.47/20.35 | End of split
% 136.47/20.35 |
% 136.47/20.35 End of proof
% 136.47/20.35
% 136.47/20.35 Sub-proof #550 shows that the following formulas are inconsistent:
% 136.47/20.35 ----------------------------------------------------------------
% 136.47/20.35 (1) all_57_1 = e3
% 136.47/20.35 (2) ~ (e2 = e0)
% 136.47/20.35 (3) op(e3, e3) = e1
% 136.47/20.35 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.35 (5) ~ (e2 = e1)
% 136.47/20.35 (6) ~ (e3 = e2)
% 136.47/20.35 (7) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 136.47/20.35 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 136.47/20.35 (8) ( ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 & $i(all_34_0)) | ( ~
% 136.47/20.35 (all_34_1 = e1) & op(e3, e3) = all_34_1 & $i(all_34_1))
% 136.47/20.35 (9) all_57_4 = e0
% 136.47/20.35
% 136.47/20.35 Begin of proof
% 136.47/20.35 |
% 136.47/20.35 | BETA: splitting (8) gives:
% 136.47/20.35 |
% 136.47/20.35 | Case 1:
% 136.47/20.35 | |
% 136.47/20.35 | | (10) ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 & $i(all_34_0)
% 136.47/20.35 | |
% 136.47/20.35 | | ALPHA: (10) implies:
% 136.47/20.35 | | (11) ~ (all_34_0 = e2)
% 136.47/20.35 | | (12) op(e3, e0) = all_34_0
% 136.47/20.35 | |
% 136.47/20.35 | | BETA: splitting (7) gives:
% 136.47/20.35 | |
% 136.47/20.35 | | Case 1:
% 136.47/20.35 | | |
% 136.47/20.35 | | | (13) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) =
% 136.47/20.35 | | | e2)
% 136.47/20.35 | | |
% 136.47/20.35 | | | REF_CLOSE: (1), (3), (4), (5), (6), (13) are inconsistent by sub-proof
% 136.47/20.35 | | | #562.
% 136.47/20.35 | | |
% 136.47/20.35 | | Case 2:
% 136.47/20.35 | | |
% 136.47/20.35 | | | (14) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) =
% 136.47/20.35 | | | e2)
% 136.47/20.35 | | |
% 136.47/20.35 | | | BETA: splitting (14) gives:
% 136.47/20.35 | | |
% 136.47/20.35 | | | Case 1:
% 136.47/20.35 | | | |
% 136.47/20.35 | | | | (15) all_57_4 = e2 & op(e3, e1) = e2
% 136.47/20.35 | | | |
% 136.47/20.35 | | | | REF_CLOSE: (2), (9), (15) are inconsistent by sub-proof #689.
% 136.47/20.35 | | | |
% 136.47/20.35 | | | Case 2:
% 136.47/20.35 | | | |
% 136.47/20.35 | | | | (16) all_57_9 = e2 & op(e3, e0) = e2
% 136.47/20.35 | | | |
% 136.47/20.35 | | | | ALPHA: (16) implies:
% 136.47/20.35 | | | | (17) op(e3, e0) = e2
% 136.47/20.35 | | | |
% 136.47/20.35 | | | | REF_CLOSE: (4), (11), (12), (17) are inconsistent by sub-proof #551.
% 136.47/20.35 | | | |
% 136.47/20.35 | | | End of split
% 136.47/20.35 | | |
% 136.47/20.35 | | End of split
% 136.47/20.35 | |
% 136.47/20.35 | Case 2:
% 136.47/20.35 | |
% 136.47/20.35 | | (18) ~ (all_34_1 = e1) & op(e3, e3) = all_34_1 & $i(all_34_1)
% 136.47/20.35 | |
% 136.47/20.35 | | ALPHA: (18) implies:
% 136.47/20.35 | | (19) ~ (all_34_1 = e1)
% 136.47/20.35 | | (20) op(e3, e3) = all_34_1
% 136.47/20.35 | |
% 136.47/20.35 | | REF_CLOSE: (3), (4), (19), (20) are inconsistent by sub-proof #626.
% 136.47/20.35 | |
% 136.47/20.35 | End of split
% 136.47/20.35 |
% 136.47/20.35 End of proof
% 136.47/20.35
% 136.47/20.35 Sub-proof #551 shows that the following formulas are inconsistent:
% 136.47/20.35 ----------------------------------------------------------------
% 136.47/20.35 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.35 (2) op(e3, e0) = all_34_0
% 136.47/20.35 (3) op(e3, e0) = e2
% 136.47/20.35 (4) ~ (all_34_0 = e2)
% 136.47/20.35
% 136.47/20.35 Begin of proof
% 136.47/20.35 |
% 136.47/20.35 | GROUND_INST: instantiating (1) with e2, all_34_0, e0, e3, simplifying with
% 136.47/20.35 | (2), (3) gives:
% 136.47/20.35 | (5) all_34_0 = e2
% 136.47/20.35 |
% 136.47/20.35 | REDUCE: (4), (5) imply:
% 136.47/20.35 | (6) $false
% 136.47/20.35 |
% 136.47/20.35 | CLOSE: (6) is inconsistent.
% 136.47/20.35 |
% 136.47/20.35 End of proof
% 136.47/20.35
% 136.47/20.35 Sub-proof #552 shows that the following formulas are inconsistent:
% 136.47/20.35 ----------------------------------------------------------------
% 136.47/20.36 (1) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2)
% 136.47/20.36 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3,
% 136.47/20.36 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 136.47/20.36 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 136.47/20.36 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 136.47/20.36 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.47/20.36 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) =
% 136.47/20.36 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.47/20.36 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 136.47/20.36 $i(all_56_21) & $i(all_56_29))
% 136.47/20.36 (2) op(e3, e3) = e1
% 136.47/20.36 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.36 (4) ~ (e2 = e1)
% 136.47/20.36 (5) op(e3, e1) = all_52_8
% 136.47/20.36 (6) ~ (all_52_8 = e3)
% 136.47/20.36
% 136.47/20.36 Begin of proof
% 136.47/20.36 |
% 136.47/20.36 | BETA: splitting (1) gives:
% 136.47/20.36 |
% 136.47/20.36 | Case 1:
% 136.47/20.36 | |
% 136.47/20.36 | | (7) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 136.47/20.36 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 136.47/20.36 | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 136.47/20.36 | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 136.47/20.36 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)
% 136.47/20.36 | |
% 136.47/20.36 | | ALPHA: (7) implies:
% 136.47/20.36 | | (8) op(e3, e3) = e2
% 136.47/20.36 | |
% 136.47/20.36 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #743.
% 136.47/20.36 | |
% 136.47/20.36 | Case 2:
% 136.47/20.36 | |
% 136.47/20.36 | | (9) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 =
% 136.47/20.36 | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 &
% 136.47/20.36 | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 &
% 136.47/20.36 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) &
% 136.47/20.36 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)
% 136.47/20.36 | |
% 136.47/20.36 | | ALPHA: (9) implies:
% 136.47/20.36 | | (10) op(e3, e1) = e3
% 136.47/20.36 | |
% 136.47/20.36 | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #705.
% 136.47/20.36 | |
% 136.47/20.36 | End of split
% 136.47/20.36 |
% 136.47/20.36 End of proof
% 136.47/20.36
% 136.47/20.36 Sub-proof #553 shows that the following formulas are inconsistent:
% 136.47/20.36 ----------------------------------------------------------------
% 136.47/20.36 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.36 (2) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.47/20.36 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 136.47/20.36 op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.47/20.36 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.47/20.36 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 &
% 136.47/20.36 all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~
% 136.47/20.36 (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3,
% 136.47/20.36 e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 136.47/20.36 op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) &
% 136.47/20.36 $i(all_56_17) & $i(all_56_25))
% 136.47/20.36 (3) op(e3, e3) = e3
% 136.47/20.36 (4) op(e3, e0) = all_52_12
% 136.47/20.36 (5) ~ (all_52_12 = e3)
% 136.47/20.36
% 136.47/20.36 Begin of proof
% 136.47/20.36 |
% 136.47/20.36 | BETA: splitting (2) gives:
% 136.47/20.36 |
% 136.47/20.36 | Case 1:
% 136.47/20.36 | |
% 136.47/20.36 | | (6) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 =
% 136.47/20.36 | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 &
% 136.47/20.36 | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 &
% 136.47/20.36 | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) &
% 136.47/20.36 | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)
% 136.47/20.36 | |
% 136.47/20.36 | | ALPHA: (6) implies:
% 136.47/20.36 | | (7) op(e3, e0) = e3
% 136.47/20.36 | |
% 136.47/20.36 | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #733.
% 136.47/20.36 | |
% 136.47/20.36 | Case 2:
% 136.47/20.36 | |
% 136.47/20.36 | | (8) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.47/20.36 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.47/20.36 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.47/20.36 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1)
% 136.47/20.36 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)
% 136.47/20.36 | |
% 136.47/20.36 | | ALPHA: (8) implies:
% 136.47/20.36 | | (9) ~ (all_56_1 = e3)
% 136.47/20.36 | | (10) op(e3, e3) = all_56_1
% 136.47/20.36 | |
% 136.47/20.36 | | REF_CLOSE: (1), (3), (9), (10) are inconsistent by sub-proof #766.
% 136.47/20.36 | |
% 136.47/20.36 | End of split
% 136.47/20.36 |
% 136.47/20.36 End of proof
% 136.47/20.36
% 136.47/20.36 Sub-proof #554 shows that the following formulas are inconsistent:
% 136.47/20.36 ----------------------------------------------------------------
% 136.47/20.36 (1) all_54_5 = all_8_2
% 136.47/20.36 (2) all_54_5 = e3
% 136.47/20.36 (3) ~ (all_8_2 = e3)
% 136.47/20.36
% 136.47/20.36 Begin of proof
% 136.47/20.36 |
% 136.47/20.36 | COMBINE_EQS: (1), (2) imply:
% 136.47/20.36 | (4) all_8_2 = e3
% 136.47/20.36 |
% 136.47/20.36 | SIMP: (4) implies:
% 136.47/20.36 | (5) all_8_2 = e3
% 136.47/20.36 |
% 136.47/20.36 | REDUCE: (3), (5) imply:
% 136.47/20.36 | (6) $false
% 136.47/20.36 |
% 136.47/20.36 | CLOSE: (6) is inconsistent.
% 136.47/20.36 |
% 136.47/20.36 End of proof
% 136.47/20.36
% 136.47/20.36 Sub-proof #555 shows that the following formulas are inconsistent:
% 136.47/20.36 ----------------------------------------------------------------
% 136.47/20.36 (1) ~ (all_52_6 = e3)
% 136.47/20.36 (2) ~ (all_52_7 = e3)
% 136.47/20.36 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.36 (4) op(e0, e2) = all_52_7
% 136.47/20.36 (5) op(e1, e2) = all_52_6
% 136.47/20.36 (6) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 136.47/20.36
% 136.47/20.36 Begin of proof
% 136.47/20.36 |
% 136.47/20.36 | BETA: splitting (6) gives:
% 136.47/20.36 |
% 136.47/20.36 | Case 1:
% 136.47/20.36 | |
% 136.47/20.36 | | (7) all_57_7 = e3 & op(e1, e2) = e3
% 136.47/20.36 | |
% 136.47/20.36 | | ALPHA: (7) implies:
% 136.47/20.36 | | (8) op(e1, e2) = e3
% 136.47/20.36 | |
% 136.47/20.36 | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #654.
% 136.47/20.36 | |
% 136.47/20.36 | Case 2:
% 136.47/20.36 | |
% 136.47/20.36 | | (9) all_57_13 = e3 & op(e0, e2) = e3
% 136.47/20.36 | |
% 136.47/20.36 | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #556.
% 136.47/20.36 | |
% 136.47/20.36 | End of split
% 136.47/20.36 |
% 136.47/20.36 End of proof
% 136.47/20.36
% 136.47/20.36 Sub-proof #556 shows that the following formulas are inconsistent:
% 136.47/20.36 ----------------------------------------------------------------
% 136.47/20.36 (1) all_57_13 = e3 & op(e0, e2) = e3
% 136.47/20.36 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.36 (3) op(e0, e2) = all_52_7
% 136.47/20.36 (4) ~ (all_52_7 = e3)
% 136.47/20.36
% 136.47/20.36 Begin of proof
% 136.47/20.36 |
% 136.47/20.36 | ALPHA: (1) implies:
% 136.47/20.36 | (5) op(e0, e2) = e3
% 136.47/20.36 |
% 136.47/20.36 | GROUND_INST: instantiating (2) with all_52_7, e3, e2, e0, simplifying with
% 136.47/20.36 | (3), (5) gives:
% 136.47/20.36 | (6) all_52_7 = e3
% 136.47/20.36 |
% 136.47/20.36 | REDUCE: (4), (6) imply:
% 136.47/20.36 | (7) $false
% 136.47/20.36 |
% 136.47/20.36 | CLOSE: (7) is inconsistent.
% 136.47/20.36 |
% 136.47/20.36 End of proof
% 136.47/20.36
% 136.47/20.36 Sub-proof #557 shows that the following formulas are inconsistent:
% 136.47/20.36 ----------------------------------------------------------------
% 136.47/20.36 (1) op(e1, e0) = e2
% 136.47/20.36 (2) op(e0, e0) = e3
% 136.47/20.36 (3) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 136.47/20.36 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.36 (5) ~ (e2 = e1)
% 136.47/20.36 (6) ~ (e3 = e1)
% 136.47/20.36
% 136.47/20.36 Begin of proof
% 136.47/20.36 |
% 136.47/20.36 | BETA: splitting (3) gives:
% 136.47/20.36 |
% 136.47/20.36 | Case 1:
% 136.47/20.36 | |
% 136.47/20.36 | | (7) all_57_11 = e1 & op(e1, e0) = e1
% 136.47/20.36 | |
% 136.47/20.36 | | ALPHA: (7) implies:
% 136.47/20.36 | | (8) op(e1, e0) = e1
% 136.47/20.36 | |
% 136.47/20.36 | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #720.
% 136.47/20.36 | |
% 136.47/20.36 | Case 2:
% 136.47/20.36 | |
% 136.47/20.36 | | (9) all_57_15 = e1 & op(e0, e0) = e1
% 136.47/20.36 | |
% 136.47/20.36 | | ALPHA: (9) implies:
% 136.47/20.36 | | (10) op(e0, e0) = e1
% 136.47/20.36 | |
% 136.47/20.36 | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #606.
% 136.47/20.36 | |
% 136.47/20.36 | End of split
% 136.47/20.36 |
% 136.47/20.36 End of proof
% 136.47/20.36
% 136.47/20.36 Sub-proof #558 shows that the following formulas are inconsistent:
% 136.47/20.36 ----------------------------------------------------------------
% 136.47/20.36 (1) op(e1, e1) = all_6_2
% 136.47/20.36 (2) ~ (e2 = e0)
% 136.47/20.36 (3) ~ (all_6_2 = e3)
% 136.47/20.36 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.36 (5) ~ (e2 = e1)
% 136.47/20.36 (6) ~ (e3 = e0)
% 136.47/20.36 (7) ~ (e3 = e2)
% 136.47/20.36 (8) ~ (all_6_2 = e2)
% 136.47/20.36 (9) all_57_4 = e0
% 136.47/20.36 (10) ~ (e3 = e1)
% 136.47/20.36 (11) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 136.47/20.36 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 136.47/20.36 (12) all_57_14 = e1
% 136.47/20.36 (13) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 136.47/20.36 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 136.47/20.36
% 136.47/20.36 Begin of proof
% 136.47/20.36 |
% 136.47/20.36 | BETA: splitting (13) gives:
% 136.47/20.36 |
% 136.47/20.36 | Case 1:
% 136.47/20.36 | |
% 136.47/20.36 | | (14) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 136.47/20.36 | | e2)
% 136.47/20.36 | |
% 136.47/20.36 | | BETA: splitting (14) gives:
% 136.47/20.36 | |
% 136.47/20.36 | | Case 1:
% 136.47/20.36 | | |
% 136.47/20.36 | | | (15) all_57_4 = e2 & op(e3, e1) = e2
% 136.47/20.36 | | |
% 136.47/20.36 | | | REF_CLOSE: (2), (9), (15) are inconsistent by sub-proof #689.
% 136.47/20.36 | | |
% 136.47/20.36 | | Case 2:
% 136.47/20.36 | | |
% 136.47/20.36 | | | (16) all_57_5 = e2 & op(e2, e1) = e2
% 136.47/20.36 | | |
% 136.47/20.36 | | | ALPHA: (16) implies:
% 136.47/20.36 | | | (17) all_57_5 = e2
% 136.47/20.36 | | |
% 136.47/20.36 | | | BETA: splitting (11) gives:
% 136.47/20.36 | | |
% 136.47/20.36 | | | Case 1:
% 136.47/20.36 | | | |
% 136.47/20.36 | | | | (18) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1)
% 136.47/20.36 | | | | = e3)
% 136.47/20.36 | | | |
% 136.47/20.36 | | | | BETA: splitting (18) gives:
% 136.47/20.36 | | | |
% 136.47/20.36 | | | | Case 1:
% 136.47/20.36 | | | | |
% 136.47/20.36 | | | | | (19) all_57_4 = e3 & op(e3, e1) = e3
% 136.47/20.36 | | | | |
% 136.47/20.36 | | | | | REF_CLOSE: (6), (9), (19) are inconsistent by sub-proof #691.
% 136.47/20.36 | | | | |
% 136.47/20.36 | | | | Case 2:
% 136.47/20.36 | | | | |
% 136.47/20.36 | | | | | (20) all_57_5 = e3 & op(e2, e1) = e3
% 136.47/20.36 | | | | |
% 136.47/20.36 | | | | | REF_CLOSE: (7), (17), (20) are inconsistent by sub-proof #663.
% 136.47/20.36 | | | | |
% 136.47/20.36 | | | | End of split
% 136.47/20.36 | | | |
% 136.47/20.36 | | | Case 2:
% 136.47/20.36 | | | |
% 136.47/20.36 | | | | (21) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1)
% 136.47/20.36 | | | | = e3)
% 136.47/20.36 | | | |
% 136.47/20.36 | | | | BETA: splitting (21) gives:
% 136.47/20.36 | | | |
% 136.47/20.36 | | | | Case 1:
% 136.47/20.36 | | | | |
% 136.47/20.36 | | | | | (22) all_57_8 = e3 & op(e1, e1) = e3
% 136.47/20.36 | | | | |
% 136.47/20.36 | | | | | ALPHA: (22) implies:
% 136.47/20.36 | | | | | (23) op(e1, e1) = e3
% 136.47/20.36 | | | | |
% 136.47/20.36 | | | | | REF_CLOSE: (1), (3), (4), (23) are inconsistent by sub-proof #771.
% 136.47/20.36 | | | | |
% 136.47/20.36 | | | | Case 2:
% 136.47/20.36 | | | | |
% 136.47/20.36 | | | | | (24) all_57_14 = e3 & op(e0, e1) = e3
% 136.47/20.36 | | | | |
% 136.47/20.36 | | | | | ALPHA: (24) implies:
% 136.47/20.36 | | | | | (25) all_57_14 = e3
% 136.47/20.36 | | | | |
% 136.47/20.36 | | | | | REF_CLOSE: (10), (12), (25) are inconsistent by sub-proof #561.
% 136.47/20.36 | | | | |
% 136.47/20.36 | | | | End of split
% 136.47/20.36 | | | |
% 136.47/20.36 | | | End of split
% 136.47/20.36 | | |
% 136.47/20.36 | | End of split
% 136.47/20.36 | |
% 136.47/20.36 | Case 2:
% 136.47/20.36 | |
% 136.47/20.36 | | (26) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 136.47/20.36 | | e2)
% 136.47/20.36 | |
% 136.47/20.36 | | REF_CLOSE: (1), (4), (5), (8), (12), (26) are inconsistent by sub-proof
% 136.47/20.36 | | #559.
% 136.47/20.36 | |
% 136.47/20.36 | End of split
% 136.47/20.36 |
% 136.47/20.36 End of proof
% 136.47/20.36
% 136.47/20.36 Sub-proof #559 shows that the following formulas are inconsistent:
% 136.47/20.36 ----------------------------------------------------------------
% 136.47/20.36 (1) op(e1, e1) = all_6_2
% 136.47/20.36 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.36 (3) ~ (e2 = e1)
% 136.47/20.36 (4) ~ (all_6_2 = e2)
% 136.47/20.36 (5) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 136.47/20.36 (6) all_57_14 = e1
% 136.47/20.36
% 136.47/20.36 Begin of proof
% 136.47/20.36 |
% 136.47/20.36 | BETA: splitting (5) gives:
% 136.47/20.36 |
% 136.47/20.36 | Case 1:
% 136.47/20.36 | |
% 136.47/20.36 | | (7) all_57_8 = e2 & op(e1, e1) = e2
% 136.47/20.36 | |
% 136.47/20.36 | | ALPHA: (7) implies:
% 136.47/20.36 | | (8) op(e1, e1) = e2
% 136.47/20.36 | |
% 136.47/20.36 | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #767.
% 136.47/20.36 | |
% 136.47/20.36 | Case 2:
% 136.47/20.36 | |
% 136.47/20.36 | | (9) all_57_14 = e2 & op(e0, e1) = e2
% 136.47/20.36 | |
% 136.47/20.36 | | ALPHA: (9) implies:
% 136.47/20.36 | | (10) all_57_14 = e2
% 136.47/20.36 | |
% 136.47/20.36 | | REF_CLOSE: (3), (6), (10) are inconsistent by sub-proof #560.
% 136.47/20.36 | |
% 136.47/20.36 | End of split
% 136.47/20.36 |
% 136.47/20.36 End of proof
% 136.47/20.36
% 136.47/20.36 Sub-proof #560 shows that the following formulas are inconsistent:
% 136.47/20.36 ----------------------------------------------------------------
% 136.47/20.36 (1) all_57_14 = e2
% 136.47/20.36 (2) all_57_14 = e1
% 136.47/20.36 (3) ~ (e2 = e1)
% 136.47/20.36
% 136.47/20.36 Begin of proof
% 136.47/20.36 |
% 136.47/20.36 | COMBINE_EQS: (1), (2) imply:
% 136.47/20.36 | (4) e2 = e1
% 136.47/20.36 |
% 136.47/20.36 | SIMP: (4) implies:
% 136.47/20.36 | (5) e2 = e1
% 136.47/20.36 |
% 136.47/20.36 | REDUCE: (3), (5) imply:
% 136.47/20.36 | (6) $false
% 136.47/20.36 |
% 136.47/20.36 | CLOSE: (6) is inconsistent.
% 136.47/20.36 |
% 136.47/20.36 End of proof
% 136.47/20.36
% 136.47/20.36 Sub-proof #561 shows that the following formulas are inconsistent:
% 136.47/20.36 ----------------------------------------------------------------
% 136.47/20.36 (1) all_57_14 = e3
% 136.47/20.36 (2) all_57_14 = e1
% 136.47/20.36 (3) ~ (e3 = e1)
% 136.47/20.36
% 136.47/20.36 Begin of proof
% 136.47/20.36 |
% 136.47/20.36 | COMBINE_EQS: (1), (2) imply:
% 136.47/20.36 | (4) e3 = e1
% 136.47/20.36 |
% 136.47/20.36 | SIMP: (4) implies:
% 136.47/20.36 | (5) e3 = e1
% 136.47/20.36 |
% 136.47/20.36 | REDUCE: (3), (5) imply:
% 136.47/20.36 | (6) $false
% 136.47/20.36 |
% 136.47/20.36 | CLOSE: (6) is inconsistent.
% 136.47/20.36 |
% 136.47/20.36 End of proof
% 136.47/20.36
% 136.47/20.36 Sub-proof #562 shows that the following formulas are inconsistent:
% 136.47/20.36 ----------------------------------------------------------------
% 136.47/20.36 (1) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2)
% 136.47/20.36 (2) all_57_1 = e3
% 136.47/20.36 (3) op(e3, e3) = e1
% 136.47/20.36 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.36 (5) ~ (e2 = e1)
% 136.47/20.36 (6) ~ (e3 = e2)
% 136.47/20.36
% 136.47/20.36 Begin of proof
% 136.47/20.36 |
% 136.47/20.36 | BETA: splitting (1) gives:
% 136.47/20.36 |
% 136.47/20.36 | Case 1:
% 136.47/20.36 | |
% 136.47/20.36 | | (7) all_57_0 = e2 & op(e3, e3) = e2
% 136.47/20.36 | |
% 136.47/20.36 | | ALPHA: (7) implies:
% 136.47/20.36 | | (8) op(e3, e3) = e2
% 136.47/20.36 | |
% 136.47/20.36 | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #743.
% 136.47/20.36 | |
% 136.47/20.36 | Case 2:
% 136.47/20.36 | |
% 136.47/20.36 | | (9) all_57_1 = e2 & op(e3, e2) = e2
% 136.47/20.36 | |
% 136.47/20.36 | | REF_CLOSE: (2), (6), (9) are inconsistent by sub-proof #563.
% 136.47/20.36 | |
% 136.47/20.36 | End of split
% 136.47/20.36 |
% 136.47/20.36 End of proof
% 136.47/20.36
% 136.47/20.36 Sub-proof #563 shows that the following formulas are inconsistent:
% 136.47/20.36 ----------------------------------------------------------------
% 136.47/20.36 (1) all_57_1 = e2 & op(e3, e2) = e2
% 136.47/20.36 (2) all_57_1 = e3
% 136.47/20.36 (3) ~ (e3 = e2)
% 136.47/20.36
% 136.47/20.36 Begin of proof
% 136.47/20.36 |
% 136.47/20.36 | ALPHA: (1) implies:
% 136.47/20.36 | (4) all_57_1 = e2
% 136.47/20.36 |
% 136.47/20.36 | COMBINE_EQS: (2), (4) imply:
% 136.47/20.36 | (5) e3 = e2
% 136.47/20.36 |
% 136.47/20.36 | REDUCE: (3), (5) imply:
% 136.47/20.36 | (6) $false
% 136.47/20.36 |
% 136.47/20.36 | CLOSE: (6) is inconsistent.
% 136.47/20.36 |
% 136.47/20.36 End of proof
% 136.47/20.36
% 136.47/20.36 Sub-proof #564 shows that the following formulas are inconsistent:
% 136.47/20.36 ----------------------------------------------------------------
% 136.47/20.36 (1) op(e2, e2) = e0
% 136.47/20.36 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.36 (3) op(e3, e2) = all_52_4
% 136.47/20.36 (4) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 136.47/20.36 (5) ~ (e1 = e0)
% 136.47/20.36 (6) ~ (all_52_4 = e1)
% 136.47/20.36
% 136.47/20.36 Begin of proof
% 136.47/20.36 |
% 136.47/20.36 | BETA: splitting (4) gives:
% 136.47/20.36 |
% 136.47/20.36 | Case 1:
% 136.47/20.36 | |
% 136.47/20.36 | | (7) all_57_1 = e1 & op(e3, e2) = e1
% 136.47/20.36 | |
% 136.47/20.36 | | REF_CLOSE: (2), (3), (6), (7) are inconsistent by sub-proof #684.
% 136.47/20.36 | |
% 136.47/20.36 | Case 2:
% 136.47/20.36 | |
% 136.47/20.36 | | (8) all_57_3 = e1 & op(e2, e2) = e1
% 136.47/20.36 | |
% 136.47/20.36 | | ALPHA: (8) implies:
% 136.47/20.36 | | (9) op(e2, e2) = e1
% 136.47/20.36 | |
% 136.47/20.36 | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #675.
% 136.47/20.36 | |
% 136.47/20.36 | End of split
% 136.47/20.36 |
% 136.47/20.36 End of proof
% 136.47/20.36
% 136.47/20.36 Sub-proof #565 shows that the following formulas are inconsistent:
% 136.47/20.36 ----------------------------------------------------------------
% 136.47/20.36 (1) op(e1, e1) = all_6_2
% 136.47/20.36 (2) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 136.47/20.36 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 136.47/20.36 (3) op(e0, e0) = e3
% 136.47/20.36 (4) ~ (all_52_4 = e0)
% 136.47/20.36 (5) op(e2, e2) = e0
% 136.47/20.36 (6) ~ (all_52_6 = e3)
% 136.47/20.36 (7) ~ (all_52_14 = e3)
% 136.47/20.36 (8) ~ (e2 = e0)
% 136.47/20.36 (9) all_57_3 = e0
% 136.47/20.36 (10) op(e3, e3) = e1
% 136.47/20.36 (11) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 136.47/20.36 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 136.47/20.36 (12) ~ (all_6_2 = e3)
% 136.47/20.36 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.36 (14) ~ (e2 = e1)
% 136.47/20.36 (15) ~ (all_52_6 = e2)
% 136.47/20.36 (16) ~ (e3 = e0)
% 136.47/20.36 (17) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 136.47/20.36 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 136.47/20.36 e2)
% 136.47/20.36 (18) ~ (e3 = e2)
% 136.47/20.36 (19) all_57_13 = e1
% 136.47/20.36 (20) ~ (all_46_2 = e0) | ( ~ (all_46_0 = e2) & op(e0, e1) = all_46_0 &
% 136.47/20.36 $i(all_46_0)) | ( ~ (all_46_1 = e3) & op(e0, e0) = all_46_1 &
% 136.47/20.36 $i(all_46_1))
% 136.47/20.36 (21) ~ (all_52_6 = all_6_2)
% 136.47/20.36 (22) ~ (all_52_1 = e1)
% 136.47/20.36 (23) op(e0, e1) = all_52_11
% 136.47/20.36 (24) ~ (all_52_6 = e0)
% 136.47/20.36 (25) all_54_9 = all_52_6
% 136.47/20.36 (26) all_54_10 = all_6_2
% 136.47/20.36 (27) ~ (all_52_11 = e3)
% 136.47/20.36 (28) ~ (all_6_2 = e2)
% 136.47/20.36 (29) op(e1, e2) = all_52_6
% 136.47/20.36 (30) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 136.47/20.36 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 136.47/20.36 (31) ~ (all_52_8 = all_6_2)
% 136.47/20.36 (32) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 136.47/20.36 (33) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 136.47/20.36 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 136.47/20.36 (34) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 136.47/20.36 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 136.47/20.36 (35) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 136.47/20.36 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 136.47/20.36 (36) op(e3, e2) = all_52_4
% 136.47/20.36 (37) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 136.47/20.36 (38) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 136.47/20.36 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 136.47/20.36 (39) all_46_2 = all_6_2
% 136.47/20.36 (40) op(e2, e3) = all_52_1
% 136.47/20.36 (41) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 136.47/20.36 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 136.47/20.36 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 136.47/20.36 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 136.47/20.36 (42) op(e3, e1) = all_52_8
% 136.47/20.36 (43) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 136.47/20.36 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 136.47/20.36 (44) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 136.47/20.36 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 136.47/20.36 (45) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 136.47/20.36 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 136.47/20.36 (46) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 136.47/20.36 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 136.47/20.36 (47) op(e1, e0) = all_52_14
% 136.47/20.36 (48) ~ (all_52_8 = e3)
% 136.47/20.36 (49) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 136.47/20.36 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 136.47/20.36
% 136.47/20.36 Begin of proof
% 136.47/20.36 |
% 136.47/20.36 | BETA: splitting (17) gives:
% 136.47/20.36 |
% 136.47/20.36 | Case 1:
% 136.47/20.36 | |
% 136.47/20.36 | | (50) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 136.47/20.36 | | e2)
% 136.47/20.36 | |
% 136.47/20.36 | | BETA: splitting (50) gives:
% 136.47/20.36 | |
% 136.47/20.36 | | Case 1:
% 136.47/20.36 | | |
% 136.47/20.36 | | | (51) all_57_12 = e2 & op(e0, e3) = e2
% 136.47/20.36 | | |
% 136.47/20.36 | | | ALPHA: (51) implies:
% 136.47/20.36 | | | (52) all_57_12 = e2
% 136.47/20.36 | | |
% 136.47/20.36 | | | BETA: splitting (37) gives:
% 136.47/20.36 | | |
% 136.47/20.36 | | | Case 1:
% 136.47/20.36 | | | |
% 136.47/20.36 | | | | (53) all_54_9 = e2
% 136.47/20.36 | | | |
% 136.47/20.36 | | | | REF_CLOSE: (15), (25), (53) are inconsistent by sub-proof #582.
% 136.47/20.36 | | | |
% 136.47/20.36 | | | Case 2:
% 136.47/20.36 | | | |
% 136.47/20.36 | | | | (54) ~ (all_54_9 = e2)
% 136.47/20.36 | | | | (55) all_54_9 = e1 | all_54_9 = e0
% 136.47/20.36 | | | |
% 136.47/20.36 | | | | BETA: splitting (55) gives:
% 136.47/20.36 | | | |
% 136.47/20.36 | | | | Case 1:
% 136.47/20.36 | | | | |
% 136.47/20.36 | | | | | (56) all_54_9 = e1
% 136.47/20.36 | | | | |
% 136.47/20.36 | | | | | COMBINE_EQS: (25), (56) imply:
% 136.47/20.36 | | | | | (57) all_52_6 = e1
% 136.47/20.36 | | | | |
% 136.47/20.36 | | | | | SIMP: (57) implies:
% 136.47/20.36 | | | | | (58) all_52_6 = e1
% 136.47/20.36 | | | | |
% 136.47/20.36 | | | | | REDUCE: (21), (58) imply:
% 136.47/20.36 | | | | | (59) ~ (all_6_2 = e1)
% 136.47/20.36 | | | | |
% 136.47/20.36 | | | | | SIMP: (59) implies:
% 136.47/20.36 | | | | | (60) ~ (all_6_2 = e1)
% 136.47/20.36 | | | | |
% 136.47/20.36 | | | | | REDUCE: (6), (58) imply:
% 136.47/20.36 | | | | | (61) ~ (e3 = e1)
% 136.47/20.36 | | | | |
% 136.47/20.36 | | | | | SIMP: (61) implies:
% 136.47/20.36 | | | | | (62) ~ (e3 = e1)
% 136.47/20.36 | | | | |
% 136.47/20.36 | | | | | REDUCE: (15), (58) imply:
% 136.47/20.36 | | | | | (63) ~ (e2 = e1)
% 136.47/20.36 | | | | |
% 136.47/20.36 | | | | | REDUCE: (24), (58) imply:
% 136.47/20.36 | | | | | (64) ~ (e1 = e0)
% 136.47/20.36 | | | | |
% 136.47/20.36 | | | | | BETA: splitting (32) gives:
% 136.47/20.36 | | | | |
% 136.47/20.36 | | | | | Case 1:
% 136.47/20.36 | | | | | |
% 136.47/20.36 | | | | | | (65) all_54_10 = e3
% 136.47/20.36 | | | | | |
% 136.47/20.36 | | | | | | REF_CLOSE: (12), (26), (65) are inconsistent by sub-proof #742.
% 136.47/20.36 | | | | | |
% 136.47/20.36 | | | | | Case 2:
% 136.47/20.36 | | | | | |
% 136.47/20.36 | | | | | | (66) ~ (all_54_10 = e3)
% 136.47/20.36 | | | | | | (67) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 136.47/20.36 | | | | | |
% 136.47/20.36 | | | | | | BETA: splitting (67) gives:
% 136.47/20.36 | | | | | |
% 136.47/20.36 | | | | | | Case 1:
% 136.47/20.36 | | | | | | |
% 136.47/20.36 | | | | | | | (68) all_54_10 = e2
% 136.47/20.36 | | | | | | |
% 136.47/20.36 | | | | | | | REF_CLOSE: (26), (28), (68) are inconsistent by sub-proof #741.
% 136.47/20.36 | | | | | | |
% 136.47/20.36 | | | | | | Case 2:
% 136.47/20.36 | | | | | | |
% 136.47/20.36 | | | | | | | (69) ~ (all_54_10 = e2)
% 136.47/20.36 | | | | | | | (70) all_54_10 = e1 | all_54_10 = e0
% 136.47/20.36 | | | | | | |
% 136.47/20.36 | | | | | | | BETA: splitting (43) gives:
% 136.47/20.36 | | | | | | |
% 136.47/20.36 | | | | | | | Case 1:
% 136.47/20.36 | | | | | | | |
% 136.47/20.36 | | | | | | | | (71) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 &
% 136.47/20.36 | | | | | | | | op(e2, e1) = e3)
% 136.47/20.36 | | | | | | | |
% 136.47/20.36 | | | | | | | | BETA: splitting (71) gives:
% 136.47/20.36 | | | | | | | |
% 136.47/20.36 | | | | | | | | Case 1:
% 136.47/20.36 | | | | | | | | |
% 136.47/20.36 | | | | | | | | | (72) all_57_4 = e3 & op(e3, e1) = e3
% 136.47/20.36 | | | | | | | | |
% 136.47/20.36 | | | | | | | | | ALPHA: (72) implies:
% 136.47/20.36 | | | | | | | | | (73) op(e3, e1) = e3
% 136.47/20.36 | | | | | | | | |
% 136.47/20.36 | | | | | | | | | REF_CLOSE: (13), (42), (48), (73) are inconsistent by
% 136.47/20.36 | | | | | | | | | sub-proof #705.
% 136.47/20.36 | | | | | | | | |
% 136.47/20.36 | | | | | | | | Case 2:
% 136.47/20.36 | | | | | | | | |
% 136.47/20.36 | | | | | | | | | (74) all_57_5 = e3 & op(e2, e1) = e3
% 136.47/20.36 | | | | | | | | |
% 136.47/20.36 | | | | | | | | | ALPHA: (74) implies:
% 136.47/20.36 | | | | | | | | | (75) all_57_5 = e3
% 136.47/20.36 | | | | | | | | |
% 136.47/20.36 | | | | | | | | | BETA: splitting (35) gives:
% 136.47/20.36 | | | | | | | | |
% 136.47/20.36 | | | | | | | | | Case 1:
% 136.47/20.36 | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | (76) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 &
% 136.47/20.36 | | | | | | | | | | op(e1, e2) = e3)
% 136.47/20.36 | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | BETA: splitting (76) gives:
% 136.47/20.36 | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | Case 1:
% 136.47/20.36 | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | (77) all_57_6 = e3 & op(e1, e3) = e3
% 136.47/20.36 | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | ALPHA: (77) implies:
% 136.47/20.36 | | | | | | | | | | | (78) all_57_6 = e3
% 136.47/20.36 | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | BETA: splitting (33) gives:
% 136.47/20.36 | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | Case 1:
% 136.47/20.36 | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | (79) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 136.47/20.36 | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 136.47/20.36 | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | BETA: splitting (79) gives:
% 136.47/20.36 | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | Case 1:
% 136.47/20.36 | | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | | (80) all_57_9 = e2 & op(e3, e0) = e2
% 136.47/20.36 | | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | | ALPHA: (80) implies:
% 136.47/20.36 | | | | | | | | | | | | | (81) all_57_9 = e2
% 136.47/20.36 | | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | | BETA: splitting (11) gives:
% 136.47/20.36 | | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | | Case 1:
% 136.47/20.36 | | | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | | | (82) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 136.47/20.36 | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 136.47/20.36 | | | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | | | REF_CLOSE: (4), (10), (13), (36), (64), (82) are inconsistent
% 136.47/20.36 | | | | | | | | | | | | | | by sub-proof #692.
% 136.47/20.36 | | | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | | Case 2:
% 136.47/20.36 | | | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | | | (83) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 136.47/20.36 | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 136.47/20.36 | | | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | | | BETA: splitting (83) gives:
% 136.47/20.36 | | | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | | | Case 1:
% 136.47/20.36 | | | | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | | | | (84) all_57_4 = e0 & op(e3, e1) = e0
% 136.47/20.36 | | | | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | | | | ALPHA: (84) implies:
% 136.47/20.36 | | | | | | | | | | | | | | | (85) op(e3, e1) = e0
% 136.47/20.36 | | | | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 136.47/20.36 | | | | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | | | | Case 1:
% 136.47/20.36 | | | | | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | | | | | (86) all_54_10 = e1
% 136.47/20.36 | | | | | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | | | | | REF_CLOSE: (26), (60), (86) are inconsistent by sub-proof
% 136.47/20.36 | | | | | | | | | | | | | | | | #736.
% 136.47/20.36 | | | | | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | | | | Case 2:
% 136.47/20.36 | | | | | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | | | | | (87) all_54_10 = e0
% 136.47/20.36 | | | | | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | | | | | COMBINE_EQS: (26), (87) imply:
% 136.47/20.36 | | | | | | | | | | | | | | | | (88) all_6_2 = e0
% 136.47/20.36 | | | | | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | | | | | SIMP: (88) implies:
% 136.47/20.36 | | | | | | | | | | | | | | | | (89) all_6_2 = e0
% 136.47/20.36 | | | | | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | | | | | REDUCE: (1), (89) imply:
% 136.47/20.36 | | | | | | | | | | | | | | | | (90) op(e1, e1) = e0
% 136.47/20.36 | | | | | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | | | | | REF_CLOSE: (1), (13), (31), (42), (85), (90) are inconsistent
% 136.47/20.36 | | | | | | | | | | | | | | | | by sub-proof #619.
% 136.47/20.36 | | | | | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | | | | End of split
% 136.47/20.36 | | | | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | | | Case 2:
% 136.47/20.36 | | | | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | | | | (91) all_57_9 = e0 & op(e3, e0) = e0
% 136.47/20.36 | | | | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | | | | ALPHA: (91) implies:
% 136.47/20.36 | | | | | | | | | | | | | | | (92) all_57_9 = e0
% 136.47/20.36 | | | | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | | | | REF_CLOSE: (8), (81), (92) are inconsistent by sub-proof
% 136.47/20.36 | | | | | | | | | | | | | | | #696.
% 136.47/20.36 | | | | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | | | End of split
% 136.47/20.36 | | | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | | End of split
% 136.47/20.36 | | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | Case 2:
% 136.47/20.36 | | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | | (93) all_57_10 = e2 & op(e2, e0) = e2
% 136.47/20.36 | | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | | ALPHA: (93) implies:
% 136.47/20.36 | | | | | | | | | | | | | (94) all_57_10 = e2
% 136.47/20.36 | | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | | BETA: splitting (49) gives:
% 136.47/20.36 | | | | | | | | | | | | |
% 136.47/20.36 | | | | | | | | | | | | | Case 1:
% 136.47/20.36 | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | (95) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 136.47/20.37 | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 136.47/20.37 | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | BETA: splitting (95) gives:
% 136.47/20.37 | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | Case 1:
% 136.47/20.37 | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | (96) all_57_4 = e2 & op(e3, e1) = e2
% 136.47/20.37 | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | ALPHA: (96) implies:
% 136.47/20.37 | | | | | | | | | | | | | | | (97) all_57_4 = e2
% 136.47/20.37 | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (10), (11), (13), (14), (16), (18),
% 136.47/20.37 | | | | | | | | | | | | | | | (22), (30), (36), (40), (45), (46), (62), (64),
% 136.47/20.37 | | | | | | | | | | | | | | | (75), (94), (97) are inconsistent by sub-proof
% 136.47/20.37 | | | | | | | | | | | | | | | #666.
% 136.47/20.37 | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | Case 2:
% 136.47/20.37 | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | (98) all_57_5 = e2 & op(e2, e1) = e2
% 136.47/20.37 | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | REF_CLOSE: (18), (75), (98) are inconsistent by sub-proof
% 136.47/20.37 | | | | | | | | | | | | | | | #677.
% 136.47/20.37 | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | End of split
% 136.47/20.37 | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | Case 2:
% 136.47/20.37 | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | (99) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 136.47/20.37 | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 136.47/20.37 | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | BETA: splitting (99) gives:
% 136.47/20.37 | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | Case 1:
% 136.47/20.37 | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | (100) all_57_8 = e2 & op(e1, e1) = e2
% 136.47/20.37 | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | ALPHA: (100) implies:
% 136.47/20.37 | | | | | | | | | | | | | | | (101) op(e1, e1) = e2
% 136.47/20.37 | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | REF_CLOSE: (1), (13), (28), (101) are inconsistent by
% 136.47/20.37 | | | | | | | | | | | | | | | sub-proof #767.
% 136.47/20.37 | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | Case 2:
% 136.47/20.37 | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | (102) all_57_14 = e2 & op(e0, e1) = e2
% 136.47/20.37 | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | ALPHA: (102) implies:
% 136.47/20.37 | | | | | | | | | | | | | | | (103) all_57_14 = e2
% 136.47/20.37 | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | BETA: splitting (45) gives:
% 136.47/20.37 | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | Case 1:
% 136.47/20.37 | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | (104) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 136.47/20.37 | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 136.47/20.37 | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13), (22), (40), (64), (104) are
% 136.47/20.37 | | | | | | | | | | | | | | | | inconsistent by sub-proof #674.
% 136.47/20.37 | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | Case 2:
% 136.47/20.37 | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | (105) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 136.47/20.37 | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 136.47/20.37 | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | BETA: splitting (105) gives:
% 136.47/20.37 | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | Case 1:
% 136.47/20.37 | | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | | (106) all_57_5 = e1 & op(e2, e1) = e1
% 136.47/20.37 | | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (75), (106) are inconsistent by sub-proof
% 136.47/20.37 | | | | | | | | | | | | | | | | | #673.
% 136.47/20.37 | | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | Case 2:
% 136.47/20.37 | | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | | (107) all_57_10 = e1 & op(e2, e0) = e1
% 136.47/20.37 | | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | | ALPHA: (107) implies:
% 136.47/20.37 | | | | | | | | | | | | | | | | | (108) all_57_10 = e1
% 136.47/20.37 | | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | | COMBINE_EQS: (94), (108) imply:
% 136.47/20.37 | | | | | | | | | | | | | | | | | (109) e2 = e1
% 136.47/20.37 | | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | | SIMP: (109) implies:
% 136.47/20.37 | | | | | | | | | | | | | | | | | (110) e2 = e1
% 136.47/20.37 | | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | | COMBINE_EQS: (52), (110) imply:
% 136.47/20.37 | | | | | | | | | | | | | | | | | (111) all_57_12 = e1
% 136.47/20.37 | | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | | BETA: splitting (41) gives:
% 136.47/20.37 | | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | | Case 1:
% 136.47/20.37 | | | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | | | (112) all_57_15 = e0 & op(e0, e0) = e0
% 136.47/20.37 | | | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | | | ALPHA: (112) implies:
% 136.47/20.37 | | | | | | | | | | | | | | | | | | (113) op(e0, e0) = e0
% 136.47/20.37 | | | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (13), (16), (113) are inconsistent by
% 136.47/20.37 | | | | | | | | | | | | | | | | | | sub-proof #715.
% 136.47/20.37 | | | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | | Case 2:
% 136.47/20.37 | | | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | | | (114) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 136.47/20.37 | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 136.47/20.37 | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 136.47/20.37 | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 136.47/20.37 | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 136.47/20.37 | | | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | | | ALPHA: (114) implies:
% 136.47/20.37 | | | | | | | | | | | | | | | | | | (115) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 136.47/20.37 | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 136.47/20.37 | | | | | | | | | | | | | | | | | | e1) = e0)
% 136.47/20.37 | | | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | | | BETA: splitting (115) gives:
% 136.47/20.37 | | | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | | | Case 1:
% 136.47/20.37 | | | | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | | | | (116) all_57_12 = e0 & op(e0, e3) = e0
% 136.47/20.37 | | | | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | | | | ALPHA: (116) implies:
% 136.47/20.37 | | | | | | | | | | | | | | | | | | | (117) all_57_12 = e0
% 136.47/20.37 | | | | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (64), (111), (117) are inconsistent by sub-proof
% 136.47/20.37 | | | | | | | | | | | | | | | | | | | #581.
% 136.47/20.37 | | | | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | | | Case 2:
% 136.47/20.37 | | | | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | | | | (118) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 136.47/20.37 | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 136.47/20.37 | | | | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (19), (64), (103), (118) are inconsistent by
% 136.47/20.37 | | | | | | | | | | | | | | | | | | | sub-proof #579.
% 136.47/20.37 | | | | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | | | End of split
% 136.47/20.37 | | | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | | End of split
% 136.47/20.37 | | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | End of split
% 136.47/20.37 | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | End of split
% 136.47/20.37 | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | End of split
% 136.47/20.37 | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | End of split
% 136.47/20.37 | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | End of split
% 136.47/20.37 | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | Case 2:
% 136.47/20.37 | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | (119) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 136.47/20.37 | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 136.47/20.37 | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | BETA: splitting (119) gives:
% 136.47/20.37 | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | Case 1:
% 136.47/20.37 | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | (120) all_57_11 = e2 & op(e1, e0) = e2
% 136.47/20.37 | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | ALPHA: (120) implies:
% 136.47/20.37 | | | | | | | | | | | | | (121) all_57_11 = e2
% 136.47/20.37 | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | BETA: splitting (49) gives:
% 136.47/20.37 | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | Case 1:
% 136.47/20.37 | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | (122) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 136.47/20.37 | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 136.47/20.37 | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | BETA: splitting (122) gives:
% 136.47/20.37 | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | Case 1:
% 136.47/20.37 | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | (123) all_57_4 = e2 & op(e3, e1) = e2
% 136.47/20.37 | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | ALPHA: (123) implies:
% 136.47/20.37 | | | | | | | | | | | | | | | (124) all_57_4 = e2
% 136.47/20.37 | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | BETA: splitting (34) gives:
% 136.47/20.37 | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | Case 1:
% 136.47/20.37 | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | (125) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 136.47/20.37 | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 136.47/20.37 | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | BETA: splitting (125) gives:
% 136.47/20.37 | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | Case 1:
% 136.47/20.37 | | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | | (126) all_57_0 = e0 & op(e3, e3) = e0
% 136.47/20.37 | | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | | ALPHA: (126) implies:
% 136.47/20.37 | | | | | | | | | | | | | | | | | (127) op(e3, e3) = e0
% 136.47/20.37 | | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (13), (64), (127) are inconsistent by
% 136.47/20.37 | | | | | | | | | | | | | | | | | sub-proof #717.
% 136.47/20.37 | | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | Case 2:
% 136.47/20.37 | | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | | (128) all_57_2 = e0 & op(e2, e3) = e0
% 136.47/20.37 | | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | | ALPHA: (128) implies:
% 136.47/20.37 | | | | | | | | | | | | | | | | | (129) all_57_2 = e0
% 136.47/20.37 | | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (8), (9), (10), (11), (13), (14),
% 136.47/20.37 | | | | | | | | | | | | | | | | | (16), (18), (22), (30), (36), (40), (45), (46),
% 136.47/20.37 | | | | | | | | | | | | | | | | | (62), (64), (75), (124), (129) are inconsistent by
% 136.47/20.37 | | | | | | | | | | | | | | | | | sub-proof #665.
% 136.47/20.37 | | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | End of split
% 136.47/20.37 | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | Case 2:
% 136.47/20.37 | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | (130) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 136.47/20.37 | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 136.47/20.37 | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (16), (52), (78), (130) are inconsistent by
% 136.47/20.37 | | | | | | | | | | | | | | | | sub-proof #577.
% 136.47/20.37 | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | End of split
% 136.47/20.37 | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | Case 2:
% 136.47/20.37 | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | (131) all_57_5 = e2 & op(e2, e1) = e2
% 136.47/20.37 | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | REF_CLOSE: (18), (75), (131) are inconsistent by sub-proof
% 136.47/20.37 | | | | | | | | | | | | | | | #677.
% 136.47/20.37 | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | End of split
% 136.47/20.37 | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | Case 2:
% 136.47/20.37 | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | (132) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 136.47/20.37 | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 136.47/20.37 | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 136.47/20.37 | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | Case 1:
% 136.47/20.37 | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | (133) all_57_8 = e2 & op(e1, e1) = e2
% 136.47/20.37 | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | ALPHA: (133) implies:
% 136.47/20.37 | | | | | | | | | | | | | | | (134) all_57_8 = e2
% 136.47/20.37 | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (13), (14), (16), (18), (29), (35),
% 136.47/20.37 | | | | | | | | | | | | | | | (38), (44), (62), (64), (121), (134) are
% 136.47/20.37 | | | | | | | | | | | | | | | inconsistent by sub-proof #571.
% 136.47/20.37 | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | Case 2:
% 136.47/20.37 | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | (135) all_57_14 = e2 & op(e0, e1) = e2
% 136.47/20.37 | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | ALPHA: (135) implies:
% 136.47/20.37 | | | | | | | | | | | | | | | (136) op(e0, e1) = e2
% 136.47/20.37 | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 136.47/20.37 | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | Case 1:
% 136.47/20.37 | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | (137) all_54_10 = e1
% 136.47/20.37 | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | REF_CLOSE: (26), (60), (137) are inconsistent by sub-proof
% 136.47/20.37 | | | | | | | | | | | | | | | | #736.
% 136.47/20.37 | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | Case 2:
% 136.47/20.37 | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | (138) all_54_10 = e0
% 136.47/20.37 | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | | REF_CLOSE: (3), (13), (20), (26), (39), (136), (138) are
% 136.47/20.37 | | | | | | | | | | | | | | | | inconsistent by sub-proof #569.
% 136.47/20.37 | | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | | End of split
% 136.47/20.37 | | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | | End of split
% 136.47/20.37 | | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | End of split
% 136.47/20.37 | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | Case 2:
% 136.47/20.37 | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | (139) all_57_15 = e2 & op(e0, e0) = e2
% 136.47/20.37 | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | ALPHA: (139) implies:
% 136.47/20.37 | | | | | | | | | | | | | (140) op(e0, e0) = e2
% 136.47/20.37 | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | | REF_CLOSE: (3), (13), (18), (140) are inconsistent by
% 136.47/20.37 | | | | | | | | | | | | | sub-proof #634.
% 136.47/20.37 | | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | | End of split
% 136.47/20.37 | | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | End of split
% 136.47/20.37 | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | Case 2:
% 136.47/20.37 | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | (141) all_57_7 = e3 & op(e1, e2) = e3
% 136.47/20.37 | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | ALPHA: (141) implies:
% 136.47/20.37 | | | | | | | | | | | (142) op(e1, e2) = e3
% 136.47/20.37 | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | | REF_CLOSE: (6), (13), (29), (142) are inconsistent by
% 136.47/20.37 | | | | | | | | | | | sub-proof #654.
% 136.47/20.37 | | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | End of split
% 136.47/20.37 | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | Case 2:
% 136.47/20.37 | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | (143) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3
% 136.47/20.37 | | | | | | | | | | & op(e1, e0) = e3)
% 136.47/20.37 | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | | REF_CLOSE: (1), (7), (12), (13), (47), (143) are inconsistent
% 136.47/20.37 | | | | | | | | | | by sub-proof #653.
% 136.47/20.37 | | | | | | | | | |
% 136.47/20.37 | | | | | | | | | End of split
% 136.47/20.37 | | | | | | | | |
% 136.47/20.37 | | | | | | | | End of split
% 136.47/20.37 | | | | | | | |
% 136.47/20.37 | | | | | | | Case 2:
% 136.47/20.37 | | | | | | | |
% 136.47/20.37 | | | | | | | | (144) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 &
% 136.47/20.37 | | | | | | | | op(e0, e1) = e3)
% 136.47/20.37 | | | | | | | |
% 136.47/20.37 | | | | | | | | REF_CLOSE: (1), (12), (13), (23), (27), (144) are inconsistent
% 136.47/20.37 | | | | | | | | by sub-proof #651.
% 136.47/20.37 | | | | | | | |
% 136.47/20.37 | | | | | | | End of split
% 136.47/20.37 | | | | | | |
% 136.47/20.37 | | | | | | End of split
% 136.47/20.37 | | | | | |
% 136.47/20.37 | | | | | End of split
% 136.47/20.37 | | | | |
% 136.47/20.37 | | | | Case 2:
% 136.47/20.37 | | | | |
% 136.47/20.37 | | | | | (145) all_54_9 = e0
% 136.47/20.37 | | | | |
% 136.47/20.37 | | | | | REF_CLOSE: (24), (25), (145) are inconsistent by sub-proof #568.
% 136.47/20.37 | | | | |
% 136.47/20.37 | | | | End of split
% 136.47/20.37 | | | |
% 136.47/20.37 | | | End of split
% 136.47/20.37 | | |
% 136.47/20.37 | | Case 2:
% 136.47/20.37 | | |
% 136.47/20.37 | | | (146) all_57_13 = e2 & op(e0, e2) = e2
% 136.47/20.37 | | |
% 136.47/20.37 | | | ALPHA: (146) implies:
% 136.47/20.37 | | | (147) all_57_13 = e2
% 136.47/20.37 | | |
% 136.47/20.37 | | | REF_CLOSE: (14), (19), (147) are inconsistent by sub-proof #567.
% 136.47/20.37 | | |
% 136.47/20.37 | | End of split
% 136.47/20.37 | |
% 136.47/20.37 | Case 2:
% 136.47/20.37 | |
% 136.47/20.37 | | (148) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 136.47/20.37 | | e2)
% 136.47/20.37 | |
% 136.47/20.37 | | BETA: splitting (148) gives:
% 136.47/20.37 | |
% 136.47/20.37 | | Case 1:
% 136.47/20.37 | | |
% 136.47/20.37 | | | (149) all_57_14 = e2 & op(e0, e1) = e2
% 136.47/20.37 | | |
% 136.47/20.37 | | | ALPHA: (149) implies:
% 136.47/20.37 | | | (150) op(e0, e1) = e2
% 136.47/20.37 | | |
% 136.47/20.37 | | | REF_CLOSE: (3), (12), (13), (15), (20), (21), (24), (25), (26), (28),
% 136.47/20.37 | | | (32), (37), (39), (150) are inconsistent by sub-proof #566.
% 136.47/20.37 | | |
% 136.47/20.37 | | Case 2:
% 136.47/20.37 | | |
% 136.47/20.37 | | | (151) all_57_15 = e2 & op(e0, e0) = e2
% 136.47/20.37 | | |
% 136.47/20.37 | | | ALPHA: (151) implies:
% 136.47/20.37 | | | (152) op(e0, e0) = e2
% 136.47/20.37 | | |
% 136.47/20.37 | | | REF_CLOSE: (3), (13), (18), (152) are inconsistent by sub-proof #634.
% 136.47/20.37 | | |
% 136.47/20.37 | | End of split
% 136.47/20.37 | |
% 136.47/20.37 | End of split
% 136.47/20.37 |
% 136.47/20.37 End of proof
% 136.47/20.37
% 136.47/20.37 Sub-proof #566 shows that the following formulas are inconsistent:
% 136.47/20.37 ----------------------------------------------------------------
% 136.47/20.37 (1) op(e0, e1) = e2
% 136.47/20.37 (2) op(e0, e0) = e3
% 136.47/20.37 (3) ~ (all_6_2 = e3)
% 136.47/20.37 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.37 (5) ~ (all_52_6 = e2)
% 136.47/20.37 (6) ~ (all_46_2 = e0) | ( ~ (all_46_0 = e2) & op(e0, e1) = all_46_0 &
% 136.47/20.37 $i(all_46_0)) | ( ~ (all_46_1 = e3) & op(e0, e0) = all_46_1 &
% 136.47/20.37 $i(all_46_1))
% 136.47/20.37 (7) ~ (all_52_6 = all_6_2)
% 136.47/20.37 (8) ~ (all_52_6 = e0)
% 136.47/20.37 (9) all_54_9 = all_52_6
% 136.47/20.37 (10) all_54_10 = all_6_2
% 136.47/20.37 (11) ~ (all_6_2 = e2)
% 136.47/20.37 (12) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 136.47/20.37 (13) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 136.47/20.37 (14) all_46_2 = all_6_2
% 136.47/20.37
% 136.47/20.37 Begin of proof
% 136.47/20.37 |
% 136.47/20.37 | BETA: splitting (13) gives:
% 136.47/20.37 |
% 136.47/20.37 | Case 1:
% 136.47/20.37 | |
% 136.47/20.37 | | (15) all_54_9 = e2
% 136.47/20.37 | |
% 136.47/20.37 | | REF_CLOSE: (5), (9), (15) are inconsistent by sub-proof #582.
% 136.47/20.37 | |
% 136.47/20.37 | Case 2:
% 136.47/20.37 | |
% 136.47/20.37 | | (16) all_54_9 = e1 | all_54_9 = e0
% 136.47/20.37 | |
% 136.47/20.37 | | BETA: splitting (16) gives:
% 136.47/20.37 | |
% 136.47/20.37 | | Case 1:
% 136.47/20.37 | | |
% 136.47/20.37 | | | (17) all_54_9 = e1
% 136.47/20.37 | | |
% 136.47/20.37 | | | COMBINE_EQS: (9), (17) imply:
% 136.47/20.37 | | | (18) all_52_6 = e1
% 136.47/20.37 | | |
% 136.47/20.37 | | | SIMP: (18) implies:
% 136.47/20.37 | | | (19) all_52_6 = e1
% 136.47/20.37 | | |
% 136.47/20.37 | | | REDUCE: (7), (19) imply:
% 136.47/20.37 | | | (20) ~ (all_6_2 = e1)
% 136.47/20.37 | | |
% 136.47/20.37 | | | SIMP: (20) implies:
% 136.47/20.37 | | | (21) ~ (all_6_2 = e1)
% 136.47/20.37 | | |
% 136.47/20.37 | | | BETA: splitting (12) gives:
% 136.47/20.37 | | |
% 136.47/20.37 | | | Case 1:
% 136.47/20.37 | | | |
% 136.47/20.37 | | | | (22) all_54_10 = e3
% 136.47/20.37 | | | |
% 136.47/20.37 | | | | REF_CLOSE: (3), (10), (22) are inconsistent by sub-proof #742.
% 136.47/20.37 | | | |
% 136.47/20.37 | | | Case 2:
% 136.47/20.37 | | | |
% 136.47/20.37 | | | | (23) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 136.47/20.37 | | | |
% 136.47/20.37 | | | | BETA: splitting (23) gives:
% 136.47/20.37 | | | |
% 136.47/20.37 | | | | Case 1:
% 136.47/20.37 | | | | |
% 136.47/20.37 | | | | | (24) all_54_10 = e2
% 136.47/20.37 | | | | |
% 136.47/20.37 | | | | | REF_CLOSE: (10), (11), (24) are inconsistent by sub-proof #741.
% 136.47/20.37 | | | | |
% 136.47/20.37 | | | | Case 2:
% 136.47/20.37 | | | | |
% 136.47/20.37 | | | | | (25) all_54_10 = e1 | all_54_10 = e0
% 136.47/20.37 | | | | |
% 136.47/20.37 | | | | | BETA: splitting (25) gives:
% 136.47/20.37 | | | | |
% 136.47/20.37 | | | | | Case 1:
% 136.47/20.37 | | | | | |
% 136.47/20.37 | | | | | | (26) all_54_10 = e1
% 136.47/20.37 | | | | | |
% 136.47/20.37 | | | | | | REF_CLOSE: (10), (21), (26) are inconsistent by sub-proof #736.
% 136.47/20.37 | | | | | |
% 136.47/20.37 | | | | | Case 2:
% 136.47/20.37 | | | | | |
% 136.47/20.37 | | | | | | (27) all_54_10 = e0
% 136.47/20.37 | | | | | |
% 136.47/20.37 | | | | | | REF_CLOSE: (1), (2), (4), (6), (10), (14), (27) are inconsistent by
% 136.47/20.37 | | | | | | sub-proof #569.
% 136.47/20.37 | | | | | |
% 136.47/20.37 | | | | | End of split
% 136.47/20.37 | | | | |
% 136.47/20.37 | | | | End of split
% 136.47/20.37 | | | |
% 136.47/20.37 | | | End of split
% 136.47/20.37 | | |
% 136.47/20.37 | | Case 2:
% 136.47/20.37 | | |
% 136.47/20.37 | | | (28) all_54_9 = e0
% 136.47/20.37 | | |
% 136.47/20.37 | | | REF_CLOSE: (8), (9), (28) are inconsistent by sub-proof #568.
% 136.47/20.37 | | |
% 136.47/20.37 | | End of split
% 136.47/20.37 | |
% 136.47/20.37 | End of split
% 136.47/20.37 |
% 136.47/20.37 End of proof
% 136.47/20.37
% 136.47/20.37 Sub-proof #567 shows that the following formulas are inconsistent:
% 136.47/20.37 ----------------------------------------------------------------
% 136.47/20.37 (1) all_57_13 = e2
% 136.47/20.37 (2) all_57_13 = e1
% 136.47/20.37 (3) ~ (e2 = e1)
% 136.47/20.37
% 136.47/20.37 Begin of proof
% 136.47/20.37 |
% 136.47/20.37 | COMBINE_EQS: (1), (2) imply:
% 136.47/20.37 | (4) e2 = e1
% 136.47/20.37 |
% 136.47/20.37 | SIMP: (4) implies:
% 136.47/20.37 | (5) e2 = e1
% 136.47/20.37 |
% 136.47/20.37 | REDUCE: (3), (5) imply:
% 136.47/20.37 | (6) $false
% 136.47/20.37 |
% 136.47/20.37 | CLOSE: (6) is inconsistent.
% 136.47/20.37 |
% 136.47/20.37 End of proof
% 136.47/20.37
% 136.47/20.37 Sub-proof #568 shows that the following formulas are inconsistent:
% 136.47/20.37 ----------------------------------------------------------------
% 136.47/20.37 (1) all_54_9 = all_52_6
% 136.47/20.37 (2) all_54_9 = e0
% 136.47/20.37 (3) ~ (all_52_6 = e0)
% 136.47/20.37
% 136.47/20.37 Begin of proof
% 136.47/20.37 |
% 136.47/20.37 | COMBINE_EQS: (1), (2) imply:
% 136.47/20.37 | (4) all_52_6 = e0
% 136.47/20.37 |
% 136.47/20.37 | SIMP: (4) implies:
% 136.47/20.37 | (5) all_52_6 = e0
% 136.47/20.37 |
% 136.47/20.37 | REDUCE: (3), (5) imply:
% 136.47/20.37 | (6) $false
% 136.47/20.37 |
% 136.47/20.37 | CLOSE: (6) is inconsistent.
% 136.47/20.37 |
% 136.47/20.37 End of proof
% 136.47/20.37
% 136.47/20.37 Sub-proof #569 shows that the following formulas are inconsistent:
% 136.47/20.37 ----------------------------------------------------------------
% 136.47/20.37 (1) op(e0, e1) = e2
% 136.47/20.37 (2) op(e0, e0) = e3
% 136.47/20.37 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.47/20.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.47/20.37 (4) all_54_10 = e0
% 136.47/20.37 (5) ~ (all_46_2 = e0) | ( ~ (all_46_0 = e2) & op(e0, e1) = all_46_0 &
% 136.47/20.37 $i(all_46_0)) | ( ~ (all_46_1 = e3) & op(e0, e0) = all_46_1 &
% 136.47/20.37 $i(all_46_1))
% 136.47/20.37 (6) all_54_10 = all_6_2
% 136.47/20.37 (7) all_46_2 = all_6_2
% 136.47/20.37
% 136.47/20.37 Begin of proof
% 136.47/20.37 |
% 136.47/20.37 | COMBINE_EQS: (4), (6) imply:
% 136.47/20.37 | (8) all_6_2 = e0
% 136.47/20.37 |
% 136.47/20.37 | SIMP: (8) implies:
% 136.47/20.37 | (9) all_6_2 = e0
% 136.47/20.37 |
% 136.47/20.37 | COMBINE_EQS: (7), (9) imply:
% 136.47/20.37 | (10) all_46_2 = e0
% 136.47/20.37 |
% 136.47/20.37 | REF_CLOSE: (1), (2), (3), (5), (10) are inconsistent by sub-proof #570.
% 136.47/20.37 |
% 136.47/20.37 End of proof
% 136.47/20.37
% 136.47/20.37 Sub-proof #570 shows that the following formulas are inconsistent:
% 136.76/20.37 ----------------------------------------------------------------
% 136.76/20.37 (1) op(e0, e1) = e2
% 136.76/20.37 (2) op(e0, e0) = e3
% 136.76/20.37 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.76/20.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.76/20.37 (4) ~ (all_46_2 = e0) | ( ~ (all_46_0 = e2) & op(e0, e1) = all_46_0 &
% 136.76/20.37 $i(all_46_0)) | ( ~ (all_46_1 = e3) & op(e0, e0) = all_46_1 &
% 136.76/20.37 $i(all_46_1))
% 136.76/20.37 (5) all_46_2 = e0
% 136.76/20.37
% 136.76/20.37 Begin of proof
% 136.76/20.37 |
% 136.76/20.37 | BETA: splitting (4) gives:
% 136.76/20.37 |
% 136.76/20.37 | Case 1:
% 136.76/20.37 | |
% 136.76/20.37 | | (6) ~ (all_46_2 = e0)
% 136.76/20.37 | |
% 136.76/20.37 | | REDUCE: (5), (6) imply:
% 136.76/20.37 | | (7) $false
% 136.76/20.37 | |
% 136.76/20.37 | | CLOSE: (7) is inconsistent.
% 136.76/20.37 | |
% 136.76/20.37 | Case 2:
% 136.76/20.37 | |
% 136.76/20.37 | | (8) ( ~ (all_46_0 = e2) & op(e0, e1) = all_46_0 & $i(all_46_0)) | ( ~
% 136.76/20.37 | | (all_46_1 = e3) & op(e0, e0) = all_46_1 & $i(all_46_1))
% 136.76/20.37 | |
% 136.76/20.37 | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #757.
% 136.76/20.37 | |
% 136.76/20.37 | End of split
% 136.76/20.37 |
% 136.76/20.37 End of proof
% 136.76/20.37
% 136.76/20.37 Sub-proof #571 shows that the following formulas are inconsistent:
% 136.76/20.37 ----------------------------------------------------------------
% 136.76/20.37 (1) ~ (all_52_6 = e3)
% 136.76/20.37 (2) ~ (e2 = e0)
% 136.76/20.37 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.76/20.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.76/20.37 (4) ~ (e2 = e1)
% 136.76/20.37 (5) ~ (e3 = e0)
% 136.76/20.37 (6) ~ (e3 = e2)
% 136.76/20.37 (7) all_57_8 = e2
% 136.76/20.37 (8) op(e1, e2) = all_52_6
% 136.76/20.37 (9) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 136.76/20.37 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 136.76/20.37 (10) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 136.76/20.37 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 136.76/20.37 (11) all_57_11 = e2
% 136.76/20.37 (12) ~ (e3 = e1)
% 136.76/20.37 (13) ~ (e1 = e0)
% 136.76/20.37 (14) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 136.76/20.37 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 136.76/20.37
% 136.76/20.37 Begin of proof
% 136.76/20.37 |
% 136.76/20.37 | BETA: splitting (9) gives:
% 136.76/20.37 |
% 136.76/20.37 | Case 1:
% 136.76/20.37 | |
% 136.76/20.37 | | (15) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 136.76/20.37 | | e3)
% 136.76/20.37 | |
% 136.76/20.37 | | BETA: splitting (15) gives:
% 136.76/20.37 | |
% 136.76/20.37 | | Case 1:
% 136.76/20.37 | | |
% 136.76/20.37 | | | (16) all_57_6 = e3 & op(e1, e3) = e3
% 136.76/20.37 | | |
% 136.76/20.37 | | | ALPHA: (16) implies:
% 136.76/20.37 | | | (17) all_57_6 = e3
% 136.76/20.37 | | |
% 136.76/20.37 | | | REF_CLOSE: (2), (4), (5), (7), (10), (11), (12), (13), (14), (17) are
% 136.76/20.37 | | | inconsistent by sub-proof #572.
% 136.76/20.37 | | |
% 136.76/20.37 | | Case 2:
% 136.76/20.37 | | |
% 136.76/20.37 | | | (18) all_57_7 = e3 & op(e1, e2) = e3
% 136.76/20.37 | | |
% 136.76/20.37 | | | ALPHA: (18) implies:
% 136.76/20.37 | | | (19) op(e1, e2) = e3
% 136.76/20.37 | | |
% 136.76/20.37 | | | REF_CLOSE: (1), (3), (8), (19) are inconsistent by sub-proof #654.
% 136.76/20.37 | | |
% 136.76/20.37 | | End of split
% 136.76/20.37 | |
% 136.76/20.37 | Case 2:
% 136.76/20.37 | |
% 136.76/20.37 | | (20) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 136.76/20.37 | | e3)
% 136.76/20.37 | |
% 136.76/20.37 | | BETA: splitting (20) gives:
% 136.76/20.37 | |
% 136.76/20.37 | | Case 1:
% 136.76/20.37 | | |
% 136.76/20.37 | | | (21) all_57_8 = e3 & op(e1, e1) = e3
% 136.76/20.37 | | |
% 136.76/20.37 | | | ALPHA: (21) implies:
% 136.76/20.37 | | | (22) all_57_8 = e3
% 136.76/20.37 | | |
% 136.76/20.37 | | | COMBINE_EQS: (7), (22) imply:
% 136.76/20.37 | | | (23) e3 = e2
% 136.76/20.37 | | |
% 136.76/20.37 | | | SIMP: (23) implies:
% 136.76/20.37 | | | (24) e3 = e2
% 136.76/20.37 | | |
% 136.76/20.37 | | | REDUCE: (6), (24) imply:
% 136.76/20.37 | | | (25) $false
% 136.76/20.37 | | |
% 136.76/20.37 | | | CLOSE: (25) is inconsistent.
% 136.76/20.37 | | |
% 136.76/20.37 | | Case 2:
% 136.76/20.37 | | |
% 136.76/20.37 | | | (26) all_57_11 = e3 & op(e1, e0) = e3
% 136.76/20.37 | | |
% 136.76/20.37 | | | REF_CLOSE: (6), (11), (26) are inconsistent by sub-proof #723.
% 136.76/20.37 | | |
% 136.76/20.37 | | End of split
% 136.76/20.37 | |
% 136.76/20.37 | End of split
% 136.76/20.37 |
% 136.76/20.37 End of proof
% 136.76/20.37
% 136.76/20.37 Sub-proof #572 shows that the following formulas are inconsistent:
% 136.76/20.37 ----------------------------------------------------------------
% 136.76/20.37 (1) ~ (e2 = e0)
% 136.76/20.37 (2) ~ (e2 = e1)
% 136.76/20.37 (3) ~ (e3 = e0)
% 136.76/20.37 (4) all_57_8 = e2
% 136.76/20.37 (5) all_57_6 = e3
% 136.76/20.37 (6) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 136.76/20.37 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 136.76/20.37 (7) all_57_11 = e2
% 136.76/20.37 (8) ~ (e3 = e1)
% 136.76/20.37 (9) ~ (e1 = e0)
% 136.76/20.37 (10) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 136.76/20.37 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 136.76/20.37
% 136.76/20.37 Begin of proof
% 136.76/20.37 |
% 136.76/20.37 | BETA: splitting (10) gives:
% 136.76/20.37 |
% 136.76/20.37 | Case 1:
% 136.76/20.37 | |
% 136.76/20.37 | | (11) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) =
% 136.76/20.37 | | e0)
% 136.76/20.37 | |
% 136.76/20.37 | | BETA: splitting (11) gives:
% 136.76/20.37 | |
% 136.76/20.37 | | Case 1:
% 136.76/20.37 | | |
% 136.76/20.37 | | | (12) all_57_6 = e0 & op(e1, e3) = e0
% 136.76/20.37 | | |
% 136.76/20.37 | | | REF_CLOSE: (3), (5), (12) are inconsistent by sub-proof #576.
% 136.76/20.37 | | |
% 136.76/20.37 | | Case 2:
% 136.76/20.37 | | |
% 136.76/20.37 | | | (13) all_57_7 = e0 & op(e1, e2) = e0
% 136.76/20.37 | | |
% 136.76/20.37 | | | ALPHA: (13) implies:
% 136.76/20.37 | | | (14) all_57_7 = e0
% 136.76/20.37 | | |
% 136.76/20.37 | | | BETA: splitting (6) gives:
% 136.76/20.37 | | |
% 136.76/20.37 | | | Case 1:
% 136.76/20.37 | | | |
% 136.76/20.37 | | | | (15) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2)
% 136.76/20.37 | | | | = e1)
% 136.76/20.37 | | | |
% 136.76/20.37 | | | | BETA: splitting (15) gives:
% 136.76/20.37 | | | |
% 136.76/20.37 | | | | Case 1:
% 136.76/20.37 | | | | |
% 136.76/20.37 | | | | | (16) all_57_6 = e1 & op(e1, e3) = e1
% 136.76/20.37 | | | | |
% 136.76/20.37 | | | | | ALPHA: (16) implies:
% 136.76/20.37 | | | | | (17) all_57_6 = e1
% 136.76/20.37 | | | | |
% 136.76/20.37 | | | | | REF_CLOSE: (5), (8), (17) are inconsistent by sub-proof #575.
% 136.76/20.37 | | | | |
% 136.76/20.37 | | | | Case 2:
% 136.76/20.37 | | | | |
% 136.76/20.37 | | | | | (18) all_57_7 = e1 & op(e1, e2) = e1
% 136.76/20.37 | | | | |
% 136.76/20.37 | | | | | ALPHA: (18) implies:
% 136.76/20.37 | | | | | (19) all_57_7 = e1
% 136.76/20.37 | | | | |
% 136.76/20.37 | | | | | COMBINE_EQS: (14), (19) imply:
% 136.76/20.37 | | | | | (20) e1 = e0
% 136.76/20.37 | | | | |
% 136.76/20.37 | | | | | REDUCE: (9), (20) imply:
% 136.76/20.37 | | | | | (21) $false
% 136.76/20.37 | | | | |
% 136.76/20.37 | | | | | CLOSE: (21) is inconsistent.
% 136.76/20.37 | | | | |
% 136.76/20.37 | | | | End of split
% 136.76/20.37 | | | |
% 136.76/20.37 | | | Case 2:
% 136.76/20.37 | | | |
% 136.76/20.37 | | | | (22) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0)
% 136.76/20.37 | | | | = e1)
% 136.76/20.37 | | | |
% 136.76/20.37 | | | | BETA: splitting (22) gives:
% 136.76/20.37 | | | |
% 136.76/20.37 | | | | Case 1:
% 136.76/20.37 | | | | |
% 136.76/20.37 | | | | | (23) all_57_8 = e1 & op(e1, e1) = e1
% 136.76/20.37 | | | | |
% 136.76/20.37 | | | | | REF_CLOSE: (2), (4), (23) are inconsistent by sub-proof #574.
% 136.76/20.37 | | | | |
% 136.76/20.37 | | | | Case 2:
% 136.76/20.37 | | | | |
% 136.76/20.37 | | | | | (24) all_57_11 = e1 & op(e1, e0) = e1
% 136.76/20.37 | | | | |
% 136.76/20.37 | | | | | ALPHA: (24) implies:
% 136.76/20.37 | | | | | (25) all_57_11 = e1
% 136.76/20.37 | | | | |
% 136.76/20.37 | | | | | COMBINE_EQS: (7), (25) imply:
% 136.76/20.37 | | | | | (26) e2 = e1
% 136.76/20.37 | | | | |
% 136.76/20.37 | | | | | SIMP: (26) implies:
% 136.76/20.37 | | | | | (27) e2 = e1
% 136.76/20.37 | | | | |
% 136.76/20.37 | | | | | REDUCE: (2), (27) imply:
% 136.76/20.37 | | | | | (28) $false
% 136.76/20.37 | | | | |
% 136.76/20.37 | | | | | CLOSE: (28) is inconsistent.
% 136.76/20.37 | | | | |
% 136.76/20.37 | | | | End of split
% 136.76/20.37 | | | |
% 136.76/20.37 | | | End of split
% 136.76/20.37 | | |
% 136.76/20.37 | | End of split
% 136.76/20.37 | |
% 136.76/20.37 | Case 2:
% 136.76/20.37 | |
% 136.76/20.37 | | (29) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 136.76/20.37 | | e0)
% 136.76/20.37 | |
% 136.76/20.37 | | BETA: splitting (29) gives:
% 136.76/20.37 | |
% 136.76/20.37 | | Case 1:
% 136.76/20.37 | | |
% 136.76/20.37 | | | (30) all_57_8 = e0 & op(e1, e1) = e0
% 136.76/20.37 | | |
% 136.76/20.37 | | | REF_CLOSE: (1), (4), (30) are inconsistent by sub-proof #573.
% 136.76/20.37 | | |
% 136.76/20.37 | | Case 2:
% 136.76/20.37 | | |
% 136.76/20.37 | | | (31) all_57_11 = e0 & op(e1, e0) = e0
% 136.76/20.37 | | |
% 136.76/20.37 | | | REF_CLOSE: (1), (7), (31) are inconsistent by sub-proof #656.
% 136.76/20.37 | | |
% 136.76/20.37 | | End of split
% 136.76/20.37 | |
% 136.76/20.37 | End of split
% 136.76/20.37 |
% 136.76/20.37 End of proof
% 136.76/20.37
% 136.76/20.37 Sub-proof #573 shows that the following formulas are inconsistent:
% 136.76/20.37 ----------------------------------------------------------------
% 136.76/20.37 (1) all_57_8 = e0 & op(e1, e1) = e0
% 136.76/20.37 (2) all_57_8 = e2
% 136.76/20.37 (3) ~ (e2 = e0)
% 136.76/20.37
% 136.76/20.37 Begin of proof
% 136.76/20.37 |
% 136.76/20.37 | ALPHA: (1) implies:
% 136.76/20.37 | (4) all_57_8 = e0
% 136.76/20.37 |
% 136.76/20.37 | COMBINE_EQS: (2), (4) imply:
% 136.76/20.37 | (5) e2 = e0
% 136.76/20.37 |
% 136.76/20.37 | SIMP: (5) implies:
% 136.76/20.37 | (6) e2 = e0
% 136.76/20.37 |
% 136.76/20.37 | REDUCE: (3), (6) imply:
% 136.76/20.37 | (7) $false
% 136.76/20.37 |
% 136.76/20.37 | CLOSE: (7) is inconsistent.
% 136.76/20.37 |
% 136.76/20.37 End of proof
% 136.76/20.37
% 136.76/20.37 Sub-proof #574 shows that the following formulas are inconsistent:
% 136.76/20.37 ----------------------------------------------------------------
% 136.76/20.37 (1) all_57_8 = e1 & op(e1, e1) = e1
% 136.76/20.37 (2) all_57_8 = e2
% 136.76/20.37 (3) ~ (e2 = e1)
% 136.76/20.37
% 136.76/20.37 Begin of proof
% 136.76/20.37 |
% 136.76/20.37 | ALPHA: (1) implies:
% 136.76/20.37 | (4) all_57_8 = e1
% 136.76/20.37 |
% 136.76/20.37 | COMBINE_EQS: (2), (4) imply:
% 136.76/20.37 | (5) e2 = e1
% 136.76/20.37 |
% 136.76/20.37 | REDUCE: (3), (5) imply:
% 136.76/20.37 | (6) $false
% 136.76/20.37 |
% 136.76/20.37 | CLOSE: (6) is inconsistent.
% 136.76/20.37 |
% 136.76/20.37 End of proof
% 136.76/20.37
% 136.76/20.37 Sub-proof #575 shows that the following formulas are inconsistent:
% 136.76/20.37 ----------------------------------------------------------------
% 136.76/20.37 (1) all_57_6 = e3
% 136.76/20.37 (2) all_57_6 = e1
% 136.76/20.37 (3) ~ (e3 = e1)
% 136.76/20.37
% 136.76/20.37 Begin of proof
% 136.76/20.37 |
% 136.76/20.37 | COMBINE_EQS: (1), (2) imply:
% 136.76/20.37 | (4) e3 = e1
% 136.76/20.37 |
% 136.76/20.37 | SIMP: (4) implies:
% 136.76/20.37 | (5) e3 = e1
% 136.76/20.37 |
% 136.76/20.37 | REDUCE: (3), (5) imply:
% 136.76/20.37 | (6) $false
% 136.76/20.37 |
% 136.76/20.37 | CLOSE: (6) is inconsistent.
% 136.76/20.37 |
% 136.76/20.37 End of proof
% 136.76/20.37
% 136.76/20.37 Sub-proof #576 shows that the following formulas are inconsistent:
% 136.76/20.37 ----------------------------------------------------------------
% 136.76/20.37 (1) all_57_6 = e0 & op(e1, e3) = e0
% 136.76/20.37 (2) all_57_6 = e3
% 136.76/20.37 (3) ~ (e3 = e0)
% 136.76/20.37
% 136.76/20.37 Begin of proof
% 136.76/20.37 |
% 136.76/20.37 | ALPHA: (1) implies:
% 136.76/20.37 | (4) all_57_6 = e0
% 136.76/20.37 |
% 136.76/20.37 | COMBINE_EQS: (2), (4) imply:
% 136.76/20.37 | (5) e3 = e0
% 136.76/20.37 |
% 136.76/20.37 | REDUCE: (3), (5) imply:
% 136.76/20.37 | (6) $false
% 136.76/20.37 |
% 136.76/20.37 | CLOSE: (6) is inconsistent.
% 136.76/20.37 |
% 136.76/20.37 End of proof
% 136.76/20.37
% 136.76/20.37 Sub-proof #577 shows that the following formulas are inconsistent:
% 136.76/20.37 ----------------------------------------------------------------
% 136.76/20.37 (1) ~ (e2 = e0)
% 136.76/20.37 (2) ~ (e3 = e0)
% 136.76/20.37 (3) all_57_6 = e3
% 136.76/20.37 (4) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 136.76/20.37 (5) all_57_12 = e2
% 136.76/20.37
% 136.76/20.37 Begin of proof
% 136.76/20.37 |
% 136.76/20.37 | BETA: splitting (4) gives:
% 136.76/20.37 |
% 136.76/20.37 | Case 1:
% 136.76/20.37 | |
% 136.76/20.37 | | (6) all_57_6 = e0 & op(e1, e3) = e0
% 136.76/20.37 | |
% 136.76/20.37 | | ALPHA: (6) implies:
% 136.76/20.37 | | (7) all_57_6 = e0
% 136.76/20.37 | |
% 136.76/20.37 | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #588.
% 136.76/20.37 | |
% 136.76/20.37 | Case 2:
% 136.76/20.37 | |
% 136.76/20.38 | | (8) all_57_12 = e0 & op(e0, e3) = e0
% 136.76/20.38 | |
% 136.76/20.38 | | REF_CLOSE: (1), (5), (8) are inconsistent by sub-proof #578.
% 136.76/20.38 | |
% 136.76/20.38 | End of split
% 136.76/20.38 |
% 136.76/20.38 End of proof
% 136.76/20.38
% 136.76/20.38 Sub-proof #578 shows that the following formulas are inconsistent:
% 136.76/20.38 ----------------------------------------------------------------
% 136.76/20.38 (1) all_57_12 = e0 & op(e0, e3) = e0
% 136.76/20.38 (2) all_57_12 = e2
% 136.76/20.38 (3) ~ (e2 = e0)
% 136.76/20.38
% 136.76/20.38 Begin of proof
% 136.76/20.38 |
% 136.76/20.38 | ALPHA: (1) implies:
% 136.76/20.38 | (4) all_57_12 = e0
% 136.76/20.38 |
% 136.76/20.38 | COMBINE_EQS: (2), (4) imply:
% 136.76/20.38 | (5) e2 = e0
% 136.76/20.38 |
% 136.76/20.38 | REDUCE: (3), (5) imply:
% 136.76/20.38 | (6) $false
% 136.76/20.38 |
% 136.76/20.38 | CLOSE: (6) is inconsistent.
% 136.76/20.38 |
% 136.76/20.38 End of proof
% 136.76/20.38
% 136.76/20.38 Sub-proof #579 shows that the following formulas are inconsistent:
% 136.76/20.38 ----------------------------------------------------------------
% 136.76/20.38 (1) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 136.76/20.38 (2) ~ (e2 = e0)
% 136.76/20.38 (3) all_57_13 = e1
% 136.76/20.38 (4) all_57_14 = e2
% 136.76/20.38 (5) ~ (e1 = e0)
% 136.76/20.38
% 136.76/20.38 Begin of proof
% 136.76/20.38 |
% 136.76/20.38 | BETA: splitting (1) gives:
% 136.76/20.38 |
% 136.76/20.38 | Case 1:
% 136.76/20.38 | |
% 136.76/20.38 | | (6) all_57_13 = e0 & op(e0, e2) = e0
% 136.76/20.38 | |
% 136.76/20.38 | | ALPHA: (6) implies:
% 136.76/20.38 | | (7) all_57_13 = e0
% 136.76/20.38 | |
% 136.76/20.38 | | REF_CLOSE: (3), (5), (7) are inconsistent by sub-proof #681.
% 136.76/20.38 | |
% 136.76/20.38 | Case 2:
% 136.76/20.38 | |
% 136.76/20.38 | | (8) all_57_14 = e0 & op(e0, e1) = e0
% 136.76/20.38 | |
% 136.76/20.38 | | REF_CLOSE: (2), (4), (8) are inconsistent by sub-proof #580.
% 136.76/20.38 | |
% 136.76/20.38 | End of split
% 136.76/20.38 |
% 136.76/20.38 End of proof
% 136.76/20.38
% 136.76/20.38 Sub-proof #580 shows that the following formulas are inconsistent:
% 136.76/20.38 ----------------------------------------------------------------
% 136.76/20.38 (1) all_57_14 = e0 & op(e0, e1) = e0
% 136.76/20.38 (2) all_57_14 = e2
% 136.76/20.38 (3) ~ (e2 = e0)
% 136.76/20.38
% 136.76/20.38 Begin of proof
% 136.76/20.38 |
% 136.76/20.38 | ALPHA: (1) implies:
% 136.76/20.38 | (4) all_57_14 = e0
% 136.76/20.38 |
% 136.76/20.38 | COMBINE_EQS: (2), (4) imply:
% 136.76/20.38 | (5) e2 = e0
% 136.76/20.38 |
% 136.76/20.38 | SIMP: (5) implies:
% 136.76/20.38 | (6) e2 = e0
% 136.76/20.38 |
% 136.76/20.38 | REDUCE: (3), (6) imply:
% 136.76/20.38 | (7) $false
% 136.76/20.38 |
% 136.76/20.38 | CLOSE: (7) is inconsistent.
% 136.76/20.38 |
% 136.76/20.38 End of proof
% 136.76/20.38
% 136.76/20.38 Sub-proof #581 shows that the following formulas are inconsistent:
% 136.76/20.38 ----------------------------------------------------------------
% 136.76/20.38 (1) all_57_12 = e1
% 136.76/20.38 (2) all_57_12 = e0
% 136.76/20.38 (3) ~ (e1 = e0)
% 136.76/20.38
% 136.76/20.38 Begin of proof
% 136.76/20.38 |
% 136.76/20.38 | COMBINE_EQS: (1), (2) imply:
% 136.76/20.38 | (4) e1 = e0
% 136.76/20.38 |
% 136.76/20.38 | SIMP: (4) implies:
% 136.76/20.38 | (5) e1 = e0
% 136.76/20.38 |
% 136.76/20.38 | REDUCE: (3), (5) imply:
% 136.76/20.38 | (6) $false
% 136.76/20.38 |
% 136.76/20.38 | CLOSE: (6) is inconsistent.
% 136.76/20.38 |
% 136.76/20.38 End of proof
% 136.76/20.38
% 136.76/20.38 Sub-proof #582 shows that the following formulas are inconsistent:
% 136.76/20.38 ----------------------------------------------------------------
% 136.76/20.38 (1) all_54_9 = all_52_6
% 136.76/20.38 (2) all_54_9 = e2
% 136.76/20.38 (3) ~ (all_52_6 = e2)
% 136.76/20.38
% 136.76/20.38 Begin of proof
% 136.76/20.38 |
% 136.76/20.38 | COMBINE_EQS: (1), (2) imply:
% 136.76/20.38 | (4) all_52_6 = e2
% 136.76/20.38 |
% 136.76/20.38 | SIMP: (4) implies:
% 136.76/20.38 | (5) all_52_6 = e2
% 136.76/20.38 |
% 136.76/20.38 | REDUCE: (3), (5) imply:
% 136.76/20.38 | (6) $false
% 136.76/20.38 |
% 136.76/20.38 | CLOSE: (6) is inconsistent.
% 136.76/20.38 |
% 136.76/20.38 End of proof
% 136.76/20.38
% 136.76/20.38 Sub-proof #583 shows that the following formulas are inconsistent:
% 136.76/20.38 ----------------------------------------------------------------
% 136.76/20.38 (1) ~ (e2 = e0)
% 136.76/20.38 (2) op(e3, e3) = e1
% 136.76/20.38 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.76/20.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.76/20.38 (4) ~ (e2 = e1)
% 136.76/20.38 (5) ~ (e3 = e0)
% 136.76/20.38 (6) ~ (e3 = e2)
% 136.76/20.38 (7) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 136.76/20.38 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 136.76/20.38 (8) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 136.76/20.38 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 136.76/20.38 (9) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 136.76/20.38 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 136.76/20.38 (10) ~ (e3 = e1)
% 136.76/20.38 (11) ~ (e1 = e0)
% 136.76/20.38 (12) all_57_12 = e1
% 136.76/20.38
% 136.76/20.38 Begin of proof
% 136.76/20.38 |
% 136.76/20.38 | BETA: splitting (8) gives:
% 136.76/20.38 |
% 136.76/20.38 | Case 1:
% 136.76/20.38 | |
% 136.76/20.38 | | (13) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 136.76/20.38 | | e0)
% 136.76/20.38 | |
% 136.76/20.38 | | BETA: splitting (13) gives:
% 136.76/20.38 | |
% 136.76/20.38 | | Case 1:
% 136.76/20.38 | | |
% 136.76/20.38 | | | (14) all_57_0 = e0 & op(e3, e3) = e0
% 136.76/20.38 | | |
% 136.76/20.38 | | | ALPHA: (14) implies:
% 136.76/20.38 | | | (15) op(e3, e3) = e0
% 136.76/20.38 | | |
% 136.76/20.38 | | | REF_CLOSE: (2), (3), (11), (15) are inconsistent by sub-proof #717.
% 136.76/20.38 | | |
% 136.76/20.38 | | Case 2:
% 136.76/20.38 | | |
% 136.76/20.38 | | | (16) all_57_2 = e0 & op(e2, e3) = e0
% 136.76/20.38 | | |
% 136.76/20.38 | | | ALPHA: (16) implies:
% 136.76/20.38 | | | (17) all_57_2 = e0
% 136.76/20.38 | | |
% 136.76/20.38 | | | BETA: splitting (9) gives:
% 136.76/20.38 | | |
% 136.76/20.38 | | | Case 1:
% 136.76/20.38 | | | |
% 136.76/20.38 | | | | (18) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3)
% 136.76/20.38 | | | | = e2)
% 136.76/20.38 | | | |
% 136.76/20.38 | | | | BETA: splitting (18) gives:
% 136.76/20.38 | | | |
% 136.76/20.38 | | | | Case 1:
% 136.76/20.38 | | | | |
% 136.76/20.38 | | | | | (19) all_57_0 = e2 & op(e3, e3) = e2
% 136.76/20.38 | | | | |
% 136.76/20.38 | | | | | ALPHA: (19) implies:
% 136.76/20.38 | | | | | (20) op(e3, e3) = e2
% 136.76/20.38 | | | | |
% 136.76/20.38 | | | | | REF_CLOSE: (2), (3), (4), (20) are inconsistent by sub-proof #743.
% 136.76/20.38 | | | | |
% 136.76/20.38 | | | | Case 2:
% 136.76/20.38 | | | | |
% 136.76/20.38 | | | | | (21) all_57_2 = e2 & op(e2, e3) = e2
% 136.76/20.38 | | | | |
% 136.76/20.38 | | | | | REF_CLOSE: (1), (17), (21) are inconsistent by sub-proof #680.
% 136.76/20.38 | | | | |
% 136.76/20.38 | | | | End of split
% 136.76/20.38 | | | |
% 136.76/20.38 | | | Case 2:
% 136.76/20.38 | | | |
% 136.76/20.38 | | | | (22) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3)
% 136.76/20.38 | | | | = e2)
% 136.76/20.38 | | | |
% 136.76/20.38 | | | | BETA: splitting (22) gives:
% 136.76/20.38 | | | |
% 136.76/20.38 | | | | Case 1:
% 136.76/20.38 | | | | |
% 136.76/20.38 | | | | | (23) all_57_6 = e2 & op(e1, e3) = e2
% 136.76/20.38 | | | | |
% 136.76/20.38 | | | | | ALPHA: (23) implies:
% 136.76/20.38 | | | | | (24) all_57_6 = e2
% 136.76/20.38 | | | | |
% 136.76/20.38 | | | | | BETA: splitting (7) gives:
% 136.76/20.38 | | | | |
% 136.76/20.38 | | | | | Case 1:
% 136.76/20.38 | | | | | |
% 136.76/20.38 | | | | | | (25) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2,
% 136.76/20.38 | | | | | | e3) = e3)
% 136.76/20.38 | | | | | |
% 136.76/20.38 | | | | | | BETA: splitting (25) gives:
% 136.76/20.38 | | | | | |
% 136.76/20.38 | | | | | | Case 1:
% 136.76/20.38 | | | | | | |
% 136.76/20.38 | | | | | | | (26) all_57_0 = e3 & op(e3, e3) = e3
% 136.76/20.38 | | | | | | |
% 136.76/20.38 | | | | | | | ALPHA: (26) implies:
% 136.76/20.38 | | | | | | | (27) op(e3, e3) = e3
% 136.76/20.38 | | | | | | |
% 136.76/20.38 | | | | | | | REF_CLOSE: (2), (3), (10), (27) are inconsistent by sub-proof
% 136.76/20.38 | | | | | | | #775.
% 136.76/20.38 | | | | | | |
% 136.76/20.38 | | | | | | Case 2:
% 136.76/20.38 | | | | | | |
% 136.76/20.38 | | | | | | | (28) all_57_2 = e3 & op(e2, e3) = e3
% 136.76/20.38 | | | | | | |
% 136.76/20.38 | | | | | | | ALPHA: (28) implies:
% 136.76/20.38 | | | | | | | (29) all_57_2 = e3
% 136.76/20.38 | | | | | | |
% 136.76/20.38 | | | | | | | REF_CLOSE: (5), (17), (29) are inconsistent by sub-proof #593.
% 136.76/20.38 | | | | | | |
% 136.76/20.38 | | | | | | End of split
% 136.76/20.38 | | | | | |
% 136.76/20.38 | | | | | Case 2:
% 136.76/20.38 | | | | | |
% 136.76/20.38 | | | | | | (30) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0,
% 136.76/20.38 | | | | | | e3) = e3)
% 136.76/20.38 | | | | | |
% 136.76/20.38 | | | | | | BETA: splitting (30) gives:
% 136.76/20.38 | | | | | |
% 136.76/20.38 | | | | | | Case 1:
% 136.76/20.38 | | | | | | |
% 136.76/20.38 | | | | | | | (31) all_57_6 = e3 & op(e1, e3) = e3
% 136.76/20.38 | | | | | | |
% 136.76/20.38 | | | | | | | ALPHA: (31) implies:
% 136.76/20.38 | | | | | | | (32) all_57_6 = e3
% 136.76/20.38 | | | | | | |
% 136.76/20.38 | | | | | | | REF_CLOSE: (6), (24), (32) are inconsistent by sub-proof #592.
% 136.76/20.38 | | | | | | |
% 136.76/20.38 | | | | | | Case 2:
% 136.76/20.38 | | | | | | |
% 136.76/20.38 | | | | | | | (33) all_57_12 = e3 & op(e0, e3) = e3
% 136.76/20.38 | | | | | | |
% 136.76/20.38 | | | | | | | ALPHA: (33) implies:
% 136.76/20.38 | | | | | | | (34) all_57_12 = e3
% 136.76/20.38 | | | | | | |
% 136.76/20.38 | | | | | | | REF_CLOSE: (10), (12), (34) are inconsistent by sub-proof #591.
% 136.76/20.38 | | | | | | |
% 136.76/20.38 | | | | | | End of split
% 136.76/20.38 | | | | | |
% 136.76/20.38 | | | | | End of split
% 136.76/20.38 | | | | |
% 136.76/20.38 | | | | Case 2:
% 136.76/20.38 | | | | |
% 136.76/20.38 | | | | | (35) all_57_12 = e2 & op(e0, e3) = e2
% 136.76/20.38 | | | | |
% 136.76/20.38 | | | | | ALPHA: (35) implies:
% 136.76/20.38 | | | | | (36) all_57_12 = e2
% 136.76/20.38 | | | | |
% 136.76/20.38 | | | | | REF_CLOSE: (4), (12), (36) are inconsistent by sub-proof #644.
% 136.76/20.38 | | | | |
% 136.76/20.38 | | | | End of split
% 136.76/20.38 | | | |
% 136.76/20.38 | | | End of split
% 136.76/20.38 | | |
% 136.76/20.38 | | End of split
% 136.76/20.38 | |
% 136.76/20.38 | Case 2:
% 136.76/20.38 | |
% 136.76/20.38 | | (37) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 136.76/20.38 | | e0)
% 136.76/20.38 | |
% 136.76/20.38 | | BETA: splitting (37) gives:
% 136.76/20.38 | |
% 136.76/20.38 | | Case 1:
% 136.76/20.38 | | |
% 136.76/20.38 | | | (38) all_57_6 = e0 & op(e1, e3) = e0
% 136.76/20.38 | | |
% 136.76/20.38 | | | ALPHA: (38) implies:
% 136.76/20.38 | | | (39) all_57_6 = e0
% 136.76/20.38 | | |
% 136.76/20.38 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (12), (39) are
% 136.76/20.38 | | | inconsistent by sub-proof #585.
% 136.76/20.38 | | |
% 136.76/20.38 | | Case 2:
% 136.76/20.38 | | |
% 136.76/20.38 | | | (40) all_57_12 = e0 & op(e0, e3) = e0
% 136.76/20.38 | | |
% 136.76/20.38 | | | REF_CLOSE: (11), (12), (40) are inconsistent by sub-proof #584.
% 136.76/20.38 | | |
% 136.76/20.38 | | End of split
% 136.76/20.38 | |
% 136.76/20.38 | End of split
% 136.76/20.38 |
% 136.76/20.38 End of proof
% 136.76/20.38
% 136.76/20.38 Sub-proof #584 shows that the following formulas are inconsistent:
% 136.76/20.38 ----------------------------------------------------------------
% 136.76/20.38 (1) all_57_12 = e0 & op(e0, e3) = e0
% 136.76/20.38 (2) all_57_12 = e1
% 136.76/20.38 (3) ~ (e1 = e0)
% 136.76/20.38
% 136.76/20.38 Begin of proof
% 136.76/20.38 |
% 136.76/20.38 | ALPHA: (1) implies:
% 136.76/20.38 | (4) all_57_12 = e0
% 136.76/20.38 |
% 136.76/20.38 | COMBINE_EQS: (2), (4) imply:
% 136.76/20.38 | (5) e1 = e0
% 136.76/20.38 |
% 136.76/20.38 | REDUCE: (3), (5) imply:
% 136.76/20.38 | (6) $false
% 136.76/20.38 |
% 136.76/20.38 | CLOSE: (6) is inconsistent.
% 136.76/20.38 |
% 136.76/20.38 End of proof
% 136.76/20.38
% 136.76/20.38 Sub-proof #585 shows that the following formulas are inconsistent:
% 136.76/20.38 ----------------------------------------------------------------
% 136.76/20.38 (1) all_57_6 = e0
% 136.76/20.38 (2) ~ (e2 = e0)
% 136.76/20.38 (3) op(e3, e3) = e1
% 136.76/20.38 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.76/20.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.76/20.38 (5) ~ (e2 = e1)
% 136.76/20.38 (6) ~ (e3 = e0)
% 136.76/20.38 (7) ~ (e3 = e2)
% 136.76/20.38 (8) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 136.76/20.38 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 136.76/20.38 (9) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 136.76/20.38 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 136.76/20.38 (10) ~ (e3 = e1)
% 136.76/20.38 (11) all_57_12 = e1
% 136.76/20.38
% 136.76/20.38 Begin of proof
% 136.76/20.38 |
% 136.76/20.38 | BETA: splitting (9) gives:
% 136.76/20.38 |
% 136.76/20.38 | Case 1:
% 136.76/20.38 | |
% 136.76/20.38 | | (12) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) =
% 136.76/20.38 | | e2)
% 136.76/20.38 | |
% 136.76/20.38 | | BETA: splitting (12) gives:
% 136.76/20.38 | |
% 136.76/20.38 | | Case 1:
% 136.76/20.38 | | |
% 136.76/20.38 | | | (13) all_57_0 = e2 & op(e3, e3) = e2
% 136.76/20.38 | | |
% 136.76/20.38 | | | ALPHA: (13) implies:
% 136.76/20.38 | | | (14) op(e3, e3) = e2
% 136.76/20.38 | | |
% 136.76/20.38 | | | REF_CLOSE: (3), (4), (5), (14) are inconsistent by sub-proof #743.
% 136.76/20.38 | | |
% 136.76/20.38 | | Case 2:
% 136.76/20.38 | | |
% 136.76/20.38 | | | (15) all_57_2 = e2 & op(e2, e3) = e2
% 136.76/20.38 | | |
% 136.76/20.38 | | | ALPHA: (15) implies:
% 136.76/20.38 | | | (16) all_57_2 = e2
% 136.76/20.38 | | |
% 136.76/20.38 | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (10), (11), (16) are inconsistent
% 136.76/20.38 | | | by sub-proof #587.
% 136.76/20.38 | | |
% 136.76/20.38 | | End of split
% 136.76/20.38 | |
% 136.76/20.38 | Case 2:
% 136.76/20.38 | |
% 136.76/20.38 | | (17) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) =
% 136.76/20.38 | | e2)
% 136.76/20.38 | |
% 136.76/20.38 | | BETA: splitting (17) gives:
% 136.76/20.38 | |
% 136.76/20.38 | | Case 1:
% 136.76/20.38 | | |
% 136.76/20.38 | | | (18) all_57_6 = e2 & op(e1, e3) = e2
% 136.76/20.38 | | |
% 136.76/20.38 | | | ALPHA: (18) implies:
% 136.76/20.38 | | | (19) all_57_6 = e2
% 136.76/20.38 | | |
% 136.76/20.38 | | | REF_CLOSE: (1), (2), (19) are inconsistent by sub-proof #586.
% 136.76/20.38 | | |
% 136.76/20.38 | | Case 2:
% 136.76/20.38 | | |
% 136.76/20.38 | | | (20) all_57_12 = e2 & op(e0, e3) = e2
% 136.76/20.38 | | |
% 136.76/20.38 | | | ALPHA: (20) implies:
% 136.76/20.38 | | | (21) all_57_12 = e2
% 136.76/20.38 | | |
% 136.76/20.38 | | | REF_CLOSE: (5), (11), (21) are inconsistent by sub-proof #644.
% 136.76/20.38 | | |
% 136.76/20.38 | | End of split
% 136.76/20.38 | |
% 136.76/20.38 | End of split
% 136.76/20.38 |
% 136.76/20.38 End of proof
% 136.76/20.38
% 136.76/20.38 Sub-proof #586 shows that the following formulas are inconsistent:
% 136.76/20.38 ----------------------------------------------------------------
% 136.76/20.38 (1) all_57_6 = e2
% 136.76/20.38 (2) all_57_6 = e0
% 136.76/20.38 (3) ~ (e2 = e0)
% 136.76/20.38
% 136.76/20.38 Begin of proof
% 136.76/20.38 |
% 136.76/20.38 | COMBINE_EQS: (1), (2) imply:
% 136.76/20.38 | (4) e2 = e0
% 136.76/20.38 |
% 136.76/20.38 | SIMP: (4) implies:
% 136.76/20.38 | (5) e2 = e0
% 136.76/20.38 |
% 136.76/20.38 | REDUCE: (3), (5) imply:
% 136.76/20.38 | (6) $false
% 136.76/20.38 |
% 136.76/20.38 | CLOSE: (6) is inconsistent.
% 136.76/20.38 |
% 136.76/20.38 End of proof
% 136.76/20.38
% 136.76/20.38 Sub-proof #587 shows that the following formulas are inconsistent:
% 136.76/20.38 ----------------------------------------------------------------
% 136.76/20.38 (1) all_57_6 = e0
% 136.76/20.38 (2) op(e3, e3) = e1
% 136.76/20.38 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.76/20.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.76/20.38 (4) ~ (e3 = e0)
% 136.76/20.38 (5) ~ (e3 = e2)
% 136.76/20.38 (6) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 136.76/20.38 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 136.76/20.38 (7) all_57_2 = e2
% 136.76/20.38 (8) ~ (e3 = e1)
% 136.76/20.38 (9) all_57_12 = e1
% 136.76/20.38
% 136.76/20.38 Begin of proof
% 136.76/20.38 |
% 136.76/20.38 | BETA: splitting (6) gives:
% 136.76/20.38 |
% 136.76/20.38 | Case 1:
% 136.76/20.38 | |
% 136.76/20.38 | | (10) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 136.76/20.38 | | e3)
% 136.76/20.38 | |
% 136.76/20.38 | | REF_CLOSE: (2), (3), (5), (7), (8), (10) are inconsistent by sub-proof #589.
% 136.76/20.38 | |
% 136.76/20.38 | Case 2:
% 136.76/20.38 | |
% 136.76/20.38 | | (11) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 136.76/20.38 | | e3)
% 136.76/20.38 | |
% 136.76/20.38 | | BETA: splitting (11) gives:
% 136.76/20.38 | |
% 136.76/20.38 | | Case 1:
% 136.76/20.38 | | |
% 136.76/20.38 | | | (12) all_57_6 = e3 & op(e1, e3) = e3
% 136.76/20.38 | | |
% 136.76/20.38 | | | ALPHA: (12) implies:
% 136.76/20.38 | | | (13) all_57_6 = e3
% 136.76/20.38 | | |
% 136.76/20.38 | | | REF_CLOSE: (1), (4), (13) are inconsistent by sub-proof #588.
% 136.76/20.38 | | |
% 136.76/20.38 | | Case 2:
% 136.76/20.38 | | |
% 136.76/20.38 | | | (14) all_57_12 = e3 & op(e0, e3) = e3
% 136.76/20.38 | | |
% 136.76/20.38 | | | ALPHA: (14) implies:
% 136.76/20.38 | | | (15) all_57_12 = e3
% 136.76/20.38 | | |
% 136.76/20.38 | | | REF_CLOSE: (8), (9), (15) are inconsistent by sub-proof #591.
% 136.76/20.38 | | |
% 136.76/20.38 | | End of split
% 136.76/20.38 | |
% 136.76/20.38 | End of split
% 136.76/20.38 |
% 136.76/20.38 End of proof
% 136.76/20.38
% 136.76/20.38 Sub-proof #588 shows that the following formulas are inconsistent:
% 136.76/20.38 ----------------------------------------------------------------
% 136.76/20.38 (1) all_57_6 = e3
% 136.76/20.38 (2) all_57_6 = e0
% 136.76/20.38 (3) ~ (e3 = e0)
% 136.76/20.38
% 136.76/20.38 Begin of proof
% 136.76/20.38 |
% 136.76/20.38 | COMBINE_EQS: (1), (2) imply:
% 136.76/20.38 | (4) e3 = e0
% 136.76/20.38 |
% 136.76/20.38 | SIMP: (4) implies:
% 136.76/20.38 | (5) e3 = e0
% 136.76/20.38 |
% 136.76/20.38 | REDUCE: (3), (5) imply:
% 136.76/20.38 | (6) $false
% 136.76/20.38 |
% 136.76/20.38 | CLOSE: (6) is inconsistent.
% 136.76/20.38 |
% 136.76/20.38 End of proof
% 136.76/20.38
% 136.76/20.38 Sub-proof #589 shows that the following formulas are inconsistent:
% 136.76/20.38 ----------------------------------------------------------------
% 136.76/20.38 (1) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3)
% 136.76/20.38 (2) op(e3, e3) = e1
% 136.76/20.38 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.76/20.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.76/20.38 (4) ~ (e3 = e2)
% 136.76/20.38 (5) all_57_2 = e2
% 136.76/20.38 (6) ~ (e3 = e1)
% 136.76/20.38
% 136.76/20.38 Begin of proof
% 136.76/20.38 |
% 136.76/20.38 | BETA: splitting (1) gives:
% 136.76/20.38 |
% 136.76/20.38 | Case 1:
% 136.76/20.38 | |
% 136.76/20.38 | | (7) all_57_0 = e3 & op(e3, e3) = e3
% 136.76/20.38 | |
% 136.76/20.38 | | ALPHA: (7) implies:
% 136.76/20.38 | | (8) op(e3, e3) = e3
% 136.76/20.38 | |
% 136.76/20.38 | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #775.
% 136.76/20.38 | |
% 136.76/20.38 | Case 2:
% 136.76/20.38 | |
% 136.76/20.38 | | (9) all_57_2 = e3 & op(e2, e3) = e3
% 136.76/20.38 | |
% 136.76/20.38 | | REF_CLOSE: (4), (5), (9) are inconsistent by sub-proof #590.
% 136.76/20.38 | |
% 136.76/20.38 | End of split
% 136.76/20.38 |
% 136.76/20.38 End of proof
% 136.76/20.38
% 136.76/20.38 Sub-proof #590 shows that the following formulas are inconsistent:
% 136.76/20.38 ----------------------------------------------------------------
% 136.76/20.38 (1) all_57_2 = e3 & op(e2, e3) = e3
% 136.76/20.38 (2) all_57_2 = e2
% 136.76/20.38 (3) ~ (e3 = e2)
% 136.76/20.38
% 136.76/20.38 Begin of proof
% 136.76/20.38 |
% 136.76/20.38 | ALPHA: (1) implies:
% 136.76/20.38 | (4) all_57_2 = e3
% 136.76/20.38 |
% 136.76/20.38 | COMBINE_EQS: (2), (4) imply:
% 136.76/20.38 | (5) e3 = e2
% 136.76/20.38 |
% 136.76/20.38 | SIMP: (5) implies:
% 136.76/20.38 | (6) e3 = e2
% 136.76/20.38 |
% 136.76/20.38 | REDUCE: (3), (6) imply:
% 136.76/20.38 | (7) $false
% 136.76/20.38 |
% 136.76/20.38 | CLOSE: (7) is inconsistent.
% 136.76/20.38 |
% 136.76/20.38 End of proof
% 136.76/20.38
% 136.76/20.38 Sub-proof #591 shows that the following formulas are inconsistent:
% 136.76/20.38 ----------------------------------------------------------------
% 136.76/20.38 (1) all_57_12 = e3
% 136.76/20.38 (2) all_57_12 = e1
% 136.76/20.38 (3) ~ (e3 = e1)
% 136.76/20.38
% 136.76/20.38 Begin of proof
% 136.76/20.38 |
% 136.76/20.38 | COMBINE_EQS: (1), (2) imply:
% 136.76/20.38 | (4) e3 = e1
% 136.76/20.38 |
% 136.76/20.38 | SIMP: (4) implies:
% 136.76/20.38 | (5) e3 = e1
% 136.76/20.38 |
% 136.76/20.38 | REDUCE: (3), (5) imply:
% 136.76/20.38 | (6) $false
% 136.76/20.38 |
% 136.76/20.38 | CLOSE: (6) is inconsistent.
% 136.76/20.38 |
% 136.76/20.38 End of proof
% 136.76/20.38
% 136.76/20.38 Sub-proof #592 shows that the following formulas are inconsistent:
% 136.76/20.38 ----------------------------------------------------------------
% 136.76/20.38 (1) all_57_6 = e3
% 136.76/20.38 (2) all_57_6 = e2
% 136.76/20.38 (3) ~ (e3 = e2)
% 136.78/20.38
% 136.78/20.38 Begin of proof
% 136.78/20.38 |
% 136.78/20.38 | COMBINE_EQS: (1), (2) imply:
% 136.78/20.38 | (4) e3 = e2
% 136.78/20.38 |
% 136.78/20.38 | SIMP: (4) implies:
% 136.78/20.38 | (5) e3 = e2
% 136.78/20.38 |
% 136.78/20.38 | REDUCE: (3), (5) imply:
% 136.78/20.38 | (6) $false
% 136.78/20.38 |
% 136.78/20.38 | CLOSE: (6) is inconsistent.
% 136.78/20.38 |
% 136.78/20.38 End of proof
% 136.78/20.38
% 136.78/20.38 Sub-proof #593 shows that the following formulas are inconsistent:
% 136.78/20.38 ----------------------------------------------------------------
% 136.78/20.38 (1) all_57_2 = e3
% 136.78/20.38 (2) all_57_2 = e0
% 136.78/20.38 (3) ~ (e3 = e0)
% 136.78/20.38
% 136.78/20.38 Begin of proof
% 136.78/20.38 |
% 136.78/20.38 | COMBINE_EQS: (1), (2) imply:
% 136.78/20.38 | (4) e3 = e0
% 136.78/20.38 |
% 136.78/20.38 | SIMP: (4) implies:
% 136.78/20.38 | (5) e3 = e0
% 136.78/20.38 |
% 136.78/20.38 | REDUCE: (3), (5) imply:
% 136.78/20.38 | (6) $false
% 136.78/20.38 |
% 136.78/20.38 | CLOSE: (6) is inconsistent.
% 136.78/20.38 |
% 136.78/20.38 End of proof
% 136.78/20.38
% 136.78/20.38 Sub-proof #594 shows that the following formulas are inconsistent:
% 136.78/20.38 ----------------------------------------------------------------
% 136.78/20.38 (1) op(e0, e0) = all_4_2
% 136.78/20.38 (2) op(e1, e1) = all_6_2
% 136.78/20.38 (3) ~ (all_52_4 = e0)
% 136.78/20.38 (4) op(e2, e2) = e0
% 136.78/20.38 (5) op(e3, e3) = e1
% 136.78/20.38 (6) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 136.78/20.38 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 136.78/20.38 (7) ~ (all_6_2 = e3)
% 136.78/20.38 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.78/20.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.78/20.38 (9) ~ (e2 = e1)
% 136.78/20.38 (10) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 136.78/20.38 (11) ~ (all_4_2 = e2)
% 136.78/20.38 (12) ~ (all_4_2 = e1)
% 136.78/20.38 (13) ~ (all_6_2 = e2)
% 136.78/20.38 (14) ~ (all_4_2 = e3)
% 136.78/20.38 (15) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 136.78/20.38 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 136.78/20.38 op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 136.78/20.38 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 136.78/20.38 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 136.78/20.38 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.78/20.38 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 136.78/20.38 = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.78/20.38 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 136.78/20.38 $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~
% 136.78/20.38 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 136.78/20.38 (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) =
% 136.78/20.38 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0,
% 136.78/20.38 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 136.78/20.38 $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3)
% 136.78/20.38 & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 136.78/20.38 op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17
% 136.78/20.38 & op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 136.78/20.38 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.78/20.38 (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.78/20.38 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.78/20.38 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0)
% 136.78/20.38 = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) &
% 136.78/20.38 $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 &
% 136.78/20.38 all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.78/20.38 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 136.78/20.38 = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.78/20.38 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 136.78/20.38 $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~
% 136.78/20.38 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 136.78/20.38 (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 136.78/20.38 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0,
% 136.78/20.38 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 136.78/20.38 $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3)
% 136.78/20.38 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.78/20.38 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.78/20.38 all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2
% 136.78/20.38 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.78/20.38 (op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 =
% 136.78/20.38 e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 136.78/20.38 & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) =
% 136.78/20.38 all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 136.78/20.38 op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 136.78/20.38 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 136.78/20.38 e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 136.78/20.38 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 136.78/20.38 e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.78/20.38 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.78/20.38 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.78/20.38 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.78/20.38 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 136.78/20.38 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 136.78/20.38 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 136.78/20.38 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 136.78/20.38 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 136.78/20.38 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 136.78/20.38 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.78/20.38 $i(all_56_29))))
% 136.78/20.38 (16) all_54_15 = all_4_2
% 136.78/20.38 (17) op(e3, e2) = all_52_4
% 136.78/20.38 (18) op(e3, e0) = all_52_12
% 136.78/20.38 (19) op(e3, e1) = all_52_8
% 136.78/20.38 (20) ~ (all_52_12 = all_4_2)
% 136.78/20.38
% 136.78/20.38 Begin of proof
% 136.78/20.38 |
% 136.78/20.38 | BETA: splitting (10) gives:
% 136.78/20.38 |
% 136.78/20.38 | Case 1:
% 136.78/20.38 | |
% 136.78/20.38 | | (21) all_54_15 = e2
% 136.78/20.38 | |
% 136.78/20.38 | | REF_CLOSE: (11), (16), (21) are inconsistent by sub-proof #748.
% 136.78/20.38 | |
% 136.78/20.38 | Case 2:
% 136.78/20.38 | |
% 136.78/20.38 | | (22) ~ (all_54_15 = e2)
% 136.78/20.38 | | (23) all_54_15 = e1 | all_54_15 = e0
% 136.78/20.38 | |
% 136.78/20.38 | | BETA: splitting (23) gives:
% 136.78/20.38 | |
% 136.78/20.38 | | Case 1:
% 136.78/20.38 | | |
% 136.78/20.38 | | | (24) all_54_15 = e1
% 136.78/20.38 | | |
% 136.78/20.38 | | | REF_CLOSE: (12), (16), (24) are inconsistent by sub-proof #747.
% 136.78/20.38 | | |
% 136.78/20.38 | | Case 2:
% 136.78/20.38 | | |
% 136.78/20.38 | | | (25) all_54_15 = e0
% 136.78/20.38 | | |
% 136.78/20.38 | | | COMBINE_EQS: (16), (25) imply:
% 136.78/20.38 | | | (26) all_4_2 = e0
% 136.78/20.38 | | |
% 136.78/20.38 | | | SIMP: (26) implies:
% 136.78/20.38 | | | (27) all_4_2 = e0
% 136.78/20.38 | | |
% 136.78/20.38 | | | REDUCE: (20), (27) imply:
% 136.78/20.38 | | | (28) ~ (all_52_12 = e0)
% 136.78/20.38 | | |
% 136.78/20.38 | | | REDUCE: (14), (27) imply:
% 136.78/20.38 | | | (29) ~ (e3 = e0)
% 136.78/20.38 | | |
% 136.78/20.38 | | | SIMP: (29) implies:
% 136.78/20.38 | | | (30) ~ (e3 = e0)
% 136.78/20.38 | | |
% 136.78/20.38 | | | REDUCE: (11), (27) imply:
% 136.78/20.38 | | | (31) ~ (e2 = e0)
% 136.78/20.38 | | |
% 136.78/20.38 | | | SIMP: (31) implies:
% 136.78/20.38 | | | (32) ~ (e2 = e0)
% 136.78/20.38 | | |
% 136.78/20.38 | | | REDUCE: (12), (27) imply:
% 136.78/20.38 | | | (33) ~ (e1 = e0)
% 136.78/20.38 | | |
% 136.78/20.38 | | | SIMP: (33) implies:
% 136.78/20.38 | | | (34) ~ (e1 = e0)
% 136.78/20.38 | | |
% 136.78/20.38 | | | REDUCE: (1), (27) imply:
% 136.78/20.38 | | | (35) op(e0, e0) = e0
% 136.78/20.38 | | |
% 136.78/20.38 | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (13), (15), (17), (18),
% 136.78/20.38 | | | (19), (28), (30), (32), (34), (35) are inconsistent by
% 136.78/20.38 | | | sub-proof #595.
% 136.78/20.38 | | |
% 136.78/20.38 | | End of split
% 136.78/20.38 | |
% 136.78/20.38 | End of split
% 136.78/20.38 |
% 136.78/20.38 End of proof
% 136.78/20.38
% 136.78/20.38 Sub-proof #595 shows that the following formulas are inconsistent:
% 136.78/20.38 ----------------------------------------------------------------
% 136.78/20.38 (1) op(e0, e0) = e0
% 136.78/20.38 (2) op(e1, e1) = all_6_2
% 136.78/20.38 (3) ~ (all_52_4 = e0)
% 136.78/20.38 (4) op(e2, e2) = e0
% 136.78/20.38 (5) ~ (e2 = e0)
% 136.78/20.38 (6) op(e3, e3) = e1
% 136.78/20.38 (7) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 136.78/20.38 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 136.78/20.38 (8) ~ (all_6_2 = e3)
% 136.78/20.38 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 136.78/20.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 136.78/20.38 (10) ~ (e2 = e1)
% 136.78/20.38 (11) ~ (e3 = e0)
% 136.78/20.38 (12) ~ (all_52_12 = e0)
% 136.78/20.38 (13) ~ (all_6_2 = e2)
% 136.78/20.39 (14) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 =
% 136.78/20.39 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 &
% 136.78/20.39 op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 &
% 136.78/20.39 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) &
% 136.78/20.39 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 &
% 136.78/20.39 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.78/20.39 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1)
% 136.78/20.39 = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.78/20.39 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 136.78/20.39 $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~
% 136.78/20.39 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 136.78/20.39 (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) =
% 136.78/20.39 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0,
% 136.78/20.39 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 136.78/20.39 $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3)
% 136.78/20.39 & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) &
% 136.78/20.39 op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17
% 136.78/20.39 & op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 136.78/20.39 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.78/20.39 (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 =
% 136.78/20.39 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.78/20.39 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0)
% 136.78/20.39 = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) &
% 136.78/20.39 $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 &
% 136.78/20.39 all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~
% 136.78/20.39 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1)
% 136.78/20.39 = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) =
% 136.78/20.39 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) &
% 136.78/20.39 $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~
% 136.78/20.39 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~
% 136.78/20.39 (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) =
% 136.78/20.39 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0,
% 136.78/20.39 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) &
% 136.78/20.39 $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3)
% 136.78/20.39 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) &
% 136.78/20.39 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) =
% 136.78/20.39 all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2
% 136.78/20.39 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.78/20.39 (op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 =
% 136.78/20.39 e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1)
% 136.78/20.39 & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) =
% 136.78/20.39 all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 &
% 136.78/20.39 op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) &
% 136.78/20.39 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 =
% 136.78/20.39 e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27
% 136.78/20.39 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2,
% 136.78/20.39 e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 &
% 136.78/20.39 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.78/20.39 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~
% 136.78/20.39 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) &
% 136.78/20.39 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0,
% 136.78/20.39 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) &
% 136.78/20.39 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1
% 136.78/20.39 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) &
% 136.78/20.39 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) =
% 136.78/20.39 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 136.78/20.39 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.78/20.39 $i(all_56_29))))
% 136.78/20.39 (15) op(e3, e2) = all_52_4
% 136.78/20.39 (16) op(e3, e0) = all_52_12
% 136.78/20.39 (17) op(e3, e1) = all_52_8
% 136.78/20.39 (18) ~ (e1 = e0)
% 136.78/20.39
% 136.78/20.39 Begin of proof
% 136.78/20.39 |
% 136.78/20.39 | BETA: splitting (14) gives:
% 136.78/20.39 |
% 136.78/20.39 | Case 1:
% 136.78/20.39 | |
% 136.78/20.39 | | (19) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11
% 136.78/20.39 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) =
% 136.78/20.39 | | e2 & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 136.78/20.39 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 &
% 136.78/20.39 | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) |
% 136.78/20.39 | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13
% 136.78/20.39 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) =
% 136.78/20.39 | | e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) =
% 136.78/20.39 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 &
% 136.78/20.39 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) |
% 136.78/20.39 | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15
% 136.78/20.39 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) =
% 136.78/20.39 | | e0 & op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) =
% 136.78/20.39 | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 &
% 136.78/20.39 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) |
% 136.78/20.39 | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 136.78/20.39 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.78/20.39 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.78/20.39 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 &
% 136.78/20.39 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25))
% 136.78/20.39 | |
% 136.78/20.39 | | REF_CLOSE: (3), (4), (6), (7), (9), (10), (11), (12), (15), (16), (17),
% 136.78/20.39 | | (18), (19) are inconsistent by sub-proof #597.
% 136.78/20.39 | |
% 136.78/20.39 | Case 2:
% 136.78/20.39 | |
% 136.78/20.39 | | (20) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9
% 136.78/20.39 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) =
% 136.78/20.39 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3,
% 136.78/20.39 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 &
% 136.78/20.39 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) |
% 136.78/20.39 | | (all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~
% 136.78/20.39 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) &
% 136.78/20.39 | | op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1,
% 136.78/20.39 | | e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) =
% 136.78/20.39 | | all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) &
% 136.78/20.39 | | $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 &